~ubuntu-branches/ubuntu/wily/ffc/wily
» Revision
17
: test/regression/references/r_auto/MixedMixedElement.h
« back to all changes in this revision
Viewing changes to test/regression/references/r_auto/MixedMixedElement.h
- browse files at revision 17
- compare with another revision
- download diff
- download tarball
- view history from revision 17
- Committer: Package Import Robot
- Author(s): Johannes Ring
- Date: 2013-06-26 14:48:32 UTC
- mfrom: (1.1.13)
- Revision ID: package-import@ubuntu.com-20130626144832-1xd8htax4s3utybz
Tags: 1.2.0-1
* New upstream release.
* debian/control:
- Bump required version for python-ufc, python-fiat, python-instant
and python-ufl in Depends field.
- Bump Standards-Version to 3.9.4.
- Remove DM-Upload-Allowed field.
- Bump required debhelper version in Build-Depends.
- Remove cdbs from Build-Depends.
- Use canonical URIs for Vcs-* fields.
* debian/compat: Bump to compatibility level 9.
* debian/rules: Rewrite for debhelper (drop cdbs).
* debian/control:
- Bump required version for python-ufc, python-fiat, python-instant
and python-ufl in Depends field.
- Bump Standards-Version to 3.9.4.
- Remove DM-Upload-Allowed field.
- Bump required debhelper version in Build-Depends.
- Remove cdbs from Build-Depends.
- Use canonical URIs for Vcs-* fields.
* debian/compat: Bump to compatibility level 9.
* debian/rules: Rewrite for debhelper (drop cdbs).
- files added:
- .pc
- ffc/uflacsrepr
- sandbox/features
- sandbox/multidomain
- files modified:
- ChangeLog
added
removed
test/regression/references/r_auto/MixedMixedElement.h
1
// This code conforms with the UFC specification version 2.0.5
2
// and was automatically generated by FFC version 1.0.0.
1
// This code conforms with the UFC specification version 2.2.0
2
// and was automatically generated by FFC version 1.2.0.
3
3
//
4
4
// This code was generated with the following parameters:
5
5
//
52
52
/// Return a string identifying the finite element
53
53
virtual const char* signature() const
54
54
{
55
return "FiniteElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, None)";
55
return "FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, None)";
56
56
}
57
57
58
58
/// Return the cell shape
62
62
}
63
63
64
64
/// Return the topological dimension of the cell shape
65
virtual unsigned int topological_dimension() const
65
virtual std::size_t topological_dimension() const
66
66
{
67
67
return 2;
68
68
}
69
69
70
70
/// Return the geometric dimension of the cell shape
71
virtual unsigned int geometric_dimension() const
71
virtual std::size_t geometric_dimension() const
72
72
{
73
73
return 2;
74
74
}
75
75
76
76
/// Return the dimension of the finite element function space
77
virtual unsigned int space_dimension() const
77
virtual std::size_t space_dimension() const
78
78
{
79
79
return 1;
80
80
}
81
81
82
82
/// Return the rank of the value space
83
virtual unsigned int value_rank() const
83
virtual std::size_t value_rank() const
84
84
{
85
85
return 0;
86
86
}
87
87
88
88
/// Return the dimension of the value space for axis i
89
virtual unsigned int value_dimension(unsigned int i) const
89
virtual std::size_t value_dimension(std::size_t i) const
90
90
{
91
91
return 1;
92
92
}
93
93
94
/// Evaluate basis function i at given point in cell
95
virtual void evaluate_basis(unsigned int i,
94
/// Evaluate basis function i at given point x in cell
95
virtual void evaluate_basis(std::size_t i,
96
96
double* values,
97
const double* coordinates,
98
const ufc::cell& c) const
97
const double* x,
98
const double* vertex_coordinates,
99
int cell_orientation) const
99
100
{
100
// Extract vertex coordinates
101
102
// Compute Jacobian of affine map from reference cell
103
104
// Compute determinant of Jacobian
105
106
// Compute inverse of Jacobian
101
// Compute Jacobian
102
double J[4];
103
compute_jacobian_triangle_2d(J, vertex_coordinates);
104
105
// Compute Jacobian inverse and determinant
106
double K[4];
107
double detJ;
108
compute_jacobian_inverse_triangle_2d(K, detJ, J);
109
107
110
108
111
// Compute constants
109
112
110
113
// Get coordinates and map to the reference (FIAT) element
111
114
112
// Reset values.
115
// Reset values
113
116
*values = 0.0;
114
117
115
// Array of basisvalues.
118
// Array of basisvalues
116
119
double basisvalues[1] = {0.0};
117
120
118
// Declare helper variables.
121
// Declare helper variables
119
122
120
// Compute basisvalues.
123
// Compute basisvalues
121
124
basisvalues[0] = 1.0;
122
125
123
// Table(s) of coefficients.
126
// Table(s) of coefficients
124
127
static const double coefficients0[1] = \
125
128
{1.0};
126
129
127
// Compute value(s).
130
// Compute value(s)
128
131
for (unsigned int r = 0; r < 1; r++)
129
132
{
130
133
*values += coefficients0[r]*basisvalues[r];
131
134
}// end loop over 'r'
132
135
}
133
136
134
/// Evaluate all basis functions at given point in cell
137
/// Evaluate all basis functions at given point x in cell
135
138
virtual void evaluate_basis_all(double* values,
136
const double* coordinates,
137
const ufc::cell& c) const
139
const double* x,
140
const double* vertex_coordinates,
141
int cell_orientation) const
138
142
{
139
143
// Element is constant, calling evaluate_basis.
140
evaluate_basis(0, values, coordinates, c);
144
evaluate_basis(0, values, x, vertex_coordinates, cell_orientation);
141
145
}
142
146
143
/// Evaluate order n derivatives of basis function i at given point in cell
144
virtual void evaluate_basis_derivatives(unsigned int i,
145
unsigned int n,
147
/// Evaluate order n derivatives of basis function i at given point x in cell
148
virtual void evaluate_basis_derivatives(std::size_t i,
149
std::size_t n,
146
150
double* values,
147
const double* coordinates,
148
const ufc::cell& c) const
151
const double* x,
152
const double* vertex_coordinates,
153
int cell_orientation) const
149
154
{
150
// Extract vertex coordinates
151
const double * const * x = c.coordinates;
152
153
// Compute Jacobian of affine map from reference cell
154
const double J_00 = x[1][0] - x[0][0];
155
const double J_01 = x[2][0] - x[0][0];
156
const double J_10 = x[1][1] - x[0][1];
157
const double J_11 = x[2][1] - x[0][1];
158
159
// Compute determinant of Jacobian
160
double detJ = J_00*J_11 - J_01*J_10;
161
162
// Compute inverse of Jacobian
163
const double K_00 = J_11 / detJ;
164
const double K_01 = -J_01 / detJ;
165
const double K_10 = -J_10 / detJ;
166
const double K_11 = J_00 / detJ;
155
// Compute Jacobian
156
double J[4];
157
compute_jacobian_triangle_2d(J, vertex_coordinates);
158
159
// Compute Jacobian inverse and determinant
160
double K[4];
161
double detJ;
162
compute_jacobian_inverse_triangle_2d(K, detJ, J);
163
167
164
168
165
// Compute constants
169
166
204
201
}
205
202
206
203
// Compute inverse of Jacobian
207
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
204
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
208
205
209
206
// Declare transformation matrix
210
207
// Declare pointer to two dimensional array and initialise
234
231
}// end loop over 'r'
235
232
236
233
237
// Array of basisvalues.
234
// Array of basisvalues
238
235
double basisvalues[1] = {0.0};
239
236
240
// Declare helper variables.
237
// Declare helper variables
241
238
242
// Compute basisvalues.
239
// Compute basisvalues
243
240
basisvalues[0] = 1.0;
244
241
245
// Table(s) of coefficients.
242
// Table(s) of coefficients
246
243
static const double coefficients0[1] = \
247
244
{1.0};
248
245
363
360
delete [] transform;
364
361
}
365
362
366
/// Evaluate order n derivatives of all basis functions at given point in cell
367
virtual void evaluate_basis_derivatives_all(unsigned int n,
363
/// Evaluate order n derivatives of all basis functions at given point x in cell
364
virtual void evaluate_basis_derivatives_all(std::size_t n,
368
365
double* values,
369
const double* coordinates,
370
const ufc::cell& c) const
366
const double* x,
367
const double* vertex_coordinates,
368
int cell_orientation) const
371
369
{
372
370
// Element is constant, calling evaluate_basis_derivatives.
373
evaluate_basis_derivatives(0, n, values, coordinates, c);
371
evaluate_basis_derivatives(0, n, values, x, vertex_coordinates, cell_orientation);
374
372
}
375
373
376
374
/// Evaluate linear functional for dof i on the function f
377
virtual double evaluate_dof(unsigned int i,
375
virtual double evaluate_dof(std::size_t i,
378
376
const ufc::function& f,
377
const double* vertex_coordinates,
378
int cell_orientation,
379
379
const ufc::cell& c) const
380
380
{
381
// Declare variables for result of evaluation.
381
// Declare variables for result of evaluation
382
382
double vals[1];
383
383
384
// Declare variable for physical coordinates.
384
// Declare variable for physical coordinates
385
385
double y[2];
386
const double * const * x = c.coordinates;
387
386
switch (i)
388
387
{
389
388
case 0:
390
389
{
391
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
392
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
390
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
391
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
393
392
f.evaluate(vals, y, c);
394
393
return vals[0];
395
394
break;
402
401
/// Evaluate linear functionals for all dofs on the function f
403
402
virtual void evaluate_dofs(double* values,
404
403
const ufc::function& f,
404
const double* vertex_coordinates,
405
int cell_orientation,
405
406
const ufc::cell& c) const
406
407
{
407
// Declare variables for result of evaluation.
408
// Declare variables for result of evaluation
408
409
double vals[1];
409
410
410
// Declare variable for physical coordinates.
411
// Declare variable for physical coordinates
411
412
double y[2];
412
const double * const * x = c.coordinates;
413
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
414
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
413
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
414
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
415
415
f.evaluate(vals, y, c);
416
416
values[0] = vals[0];
417
417
}
419
419
/// Interpolate vertex values from dof values
420
420
virtual void interpolate_vertex_values(double* vertex_values,
421
421
const double* dof_values,
422
const double* vertex_coordinates,
423
int cell_orientation,
422
424
const ufc::cell& c) const
423
425
{
424
426
// Evaluate function and change variables
432
434
const double* xhat,
433
435
const ufc::cell& c) const
434
436
{
435
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
437
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
436
438
}
437
439
438
440
/// Map from coordinate x in cell to coordinate xhat in reference cell
440
442
const double* x,
441
443
const ufc::cell& c) const
442
444
{
443
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
445
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
444
446
}
445
447
446
448
/// Return the number of sub elements (for a mixed element)
447
virtual unsigned int num_sub_elements() const
449
virtual std::size_t num_sub_elements() const
448
450
{
449
451
return 0;
450
452
}
451
453
452
454
/// Create a new finite element for sub element i (for a mixed element)
453
virtual ufc::finite_element* create_sub_element(unsigned int i) const
455
virtual ufc::finite_element* create_sub_element(std::size_t i) const
454
456
{
455
457
return 0;
456
458
}
484
486
/// Return a string identifying the finite element
485
487
virtual const char* signature() const
486
488
{
487
return "VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None)";
489
return "VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None)";
488
490
}
489
491
490
492
/// Return the cell shape
494
496
}
495
497
496
498
/// Return the topological dimension of the cell shape
497
virtual unsigned int topological_dimension() const
499
virtual std::size_t topological_dimension() const
498
500
{
499
501
return 2;
500
502
}
501
503
502
504
/// Return the geometric dimension of the cell shape
503
virtual unsigned int geometric_dimension() const
505
virtual std::size_t geometric_dimension() const
504
506
{
505
507
return 2;
506
508
}
507
509
508
510
/// Return the dimension of the finite element function space
509
virtual unsigned int space_dimension() const
511
virtual std::size_t space_dimension() const
510
512
{
511
513
return 2;
512
514
}
513
515
514
516
/// Return the rank of the value space
515
virtual unsigned int value_rank() const
517
virtual std::size_t value_rank() const
516
518
{
517
519
return 1;
518
520
}
519
521
520
522
/// Return the dimension of the value space for axis i
521
virtual unsigned int value_dimension(unsigned int i) const
523
virtual std::size_t value_dimension(std::size_t i) const
522
524
{
523
525
switch (i)
524
526
{
532
534
return 0;
533
535
}
534
536
535
/// Evaluate basis function i at given point in cell
536
virtual void evaluate_basis(unsigned int i,
537
/// Evaluate basis function i at given point x in cell
538
virtual void evaluate_basis(std::size_t i,
537
539
double* values,
538
const double* coordinates,
539
const ufc::cell& c) const
540
const double* x,
541
const double* vertex_coordinates,
542
int cell_orientation) const
540
543
{
541
// Extract vertex coordinates
542
543
// Compute Jacobian of affine map from reference cell
544
545
// Compute determinant of Jacobian
546
547
// Compute inverse of Jacobian
544
// Compute Jacobian
545
double J[4];
546
compute_jacobian_triangle_2d(J, vertex_coordinates);
547
548
// Compute Jacobian inverse and determinant
549
double K[4];
550
double detJ;
551
compute_jacobian_inverse_triangle_2d(K, detJ, J);
552
548
553
549
554
// Compute constants
550
555
551
556
// Get coordinates and map to the reference (FIAT) element
552
557
553
// Reset values.
558
// Reset values
554
559
values[0] = 0.0;
555
560
values[1] = 0.0;
556
561
switch (i)
558
563
case 0:
559
564
{
560
565
561
// Array of basisvalues.
566
// Array of basisvalues
562
567
double basisvalues[1] = {0.0};
563
568
564
// Declare helper variables.
569
// Declare helper variables
565
570
566
// Compute basisvalues.
571
// Compute basisvalues
567
572
basisvalues[0] = 1.0;
568
573
569
// Table(s) of coefficients.
574
// Table(s) of coefficients
570
575
static const double coefficients0[1] = \
571
576
{1.0};
572
577
573
// Compute value(s).
578
// Compute value(s)
574
579
for (unsigned int r = 0; r < 1; r++)
575
580
{
576
581
values[0] += coefficients0[r]*basisvalues[r];
580
585
case 1:
581
586
{
582
587
583
// Array of basisvalues.
588
// Array of basisvalues
584
589
double basisvalues[1] = {0.0};
585
590
586
// Declare helper variables.
591
// Declare helper variables
587
592
588
// Compute basisvalues.
593
// Compute basisvalues
589
594
basisvalues[0] = 1.0;
590
595
591
// Table(s) of coefficients.
596
// Table(s) of coefficients
592
597
static const double coefficients0[1] = \
593
598
{1.0};
594
599
595
// Compute value(s).
600
// Compute value(s)
596
601
for (unsigned int r = 0; r < 1; r++)
597
602
{
598
603
values[1] += coefficients0[r]*basisvalues[r];
603
608
604
609
}
605
610
606
/// Evaluate all basis functions at given point in cell
611
/// Evaluate all basis functions at given point x in cell
607
612
virtual void evaluate_basis_all(double* values,
608
const double* coordinates,
609
const ufc::cell& c) const
613
const double* x,
614
const double* vertex_coordinates,
615
int cell_orientation) const
610
616
{
611
617
// Helper variable to hold values of a single dof.
612
618
double dof_values[2] = {0.0, 0.0};
613
619
614
// Loop dofs and call evaluate_basis.
620
// Loop dofs and call evaluate_basis
615
621
for (unsigned int r = 0; r < 2; r++)
616
622
{
617
evaluate_basis(r, dof_values, coordinates, c);
623
evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
618
624
for (unsigned int s = 0; s < 2; s++)
619
625
{
620
626
values[r*2 + s] = dof_values[s];
622
628
}// end loop over 'r'
623
629
}
624
630
625
/// Evaluate order n derivatives of basis function i at given point in cell
626
virtual void evaluate_basis_derivatives(unsigned int i,
627
unsigned int n,
631
/// Evaluate order n derivatives of basis function i at given point x in cell
632
virtual void evaluate_basis_derivatives(std::size_t i,
633
std::size_t n,
628
634
double* values,
629
const double* coordinates,
630
const ufc::cell& c) const
635
const double* x,
636
const double* vertex_coordinates,
637
int cell_orientation) const
631
638
{
632
// Extract vertex coordinates
633
const double * const * x = c.coordinates;
634
635
// Compute Jacobian of affine map from reference cell
636
const double J_00 = x[1][0] - x[0][0];
637
const double J_01 = x[2][0] - x[0][0];
638
const double J_10 = x[1][1] - x[0][1];
639
const double J_11 = x[2][1] - x[0][1];
640
641
// Compute determinant of Jacobian
642
double detJ = J_00*J_11 - J_01*J_10;
643
644
// Compute inverse of Jacobian
645
const double K_00 = J_11 / detJ;
646
const double K_01 = -J_01 / detJ;
647
const double K_10 = -J_10 / detJ;
648
const double K_11 = J_00 / detJ;
639
// Compute Jacobian
640
double J[4];
641
compute_jacobian_triangle_2d(J, vertex_coordinates);
642
643
// Compute Jacobian inverse and determinant
644
double K[4];
645
double detJ;
646
compute_jacobian_inverse_triangle_2d(K, detJ, J);
647
649
648
650
649
// Compute constants
651
650
686
685
}
687
686
688
687
// Compute inverse of Jacobian
689
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
688
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
690
689
691
690
// Declare transformation matrix
692
691
// Declare pointer to two dimensional array and initialise
720
719
case 0:
721
720
{
722
721
723
// Array of basisvalues.
722
// Array of basisvalues
724
723
double basisvalues[1] = {0.0};
725
724
726
// Declare helper variables.
725
// Declare helper variables
727
726
728
// Compute basisvalues.
727
// Compute basisvalues
729
728
basisvalues[0] = 1.0;
730
729
731
// Table(s) of coefficients.
730
// Table(s) of coefficients
732
731
static const double coefficients0[1] = \
733
732
{1.0};
734
733
852
851
case 1:
853
852
{
854
853
855
// Array of basisvalues.
854
// Array of basisvalues
856
855
double basisvalues[1] = {0.0};
857
856
858
// Declare helper variables.
857
// Declare helper variables
859
858
860
// Compute basisvalues.
859
// Compute basisvalues
861
860
basisvalues[0] = 1.0;
862
861
863
// Table(s) of coefficients.
862
// Table(s) of coefficients
864
863
static const double coefficients0[1] = \
865
864
{1.0};
866
865
985
984
986
985
}
987
986
988
/// Evaluate order n derivatives of all basis functions at given point in cell
989
virtual void evaluate_basis_derivatives_all(unsigned int n,
987
/// Evaluate order n derivatives of all basis functions at given point x in cell
988
virtual void evaluate_basis_derivatives_all(std::size_t n,
990
989
double* values,
991
const double* coordinates,
992
const ufc::cell& c) const
990
const double* x,
991
const double* vertex_coordinates,
992
int cell_orientation) const
993
993
{
994
994
// Compute number of derivatives.
995
995
unsigned int num_derivatives = 1;
1008
1008
// Loop dofs and call evaluate_basis_derivatives.
1009
1009
for (unsigned int r = 0; r < 2; r++)
1010
1010
{
1011
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
1011
evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
1012
1012
for (unsigned int s = 0; s < 2*num_derivatives; s++)
1013
1013
{
1014
1014
values[r*2*num_derivatives + s] = dof_values[s];
1020
1020
}
1021
1021
1022
1022
/// Evaluate linear functional for dof i on the function f
1023
virtual double evaluate_dof(unsigned int i,
1023
virtual double evaluate_dof(std::size_t i,
1024
1024
const ufc::function& f,
1025
const double* vertex_coordinates,
1026
int cell_orientation,
1025
1027
const ufc::cell& c) const
1026
1028
{
1027
// Declare variables for result of evaluation.
1029
// Declare variables for result of evaluation
1028
1030
double vals[2];
1029
1031
1030
// Declare variable for physical coordinates.
1032
// Declare variable for physical coordinates
1031
1033
double y[2];
1032
const double * const * x = c.coordinates;
1033
1034
switch (i)
1034
1035
{
1035
1036
case 0:
1036
1037
{
1037
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
1038
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
1038
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
1039
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
1039
1040
f.evaluate(vals, y, c);
1040
1041
return vals[0];
1041
1042
break;
1042
1043
}
1043
1044
case 1:
1044
1045
{
1045
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
1046
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
1046
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
1047
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
1047
1048
f.evaluate(vals, y, c);
1048
1049
return vals[1];
1049
1050
break;
1056
1057
/// Evaluate linear functionals for all dofs on the function f
1057
1058
virtual void evaluate_dofs(double* values,
1058
1059
const ufc::function& f,
1060
const double* vertex_coordinates,
1061
int cell_orientation,
1059
1062
const ufc::cell& c) const
1060
1063
{
1061
// Declare variables for result of evaluation.
1064
// Declare variables for result of evaluation
1062
1065
double vals[2];
1063
1066
1064
// Declare variable for physical coordinates.
1067
// Declare variable for physical coordinates
1065
1068
double y[2];
1066
const double * const * x = c.coordinates;
1067
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
1068
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
1069
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
1070
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
1069
1071
f.evaluate(vals, y, c);
1070
1072
values[0] = vals[0];
1071
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
1072
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
1073
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
1074
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
1073
1075
f.evaluate(vals, y, c);
1074
1076
values[1] = vals[1];
1075
1077
}
1077
1079
/// Interpolate vertex values from dof values
1078
1080
virtual void interpolate_vertex_values(double* vertex_values,
1079
1081
const double* dof_values,
1082
const double* vertex_coordinates,
1083
int cell_orientation,
1080
1084
const ufc::cell& c) const
1081
1085
{
1082
1086
// Evaluate function and change variables
1094
1098
const double* xhat,
1095
1099
const ufc::cell& c) const
1096
1100
{
1097
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
1101
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
1098
1102
}
1099
1103
1100
1104
/// Map from coordinate x in cell to coordinate xhat in reference cell
1102
1106
const double* x,
1103
1107
const ufc::cell& c) const
1104
1108
{
1105
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
1109
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
1106
1110
}
1107
1111
1108
1112
/// Return the number of sub elements (for a mixed element)
1109
virtual unsigned int num_sub_elements() const
1113
virtual std::size_t num_sub_elements() const
1110
1114
{
1111
1115
return 2;
1112
1116
}
1113
1117
1114
1118
/// Create a new finite element for sub element i (for a mixed element)
1115
virtual ufc::finite_element* create_sub_element(unsigned int i) const
1119
virtual ufc::finite_element* create_sub_element(std::size_t i) const
1116
1120
{
1117
1121
switch (i)
1118
1122
{
1160
1164
/// Return a string identifying the finite element
1161
1165
virtual const char* signature() const
1162
1166
{
1163
return "FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)";
1167
return "FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)";
1164
1168
}
1165
1169
1166
1170
/// Return the cell shape
1170
1174
}
1171
1175
1172
1176
/// Return the topological dimension of the cell shape
1173
virtual unsigned int topological_dimension() const
1177
virtual std::size_t topological_dimension() const
1174
1178
{
1175
1179
return 2;
1176
1180
}
1177
1181
1178
1182
/// Return the geometric dimension of the cell shape
1179
virtual unsigned int geometric_dimension() const
1183
virtual std::size_t geometric_dimension() const
1180
1184
{
1181
1185
return 2;
1182
1186
}
1183
1187
1184
1188
/// Return the dimension of the finite element function space
1185
virtual unsigned int space_dimension() const
1189
virtual std::size_t space_dimension() const
1186
1190
{
1187
1191
return 6;
1188
1192
}
1189
1193
1190
1194
/// Return the rank of the value space
1191
virtual unsigned int value_rank() const
1195
virtual std::size_t value_rank() const
1192
1196
{
1193
1197
return 0;
1194
1198
}
1195
1199
1196
1200
/// Return the dimension of the value space for axis i
1197
virtual unsigned int value_dimension(unsigned int i) const
1201
virtual std::size_t value_dimension(std::size_t i) const
1198
1202
{
1199
1203
return 1;
1200
1204
}
1201
1205
1202
/// Evaluate basis function i at given point in cell
1203
virtual void evaluate_basis(unsigned int i,
1206
/// Evaluate basis function i at given point x in cell
1207
virtual void evaluate_basis(std::size_t i,
1204
1208
double* values,
1205
const double* coordinates,
1206
const ufc::cell& c) const
1209
const double* x,
1210
const double* vertex_coordinates,
1211
int cell_orientation) const
1207
1212
{
1208
// Extract vertex coordinates
1209
const double * const * x = c.coordinates;
1210
1211
// Compute Jacobian of affine map from reference cell
1212
const double J_00 = x[1][0] - x[0][0];
1213
const double J_01 = x[2][0] - x[0][0];
1214
const double J_10 = x[1][1] - x[0][1];
1215
const double J_11 = x[2][1] - x[0][1];
1216
1217
// Compute determinant of Jacobian
1218
double detJ = J_00*J_11 - J_01*J_10;
1219
1220
// Compute inverse of Jacobian
1213
// Compute Jacobian
1214
double J[4];
1215
compute_jacobian_triangle_2d(J, vertex_coordinates);
1216
1217
// Compute Jacobian inverse and determinant
1218
double K[4];
1219
double detJ;
1220
compute_jacobian_inverse_triangle_2d(K, detJ, J);
1221
1221
1222
1222
1223
// Compute constants
1223
const double C0 = x[1][0] + x[2][0];
1224
const double C1 = x[1][1] + x[2][1];
1224
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
1225
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
1225
1226
1226
1227
// Get coordinates and map to the reference (FIAT) element
1227
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
1228
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
1228
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
1229
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
1229
1230
1230
// Reset values.
1231
// Reset values
1231
1232
*values = 0.0;
1232
1233
switch (i)
1233
1234
{
1234
1235
case 0:
1235
1236
{
1236
1237
1237
// Array of basisvalues.
1238
// Array of basisvalues
1238
1239
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1239
1240
1240
// Declare helper variables.
1241
// Declare helper variables
1241
1242
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1242
1243
double tmp1 = (1.0 - Y)/2.0;
1243
1244
double tmp2 = tmp1*tmp1;
1244
1245
1245
// Compute basisvalues.
1246
// Compute basisvalues
1246
1247
basisvalues[0] = 1.0;
1247
1248
basisvalues[1] = tmp0;
1248
1249
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1256
1257
basisvalues[4] *= std::sqrt(4.5);
1257
1258
basisvalues[3] *= std::sqrt(7.5);
1258
1259
1259
// Table(s) of coefficients.
1260
// Table(s) of coefficients
1260
1261
static const double coefficients0[6] = \
1261
1262
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
1262
1263
1263
// Compute value(s).
1264
// Compute value(s)
1264
1265
for (unsigned int r = 0; r < 6; r++)
1265
1266
{
1266
1267
*values += coefficients0[r]*basisvalues[r];
1270
1271
case 1:
1271
1272
{
1272
1273
1273
// Array of basisvalues.
1274
// Array of basisvalues
1274
1275
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1275
1276
1276
// Declare helper variables.
1277
// Declare helper variables
1277
1278
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1278
1279
double tmp1 = (1.0 - Y)/2.0;
1279
1280
double tmp2 = tmp1*tmp1;
1280
1281
1281
// Compute basisvalues.
1282
// Compute basisvalues
1282
1283
basisvalues[0] = 1.0;
1283
1284
basisvalues[1] = tmp0;
1284
1285
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1292
1293
basisvalues[4] *= std::sqrt(4.5);
1293
1294
basisvalues[3] *= std::sqrt(7.5);
1294
1295
1295
// Table(s) of coefficients.
1296
// Table(s) of coefficients
1296
1297
static const double coefficients0[6] = \
1297
1298
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
1298
1299
1299
// Compute value(s).
1300
// Compute value(s)
1300
1301
for (unsigned int r = 0; r < 6; r++)
1301
1302
{
1302
1303
*values += coefficients0[r]*basisvalues[r];
1306
1307
case 2:
1307
1308
{
1308
1309
1309
// Array of basisvalues.
1310
// Array of basisvalues
1310
1311
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1311
1312
1312
// Declare helper variables.
1313
// Declare helper variables
1313
1314
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1314
1315
double tmp1 = (1.0 - Y)/2.0;
1315
1316
double tmp2 = tmp1*tmp1;
1316
1317
1317
// Compute basisvalues.
1318
// Compute basisvalues
1318
1319
basisvalues[0] = 1.0;
1319
1320
basisvalues[1] = tmp0;
1320
1321
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1328
1329
basisvalues[4] *= std::sqrt(4.5);
1329
1330
basisvalues[3] *= std::sqrt(7.5);
1330
1331
1331
// Table(s) of coefficients.
1332
// Table(s) of coefficients
1332
1333
static const double coefficients0[6] = \
1333
1334
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
1334
1335
1335
// Compute value(s).
1336
// Compute value(s)
1336
1337
for (unsigned int r = 0; r < 6; r++)
1337
1338
{
1338
1339
*values += coefficients0[r]*basisvalues[r];
1342
1343
case 3:
1343
1344
{
1344
1345
1345
// Array of basisvalues.
1346
// Array of basisvalues
1346
1347
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1347
1348
1348
// Declare helper variables.
1349
// Declare helper variables
1349
1350
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1350
1351
double tmp1 = (1.0 - Y)/2.0;
1351
1352
double tmp2 = tmp1*tmp1;
1352
1353
1353
// Compute basisvalues.
1354
// Compute basisvalues
1354
1355
basisvalues[0] = 1.0;
1355
1356
basisvalues[1] = tmp0;
1356
1357
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1364
1365
basisvalues[4] *= std::sqrt(4.5);
1365
1366
basisvalues[3] *= std::sqrt(7.5);
1366
1367
1367
// Table(s) of coefficients.
1368
// Table(s) of coefficients
1368
1369
static const double coefficients0[6] = \
1369
1370
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
1370
1371
1371
// Compute value(s).
1372
// Compute value(s)
1372
1373
for (unsigned int r = 0; r < 6; r++)
1373
1374
{
1374
1375
*values += coefficients0[r]*basisvalues[r];
1378
1379
case 4:
1379
1380
{
1380
1381
1381
// Array of basisvalues.
1382
// Array of basisvalues
1382
1383
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1383
1384
1384
// Declare helper variables.
1385
// Declare helper variables
1385
1386
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1386
1387
double tmp1 = (1.0 - Y)/2.0;
1387
1388
double tmp2 = tmp1*tmp1;
1388
1389
1389
// Compute basisvalues.
1390
// Compute basisvalues
1390
1391
basisvalues[0] = 1.0;
1391
1392
basisvalues[1] = tmp0;
1392
1393
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1400
1401
basisvalues[4] *= std::sqrt(4.5);
1401
1402
basisvalues[3] *= std::sqrt(7.5);
1402
1403
1403
// Table(s) of coefficients.
1404
// Table(s) of coefficients
1404
1405
static const double coefficients0[6] = \
1405
1406
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
1406
1407
1407
// Compute value(s).
1408
// Compute value(s)
1408
1409
for (unsigned int r = 0; r < 6; r++)
1409
1410
{
1410
1411
*values += coefficients0[r]*basisvalues[r];
1414
1415
case 5:
1415
1416
{
1416
1417
1417
// Array of basisvalues.
1418
// Array of basisvalues
1418
1419
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1419
1420
1420
// Declare helper variables.
1421
// Declare helper variables
1421
1422
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1422
1423
double tmp1 = (1.0 - Y)/2.0;
1423
1424
double tmp2 = tmp1*tmp1;
1424
1425
1425
// Compute basisvalues.
1426
// Compute basisvalues
1426
1427
basisvalues[0] = 1.0;
1427
1428
basisvalues[1] = tmp0;
1428
1429
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1436
1437
basisvalues[4] *= std::sqrt(4.5);
1437
1438
basisvalues[3] *= std::sqrt(7.5);
1438
1439
1439
// Table(s) of coefficients.
1440
// Table(s) of coefficients
1440
1441
static const double coefficients0[6] = \
1441
1442
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
1442
1443
1443
// Compute value(s).
1444
// Compute value(s)
1444
1445
for (unsigned int r = 0; r < 6; r++)
1445
1446
{
1446
1447
*values += coefficients0[r]*basisvalues[r];
1451
1452
1452
1453
}
1453
1454
1454
/// Evaluate all basis functions at given point in cell
1455
/// Evaluate all basis functions at given point x in cell
1455
1456
virtual void evaluate_basis_all(double* values,
1456
const double* coordinates,
1457
const ufc::cell& c) const
1457
const double* x,
1458
const double* vertex_coordinates,
1459
int cell_orientation) const
1458
1460
{
1459
1461
// Helper variable to hold values of a single dof.
1460
1462
double dof_values = 0.0;
1461
1463
1462
// Loop dofs and call evaluate_basis.
1464
// Loop dofs and call evaluate_basis
1463
1465
for (unsigned int r = 0; r < 6; r++)
1464
1466
{
1465
evaluate_basis(r, &dof_values, coordinates, c);
1467
evaluate_basis(r, &dof_values, x, vertex_coordinates, cell_orientation);
1466
1468
values[r] = dof_values;
1467
1469
}// end loop over 'r'
1468
1470
}
1469
1471
1470
/// Evaluate order n derivatives of basis function i at given point in cell
1471
virtual void evaluate_basis_derivatives(unsigned int i,
1472
unsigned int n,
1472
/// Evaluate order n derivatives of basis function i at given point x in cell
1473
virtual void evaluate_basis_derivatives(std::size_t i,
1474
std::size_t n,
1473
1475
double* values,
1474
const double* coordinates,
1475
const ufc::cell& c) const
1476
const double* x,
1477
const double* vertex_coordinates,
1478
int cell_orientation) const
1476
1479
{
1477
// Extract vertex coordinates
1478
const double * const * x = c.coordinates;
1479
1480
// Compute Jacobian of affine map from reference cell
1481
const double J_00 = x[1][0] - x[0][0];
1482
const double J_01 = x[2][0] - x[0][0];
1483
const double J_10 = x[1][1] - x[0][1];
1484
const double J_11 = x[2][1] - x[0][1];
1485
1486
// Compute determinant of Jacobian
1487
double detJ = J_00*J_11 - J_01*J_10;
1488
1489
// Compute inverse of Jacobian
1490
const double K_00 = J_11 / detJ;
1491
const double K_01 = -J_01 / detJ;
1492
const double K_10 = -J_10 / detJ;
1493
const double K_11 = J_00 / detJ;
1480
// Compute Jacobian
1481
double J[4];
1482
compute_jacobian_triangle_2d(J, vertex_coordinates);
1483
1484
// Compute Jacobian inverse and determinant
1485
double K[4];
1486
double detJ;
1487
compute_jacobian_inverse_triangle_2d(K, detJ, J);
1488
1494
1489
1495
1490
// Compute constants
1496
const double C0 = x[1][0] + x[2][0];
1497
const double C1 = x[1][1] + x[2][1];
1491
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
1492
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
1498
1493
1499
1494
// Get coordinates and map to the reference (FIAT) element
1500
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
1501
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
1495
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
1496
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
1502
1497
1503
1498
// Compute number of derivatives.
1504
1499
unsigned int num_derivatives = 1;
1535
1530
}
1536
1531
1537
1532
// Compute inverse of Jacobian
1538
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
1533
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
1539
1534
1540
1535
// Declare transformation matrix
1541
1536
// Declare pointer to two dimensional array and initialise
1569
1564
case 0:
1570
1565
{
1571
1566
1572
// Array of basisvalues.
1567
// Array of basisvalues
1573
1568
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1574
1569
1575
// Declare helper variables.
1570
// Declare helper variables
1576
1571
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1577
1572
double tmp1 = (1.0 - Y)/2.0;
1578
1573
double tmp2 = tmp1*tmp1;
1579
1574
1580
// Compute basisvalues.
1575
// Compute basisvalues
1581
1576
basisvalues[0] = 1.0;
1582
1577
basisvalues[1] = tmp0;
1583
1578
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1591
1586
basisvalues[4] *= std::sqrt(4.5);
1592
1587
basisvalues[3] *= std::sqrt(7.5);
1593
1588
1594
// Table(s) of coefficients.
1589
// Table(s) of coefficients
1595
1590
static const double coefficients0[6] = \
1596
1591
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
1597
1592
1735
1730
case 1:
1736
1731
{
1737
1732
1738
// Array of basisvalues.
1733
// Array of basisvalues
1739
1734
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1740
1735
1741
// Declare helper variables.
1736
// Declare helper variables
1742
1737
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1743
1738
double tmp1 = (1.0 - Y)/2.0;
1744
1739
double tmp2 = tmp1*tmp1;
1745
1740
1746
// Compute basisvalues.
1741
// Compute basisvalues
1747
1742
basisvalues[0] = 1.0;
1748
1743
basisvalues[1] = tmp0;
1749
1744
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1757
1752
basisvalues[4] *= std::sqrt(4.5);
1758
1753
basisvalues[3] *= std::sqrt(7.5);
1759
1754
1760
// Table(s) of coefficients.
1755
// Table(s) of coefficients
1761
1756
static const double coefficients0[6] = \
1762
1757
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
1763
1758
1901
1896
case 2:
1902
1897
{
1903
1898
1904
// Array of basisvalues.
1899
// Array of basisvalues
1905
1900
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1906
1901
1907
// Declare helper variables.
1902
// Declare helper variables
1908
1903
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1909
1904
double tmp1 = (1.0 - Y)/2.0;
1910
1905
double tmp2 = tmp1*tmp1;
1911
1906
1912
// Compute basisvalues.
1907
// Compute basisvalues
1913
1908
basisvalues[0] = 1.0;
1914
1909
basisvalues[1] = tmp0;
1915
1910
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1923
1918
basisvalues[4] *= std::sqrt(4.5);
1924
1919
basisvalues[3] *= std::sqrt(7.5);
1925
1920
1926
// Table(s) of coefficients.
1921
// Table(s) of coefficients
1927
1922
static const double coefficients0[6] = \
1928
1923
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
1929
1924
2067
2062
case 3:
2068
2063
{
2069
2064
2070
// Array of basisvalues.
2065
// Array of basisvalues
2071
2066
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2072
2067
2073
// Declare helper variables.
2068
// Declare helper variables
2074
2069
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2075
2070
double tmp1 = (1.0 - Y)/2.0;
2076
2071
double tmp2 = tmp1*tmp1;
2077
2072
2078
// Compute basisvalues.
2073
// Compute basisvalues
2079
2074
basisvalues[0] = 1.0;
2080
2075
basisvalues[1] = tmp0;
2081
2076
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2089
2084
basisvalues[4] *= std::sqrt(4.5);
2090
2085
basisvalues[3] *= std::sqrt(7.5);
2091
2086
2092
// Table(s) of coefficients.
2087
// Table(s) of coefficients
2093
2088
static const double coefficients0[6] = \
2094
2089
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
2095
2090
2233
2228
case 4:
2234
2229
{
2235
2230
2236
// Array of basisvalues.
2231
// Array of basisvalues
2237
2232
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2238
2233
2239
// Declare helper variables.
2234
// Declare helper variables
2240
2235
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2241
2236
double tmp1 = (1.0 - Y)/2.0;
2242
2237
double tmp2 = tmp1*tmp1;
2243
2238
2244
// Compute basisvalues.
2239
// Compute basisvalues
2245
2240
basisvalues[0] = 1.0;
2246
2241
basisvalues[1] = tmp0;
2247
2242
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2255
2250
basisvalues[4] *= std::sqrt(4.5);
2256
2251
basisvalues[3] *= std::sqrt(7.5);
2257
2252
2258
// Table(s) of coefficients.
2253
// Table(s) of coefficients
2259
2254
static const double coefficients0[6] = \
2260
2255
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
2261
2256
2399
2394
case 5:
2400
2395
{
2401
2396
2402
// Array of basisvalues.
2397
// Array of basisvalues
2403
2398
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2404
2399
2405
// Declare helper variables.
2400
// Declare helper variables
2406
2401
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2407
2402
double tmp1 = (1.0 - Y)/2.0;
2408
2403
double tmp2 = tmp1*tmp1;
2409
2404
2410
// Compute basisvalues.
2405
// Compute basisvalues
2411
2406
basisvalues[0] = 1.0;
2412
2407
basisvalues[1] = tmp0;
2413
2408
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2421
2416
basisvalues[4] *= std::sqrt(4.5);
2422
2417
basisvalues[3] *= std::sqrt(7.5);
2423
2418
2424
// Table(s) of coefficients.
2419
// Table(s) of coefficients
2425
2420
static const double coefficients0[6] = \
2426
2421
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
2427
2422
2566
2561
2567
2562
}
2568
2563
2569
/// Evaluate order n derivatives of all basis functions at given point in cell
2570
virtual void evaluate_basis_derivatives_all(unsigned int n,
2564
/// Evaluate order n derivatives of all basis functions at given point x in cell
2565
virtual void evaluate_basis_derivatives_all(std::size_t n,
2571
2566
double* values,
2572
const double* coordinates,
2573
const ufc::cell& c) const
2567
const double* x,
2568
const double* vertex_coordinates,
2569
int cell_orientation) const
2574
2570
{
2575
2571
// Compute number of derivatives.
2576
2572
unsigned int num_derivatives = 1;
2589
2585
// Loop dofs and call evaluate_basis_derivatives.
2590
2586
for (unsigned int r = 0; r < 6; r++)
2591
2587
{
2592
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
2588
evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
2593
2589
for (unsigned int s = 0; s < num_derivatives; s++)
2594
2590
{
2595
2591
values[r*num_derivatives + s] = dof_values[s];
2601
2597
}
2602
2598
2603
2599
/// Evaluate linear functional for dof i on the function f
2604
virtual double evaluate_dof(unsigned int i,
2600
virtual double evaluate_dof(std::size_t i,
2605
2601
const ufc::function& f,
2602
const double* vertex_coordinates,
2603
int cell_orientation,
2606
2604
const ufc::cell& c) const
2607
2605
{
2608
// Declare variables for result of evaluation.
2606
// Declare variables for result of evaluation
2609
2607
double vals[1];
2610
2608
2611
// Declare variable for physical coordinates.
2609
// Declare variable for physical coordinates
2612
2610
double y[2];
2613
const double * const * x = c.coordinates;
2614
2611
switch (i)
2615
2612
{
2616
2613
case 0:
2617
2614
{
2618
y[0] = x[0][0];
2619
y[1] = x[0][1];
2615
y[0] = vertex_coordinates[0];
2616
y[1] = vertex_coordinates[1];
2620
2617
f.evaluate(vals, y, c);
2621
2618
return vals[0];
2622
2619
break;
2623
2620
}
2624
2621
case 1:
2625
2622
{
2626
y[0] = x[1][0];
2627
y[1] = x[1][1];
2623
y[0] = vertex_coordinates[2];
2624
y[1] = vertex_coordinates[3];
2628
2625
f.evaluate(vals, y, c);
2629
2626
return vals[0];
2630
2627
break;
2631
2628
}
2632
2629
case 2:
2633
2630
{
2634
y[0] = x[2][0];
2635
y[1] = x[2][1];
2631
y[0] = vertex_coordinates[4];
2632
y[1] = vertex_coordinates[5];
2636
2633
f.evaluate(vals, y, c);
2637
2634
return vals[0];
2638
2635
break;
2639
2636
}
2640
2637
case 3:
2641
2638
{
2642
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
2643
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
2639
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
2640
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
2644
2641
f.evaluate(vals, y, c);
2645
2642
return vals[0];
2646
2643
break;
2647
2644
}
2648
2645
case 4:
2649
2646
{
2650
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
2651
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
2647
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
2648
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
2652
2649
f.evaluate(vals, y, c);
2653
2650
return vals[0];
2654
2651
break;
2655
2652
}
2656
2653
case 5:
2657
2654
{
2658
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
2659
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
2655
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
2656
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
2660
2657
f.evaluate(vals, y, c);
2661
2658
return vals[0];
2662
2659
break;
2669
2666
/// Evaluate linear functionals for all dofs on the function f
2670
2667
virtual void evaluate_dofs(double* values,
2671
2668
const ufc::function& f,
2669
const double* vertex_coordinates,
2670
int cell_orientation,
2672
2671
const ufc::cell& c) const
2673
2672
{
2674
// Declare variables for result of evaluation.
2673
// Declare variables for result of evaluation
2675
2674
double vals[1];
2676
2675
2677
// Declare variable for physical coordinates.
2676
// Declare variable for physical coordinates
2678
2677
double y[2];
2679
const double * const * x = c.coordinates;
2680
y[0] = x[0][0];
2681
y[1] = x[0][1];
2678
y[0] = vertex_coordinates[0];
2679
y[1] = vertex_coordinates[1];
2682
2680
f.evaluate(vals, y, c);
2683
2681
values[0] = vals[0];
2684
y[0] = x[1][0];
2685
y[1] = x[1][1];
2682
y[0] = vertex_coordinates[2];
2683
y[1] = vertex_coordinates[3];
2686
2684
f.evaluate(vals, y, c);
2687
2685
values[1] = vals[0];
2688
y[0] = x[2][0];
2689
y[1] = x[2][1];
2686
y[0] = vertex_coordinates[4];
2687
y[1] = vertex_coordinates[5];
2690
2688
f.evaluate(vals, y, c);
2691
2689
values[2] = vals[0];
2692
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
2693
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
2690
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
2691
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
2694
2692
f.evaluate(vals, y, c);
2695
2693
values[3] = vals[0];
2696
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
2697
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
2694
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
2695
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
2698
2696
f.evaluate(vals, y, c);
2699
2697
values[4] = vals[0];
2700
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
2701
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
2698
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
2699
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
2702
2700
f.evaluate(vals, y, c);
2703
2701
values[5] = vals[0];
2704
2702
}
2706
2704
/// Interpolate vertex values from dof values
2707
2705
virtual void interpolate_vertex_values(double* vertex_values,
2708
2706
const double* dof_values,
2707
const double* vertex_coordinates,
2708
int cell_orientation,
2709
2709
const ufc::cell& c) const
2710
2710
{
2711
2711
// Evaluate function and change variables
2719
2719
const double* xhat,
2720
2720
const ufc::cell& c) const
2721
2721
{
2722
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
2722
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
2723
2723
}
2724
2724
2725
2725
/// Map from coordinate x in cell to coordinate xhat in reference cell
2727
2727
const double* x,
2728
2728
const ufc::cell& c) const
2729
2729
{
2730
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
2730
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
2731
2731
}
2732
2732
2733
2733
/// Return the number of sub elements (for a mixed element)
2734
virtual unsigned int num_sub_elements() const
2734
virtual std::size_t num_sub_elements() const
2735
2735
{
2736
2736
return 0;
2737
2737
}
2738
2738
2739
2739
/// Create a new finite element for sub element i (for a mixed element)
2740
virtual ufc::finite_element* create_sub_element(unsigned int i) const
2740
virtual ufc::finite_element* create_sub_element(std::size_t i) const
2741
2741
{
2742
2742
return 0;
2743
2743
}
2771
2771
/// Return a string identifying the finite element
2772
2772
virtual const char* signature() const
2773
2773
{
2774
return "MixedElement(*[VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None), FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)], **{'value_shape': (3,) })";
2774
return "MixedElement(*[VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None), FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)], **{'value_shape': (3,) })";
2775
2775
}
2776
2776
2777
2777
/// Return the cell shape
2781
2781
}
2782
2782
2783
2783
/// Return the topological dimension of the cell shape
2784
virtual unsigned int topological_dimension() const
2784
virtual std::size_t topological_dimension() const
2785
2785
{
2786
2786
return 2;
2787
2787
}
2788
2788
2789
2789
/// Return the geometric dimension of the cell shape
2790
virtual unsigned int geometric_dimension() const
2790
virtual std::size_t geometric_dimension() const
2791
2791
{
2792
2792
return 2;
2793
2793
}
2794
2794
2795
2795
/// Return the dimension of the finite element function space
2796
virtual unsigned int space_dimension() const
2796
virtual std::size_t space_dimension() const
2797
2797
{
2798
2798
return 8;
2799
2799
}
2800
2800
2801
2801
/// Return the rank of the value space
2802
virtual unsigned int value_rank() const
2802
virtual std::size_t value_rank() const
2803
2803
{
2804
2804
return 1;
2805
2805
}
2806
2806
2807
2807
/// Return the dimension of the value space for axis i
2808
virtual unsigned int value_dimension(unsigned int i) const
2808
virtual std::size_t value_dimension(std::size_t i) const
2809
2809
{
2810
2810
switch (i)
2811
2811
{
2819
2819
return 0;
2820
2820
}
2821
2821
2822
/// Evaluate basis function i at given point in cell
2823
virtual void evaluate_basis(unsigned int i,
2822
/// Evaluate basis function i at given point x in cell
2823
virtual void evaluate_basis(std::size_t i,
2824
2824
double* values,
2825
const double* coordinates,
2826
const ufc::cell& c) const
2825
const double* x,
2826
const double* vertex_coordinates,
2827
int cell_orientation) const
2827
2828
{
2828
// Extract vertex coordinates
2829
const double * const * x = c.coordinates;
2830
2831
// Compute Jacobian of affine map from reference cell
2832
const double J_00 = x[1][0] - x[0][0];
2833
const double J_01 = x[2][0] - x[0][0];
2834
const double J_10 = x[1][1] - x[0][1];
2835
const double J_11 = x[2][1] - x[0][1];
2836
2837
// Compute determinant of Jacobian
2838
double detJ = J_00*J_11 - J_01*J_10;
2839
2840
// Compute inverse of Jacobian
2829
// Compute Jacobian
2830
double J[4];
2831
compute_jacobian_triangle_2d(J, vertex_coordinates);
2832
2833
// Compute Jacobian inverse and determinant
2834
double K[4];
2835
double detJ;
2836
compute_jacobian_inverse_triangle_2d(K, detJ, J);
2837
2841
2838
2842
2839
// Compute constants
2843
const double C0 = x[1][0] + x[2][0];
2844
const double C1 = x[1][1] + x[2][1];
2840
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
2841
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
2845
2842
2846
2843
// Get coordinates and map to the reference (FIAT) element
2847
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
2848
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
2844
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
2845
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
2849
2846
2850
// Reset values.
2847
// Reset values
2851
2848
values[0] = 0.0;
2852
2849
values[1] = 0.0;
2853
2850
values[2] = 0.0;
2856
2853
case 0:
2857
2854
{
2858
2855
2859
// Array of basisvalues.
2856
// Array of basisvalues
2860
2857
double basisvalues[1] = {0.0};
2861
2858
2862
// Declare helper variables.
2859
// Declare helper variables
2863
2860
2864
// Compute basisvalues.
2861
// Compute basisvalues
2865
2862
basisvalues[0] = 1.0;
2866
2863
2867
// Table(s) of coefficients.
2864
// Table(s) of coefficients
2868
2865
static const double coefficients0[1] = \
2869
2866
{1.0};
2870
2867
2871
// Compute value(s).
2868
// Compute value(s)
2872
2869
for (unsigned int r = 0; r < 1; r++)
2873
2870
{
2874
2871
values[0] += coefficients0[r]*basisvalues[r];
2878
2875
case 1:
2879
2876
{
2880
2877
2881
// Array of basisvalues.
2878
// Array of basisvalues
2882
2879
double basisvalues[1] = {0.0};
2883
2880
2884
// Declare helper variables.
2881
// Declare helper variables
2885
2882
2886
// Compute basisvalues.
2883
// Compute basisvalues
2887
2884
basisvalues[0] = 1.0;
2888
2885
2889
// Table(s) of coefficients.
2886
// Table(s) of coefficients
2890
2887
static const double coefficients0[1] = \
2891
2888
{1.0};
2892
2889
2893
// Compute value(s).
2890
// Compute value(s)
2894
2891
for (unsigned int r = 0; r < 1; r++)
2895
2892
{
2896
2893
values[1] += coefficients0[r]*basisvalues[r];
2900
2897
case 2:
2901
2898
{
2902
2899
2903
// Array of basisvalues.
2900
// Array of basisvalues
2904
2901
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2905
2902
2906
// Declare helper variables.
2903
// Declare helper variables
2907
2904
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2908
2905
double tmp1 = (1.0 - Y)/2.0;
2909
2906
double tmp2 = tmp1*tmp1;
2910
2907
2911
// Compute basisvalues.
2908
// Compute basisvalues
2912
2909
basisvalues[0] = 1.0;
2913
2910
basisvalues[1] = tmp0;
2914
2911
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2922
2919
basisvalues[4] *= std::sqrt(4.5);
2923
2920
basisvalues[3] *= std::sqrt(7.5);
2924
2921
2925
// Table(s) of coefficients.
2922
// Table(s) of coefficients
2926
2923
static const double coefficients0[6] = \
2927
2924
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
2928
2925
2929
// Compute value(s).
2926
// Compute value(s)
2930
2927
for (unsigned int r = 0; r < 6; r++)
2931
2928
{
2932
2929
values[2] += coefficients0[r]*basisvalues[r];
2936
2933
case 3:
2937
2934
{
2938
2935
2939
// Array of basisvalues.
2936
// Array of basisvalues
2940
2937
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2941
2938
2942
// Declare helper variables.
2939
// Declare helper variables
2943
2940
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2944
2941
double tmp1 = (1.0 - Y)/2.0;
2945
2942
double tmp2 = tmp1*tmp1;
2946
2943
2947
// Compute basisvalues.
2944
// Compute basisvalues
2948
2945
basisvalues[0] = 1.0;
2949
2946
basisvalues[1] = tmp0;
2950
2947
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2958
2955
basisvalues[4] *= std::sqrt(4.5);
2959
2956
basisvalues[3] *= std::sqrt(7.5);
2960
2957
2961
// Table(s) of coefficients.
2958
// Table(s) of coefficients
2962
2959
static const double coefficients0[6] = \
2963
2960
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
2964
2961
2965
// Compute value(s).
2962
// Compute value(s)
2966
2963
for (unsigned int r = 0; r < 6; r++)
2967
2964
{
2968
2965
values[2] += coefficients0[r]*basisvalues[r];
2972
2969
case 4:
2973
2970
{
2974
2971
2975
// Array of basisvalues.
2972
// Array of basisvalues
2976
2973
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2977
2974
2978
// Declare helper variables.
2975
// Declare helper variables
2979
2976
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2980
2977
double tmp1 = (1.0 - Y)/2.0;
2981
2978
double tmp2 = tmp1*tmp1;
2982
2979
2983
// Compute basisvalues.
2980
// Compute basisvalues
2984
2981
basisvalues[0] = 1.0;
2985
2982
basisvalues[1] = tmp0;
2986
2983
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
2994
2991
basisvalues[4] *= std::sqrt(4.5);
2995
2992
basisvalues[3] *= std::sqrt(7.5);
2996
2993
2997
// Table(s) of coefficients.
2994
// Table(s) of coefficients
2998
2995
static const double coefficients0[6] = \
2999
2996
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
3000
2997
3001
// Compute value(s).
2998
// Compute value(s)
3002
2999
for (unsigned int r = 0; r < 6; r++)
3003
3000
{
3004
3001
values[2] += coefficients0[r]*basisvalues[r];
3008
3005
case 5:
3009
3006
{
3010
3007
3011
// Array of basisvalues.
3008
// Array of basisvalues
3012
3009
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3013
3010
3014
// Declare helper variables.
3011
// Declare helper variables
3015
3012
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3016
3013
double tmp1 = (1.0 - Y)/2.0;
3017
3014
double tmp2 = tmp1*tmp1;
3018
3015
3019
// Compute basisvalues.
3016
// Compute basisvalues
3020
3017
basisvalues[0] = 1.0;
3021
3018
basisvalues[1] = tmp0;
3022
3019
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3030
3027
basisvalues[4] *= std::sqrt(4.5);
3031
3028
basisvalues[3] *= std::sqrt(7.5);
3032
3029
3033
// Table(s) of coefficients.
3030
// Table(s) of coefficients
3034
3031
static const double coefficients0[6] = \
3035
3032
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
3036
3033
3037
// Compute value(s).
3034
// Compute value(s)
3038
3035
for (unsigned int r = 0; r < 6; r++)
3039
3036
{
3040
3037
values[2] += coefficients0[r]*basisvalues[r];
3044
3041
case 6:
3045
3042
{
3046
3043
3047
// Array of basisvalues.
3044
// Array of basisvalues
3048
3045
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3049
3046
3050
// Declare helper variables.
3047
// Declare helper variables
3051
3048
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3052
3049
double tmp1 = (1.0 - Y)/2.0;
3053
3050
double tmp2 = tmp1*tmp1;
3054
3051
3055
// Compute basisvalues.
3052
// Compute basisvalues
3056
3053
basisvalues[0] = 1.0;
3057
3054
basisvalues[1] = tmp0;
3058
3055
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3066
3063
basisvalues[4] *= std::sqrt(4.5);
3067
3064
basisvalues[3] *= std::sqrt(7.5);
3068
3065
3069
// Table(s) of coefficients.
3066
// Table(s) of coefficients
3070
3067
static const double coefficients0[6] = \
3071
3068
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
3072
3069
3073
// Compute value(s).
3070
// Compute value(s)
3074
3071
for (unsigned int r = 0; r < 6; r++)
3075
3072
{
3076
3073
values[2] += coefficients0[r]*basisvalues[r];
3080
3077
case 7:
3081
3078
{
3082
3079
3083
// Array of basisvalues.
3080
// Array of basisvalues
3084
3081
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3085
3082
3086
// Declare helper variables.
3083
// Declare helper variables
3087
3084
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3088
3085
double tmp1 = (1.0 - Y)/2.0;
3089
3086
double tmp2 = tmp1*tmp1;
3090
3087
3091
// Compute basisvalues.
3088
// Compute basisvalues
3092
3089
basisvalues[0] = 1.0;
3093
3090
basisvalues[1] = tmp0;
3094
3091
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3102
3099
basisvalues[4] *= std::sqrt(4.5);
3103
3100
basisvalues[3] *= std::sqrt(7.5);
3104
3101
3105
// Table(s) of coefficients.
3102
// Table(s) of coefficients
3106
3103
static const double coefficients0[6] = \
3107
3104
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
3108
3105
3109
// Compute value(s).
3106
// Compute value(s)
3110
3107
for (unsigned int r = 0; r < 6; r++)
3111
3108
{
3112
3109
values[2] += coefficients0[r]*basisvalues[r];
3117
3114
3118
3115
}
3119
3116
3120
/// Evaluate all basis functions at given point in cell
3117
/// Evaluate all basis functions at given point x in cell
3121
3118
virtual void evaluate_basis_all(double* values,
3122
const double* coordinates,
3123
const ufc::cell& c) const
3119
const double* x,
3120
const double* vertex_coordinates,
3121
int cell_orientation) const
3124
3122
{
3125
3123
// Helper variable to hold values of a single dof.
3126
3124
double dof_values[3] = {0.0, 0.0, 0.0};
3127
3125
3128
// Loop dofs and call evaluate_basis.
3126
// Loop dofs and call evaluate_basis
3129
3127
for (unsigned int r = 0; r < 8; r++)
3130
3128
{
3131
evaluate_basis(r, dof_values, coordinates, c);
3129
evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
3132
3130
for (unsigned int s = 0; s < 3; s++)
3133
3131
{
3134
3132
values[r*3 + s] = dof_values[s];
3136
3134
}// end loop over 'r'
3137
3135
}
3138
3136
3139
/// Evaluate order n derivatives of basis function i at given point in cell
3140
virtual void evaluate_basis_derivatives(unsigned int i,
3141
unsigned int n,
3137
/// Evaluate order n derivatives of basis function i at given point x in cell
3138
virtual void evaluate_basis_derivatives(std::size_t i,
3139
std::size_t n,
3142
3140
double* values,
3143
const double* coordinates,
3144
const ufc::cell& c) const
3141
const double* x,
3142
const double* vertex_coordinates,
3143
int cell_orientation) const
3145
3144
{
3146
// Extract vertex coordinates
3147
const double * const * x = c.coordinates;
3148
3149
// Compute Jacobian of affine map from reference cell
3150
const double J_00 = x[1][0] - x[0][0];
3151
const double J_01 = x[2][0] - x[0][0];
3152
const double J_10 = x[1][1] - x[0][1];
3153
const double J_11 = x[2][1] - x[0][1];
3154
3155
// Compute determinant of Jacobian
3156
double detJ = J_00*J_11 - J_01*J_10;
3157
3158
// Compute inverse of Jacobian
3159
const double K_00 = J_11 / detJ;
3160
const double K_01 = -J_01 / detJ;
3161
const double K_10 = -J_10 / detJ;
3162
const double K_11 = J_00 / detJ;
3145
// Compute Jacobian
3146
double J[4];
3147
compute_jacobian_triangle_2d(J, vertex_coordinates);
3148
3149
// Compute Jacobian inverse and determinant
3150
double K[4];
3151
double detJ;
3152
compute_jacobian_inverse_triangle_2d(K, detJ, J);
3153
3163
3154
3164
3155
// Compute constants
3165
const double C0 = x[1][0] + x[2][0];
3166
const double C1 = x[1][1] + x[2][1];
3156
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
3157
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
3167
3158
3168
3159
// Get coordinates and map to the reference (FIAT) element
3169
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
3170
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
3160
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
3161
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
3171
3162
3172
3163
// Compute number of derivatives.
3173
3164
unsigned int num_derivatives = 1;
3204
3195
}
3205
3196
3206
3197
// Compute inverse of Jacobian
3207
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
3198
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
3208
3199
3209
3200
// Declare transformation matrix
3210
3201
// Declare pointer to two dimensional array and initialise
3238
3229
case 0:
3239
3230
{
3240
3231
3241
// Array of basisvalues.
3232
// Array of basisvalues
3242
3233
double basisvalues[1] = {0.0};
3243
3234
3244
// Declare helper variables.
3235
// Declare helper variables
3245
3236
3246
// Compute basisvalues.
3237
// Compute basisvalues
3247
3238
basisvalues[0] = 1.0;
3248
3239
3249
// Table(s) of coefficients.
3240
// Table(s) of coefficients
3250
3241
static const double coefficients0[1] = \
3251
3242
{1.0};
3252
3243
3370
3361
case 1:
3371
3362
{
3372
3363
3373
// Array of basisvalues.
3364
// Array of basisvalues
3374
3365
double basisvalues[1] = {0.0};
3375
3366
3376
// Declare helper variables.
3367
// Declare helper variables
3377
3368
3378
// Compute basisvalues.
3369
// Compute basisvalues
3379
3370
basisvalues[0] = 1.0;
3380
3371
3381
// Table(s) of coefficients.
3372
// Table(s) of coefficients
3382
3373
static const double coefficients0[1] = \
3383
3374
{1.0};
3384
3375
3502
3493
case 2:
3503
3494
{
3504
3495
3505
// Array of basisvalues.
3496
// Array of basisvalues
3506
3497
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3507
3498
3508
// Declare helper variables.
3499
// Declare helper variables
3509
3500
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3510
3501
double tmp1 = (1.0 - Y)/2.0;
3511
3502
double tmp2 = tmp1*tmp1;
3512
3503
3513
// Compute basisvalues.
3504
// Compute basisvalues
3514
3505
basisvalues[0] = 1.0;
3515
3506
basisvalues[1] = tmp0;
3516
3507
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3524
3515
basisvalues[4] *= std::sqrt(4.5);
3525
3516
basisvalues[3] *= std::sqrt(7.5);
3526
3517
3527
// Table(s) of coefficients.
3518
// Table(s) of coefficients
3528
3519
static const double coefficients0[6] = \
3529
3520
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
3530
3521
3668
3659
case 3:
3669
3660
{
3670
3661
3671
// Array of basisvalues.
3662
// Array of basisvalues
3672
3663
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3673
3664
3674
// Declare helper variables.
3665
// Declare helper variables
3675
3666
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3676
3667
double tmp1 = (1.0 - Y)/2.0;
3677
3668
double tmp2 = tmp1*tmp1;
3678
3669
3679
// Compute basisvalues.
3670
// Compute basisvalues
3680
3671
basisvalues[0] = 1.0;
3681
3672
basisvalues[1] = tmp0;
3682
3673
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3690
3681
basisvalues[4] *= std::sqrt(4.5);
3691
3682
basisvalues[3] *= std::sqrt(7.5);
3692
3683
3693
// Table(s) of coefficients.
3684
// Table(s) of coefficients
3694
3685
static const double coefficients0[6] = \
3695
3686
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
3696
3687
3834
3825
case 4:
3835
3826
{
3836
3827
3837
// Array of basisvalues.
3828
// Array of basisvalues
3838
3829
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3839
3830
3840
// Declare helper variables.
3831
// Declare helper variables
3841
3832
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3842
3833
double tmp1 = (1.0 - Y)/2.0;
3843
3834
double tmp2 = tmp1*tmp1;
3844
3835
3845
// Compute basisvalues.
3836
// Compute basisvalues
3846
3837
basisvalues[0] = 1.0;
3847
3838
basisvalues[1] = tmp0;
3848
3839
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3856
3847
basisvalues[4] *= std::sqrt(4.5);
3857
3848
basisvalues[3] *= std::sqrt(7.5);
3858
3849
3859
// Table(s) of coefficients.
3850
// Table(s) of coefficients
3860
3851
static const double coefficients0[6] = \
3861
3852
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
3862
3853
4000
3991
case 5:
4001
3992
{
4002
3993
4003
// Array of basisvalues.
3994
// Array of basisvalues
4004
3995
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4005
3996
4006
// Declare helper variables.
3997
// Declare helper variables
4007
3998
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4008
3999
double tmp1 = (1.0 - Y)/2.0;
4009
4000
double tmp2 = tmp1*tmp1;
4010
4001
4011
// Compute basisvalues.
4002
// Compute basisvalues
4012
4003
basisvalues[0] = 1.0;
4013
4004
basisvalues[1] = tmp0;
4014
4005
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4022
4013
basisvalues[4] *= std::sqrt(4.5);
4023
4014
basisvalues[3] *= std::sqrt(7.5);
4024
4015
4025
// Table(s) of coefficients.
4016
// Table(s) of coefficients
4026
4017
static const double coefficients0[6] = \
4027
4018
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
4028
4019
4166
4157
case 6:
4167
4158
{
4168
4159
4169
// Array of basisvalues.
4160
// Array of basisvalues
4170
4161
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4171
4162
4172
// Declare helper variables.
4163
// Declare helper variables
4173
4164
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4174
4165
double tmp1 = (1.0 - Y)/2.0;
4175
4166
double tmp2 = tmp1*tmp1;
4176
4167
4177
// Compute basisvalues.
4168
// Compute basisvalues
4178
4169
basisvalues[0] = 1.0;
4179
4170
basisvalues[1] = tmp0;
4180
4171
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4188
4179
basisvalues[4] *= std::sqrt(4.5);
4189
4180
basisvalues[3] *= std::sqrt(7.5);
4190
4181
4191
// Table(s) of coefficients.
4182
// Table(s) of coefficients
4192
4183
static const double coefficients0[6] = \
4193
4184
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
4194
4185
4332
4323
case 7:
4333
4324
{
4334
4325
4335
// Array of basisvalues.
4326
// Array of basisvalues
4336
4327
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4337
4328
4338
// Declare helper variables.
4329
// Declare helper variables
4339
4330
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4340
4331
double tmp1 = (1.0 - Y)/2.0;
4341
4332
double tmp2 = tmp1*tmp1;
4342
4333
4343
// Compute basisvalues.
4334
// Compute basisvalues
4344
4335
basisvalues[0] = 1.0;
4345
4336
basisvalues[1] = tmp0;
4346
4337
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4354
4345
basisvalues[4] *= std::sqrt(4.5);
4355
4346
basisvalues[3] *= std::sqrt(7.5);
4356
4347
4357
// Table(s) of coefficients.
4348
// Table(s) of coefficients
4358
4349
static const double coefficients0[6] = \
4359
4350
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
4360
4351
4499
4490
4500
4491
}
4501
4492
4502
/// Evaluate order n derivatives of all basis functions at given point in cell
4503
virtual void evaluate_basis_derivatives_all(unsigned int n,
4493
/// Evaluate order n derivatives of all basis functions at given point x in cell
4494
virtual void evaluate_basis_derivatives_all(std::size_t n,
4504
4495
double* values,
4505
const double* coordinates,
4506
const ufc::cell& c) const
4496
const double* x,
4497
const double* vertex_coordinates,
4498
int cell_orientation) const
4507
4499
{
4508
4500
// Compute number of derivatives.
4509
4501
unsigned int num_derivatives = 1;
4522
4514
// Loop dofs and call evaluate_basis_derivatives.
4523
4515
for (unsigned int r = 0; r < 8; r++)
4524
4516
{
4525
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
4517
evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
4526
4518
for (unsigned int s = 0; s < 3*num_derivatives; s++)
4527
4519
{
4528
4520
values[r*3*num_derivatives + s] = dof_values[s];
4534
4526
}
4535
4527
4536
4528
/// Evaluate linear functional for dof i on the function f
4537
virtual double evaluate_dof(unsigned int i,
4529
virtual double evaluate_dof(std::size_t i,
4538
4530
const ufc::function& f,
4531
const double* vertex_coordinates,
4532
int cell_orientation,
4539
4533
const ufc::cell& c) const
4540
4534
{
4541
// Declare variables for result of evaluation.
4535
// Declare variables for result of evaluation
4542
4536
double vals[3];
4543
4537
4544
// Declare variable for physical coordinates.
4538
// Declare variable for physical coordinates
4545
4539
double y[2];
4546
const double * const * x = c.coordinates;
4547
4540
switch (i)
4548
4541
{
4549
4542
case 0:
4550
4543
{
4551
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
4552
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
4544
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
4545
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
4553
4546
f.evaluate(vals, y, c);
4554
4547
return vals[0];
4555
4548
break;
4556
4549
}
4557
4550
case 1:
4558
4551
{
4559
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
4560
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
4552
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
4553
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
4561
4554
f.evaluate(vals, y, c);
4562
4555
return vals[1];
4563
4556
break;
4564
4557
}
4565
4558
case 2:
4566
4559
{
4567
y[0] = x[0][0];
4568
y[1] = x[0][1];
4560
y[0] = vertex_coordinates[0];
4561
y[1] = vertex_coordinates[1];
4569
4562
f.evaluate(vals, y, c);
4570
4563
return vals[2];
4571
4564
break;
4572
4565
}
4573
4566
case 3:
4574
4567
{
4575
y[0] = x[1][0];
4576
y[1] = x[1][1];
4568
y[0] = vertex_coordinates[2];
4569
y[1] = vertex_coordinates[3];
4577
4570
f.evaluate(vals, y, c);
4578
4571
return vals[2];
4579
4572
break;
4580
4573
}
4581
4574
case 4:
4582
4575
{
4583
y[0] = x[2][0];
4584
y[1] = x[2][1];
4576
y[0] = vertex_coordinates[4];
4577
y[1] = vertex_coordinates[5];
4585
4578
f.evaluate(vals, y, c);
4586
4579
return vals[2];
4587
4580
break;
4588
4581
}
4589
4582
case 5:
4590
4583
{
4591
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
4592
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
4584
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
4585
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
4593
4586
f.evaluate(vals, y, c);
4594
4587
return vals[2];
4595
4588
break;
4596
4589
}
4597
4590
case 6:
4598
4591
{
4599
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
4600
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
4592
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
4593
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
4601
4594
f.evaluate(vals, y, c);
4602
4595
return vals[2];
4603
4596
break;
4604
4597
}
4605
4598
case 7:
4606
4599
{
4607
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
4608
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
4600
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
4601
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
4609
4602
f.evaluate(vals, y, c);
4610
4603
return vals[2];
4611
4604
break;
4618
4611
/// Evaluate linear functionals for all dofs on the function f
4619
4612
virtual void evaluate_dofs(double* values,
4620
4613
const ufc::function& f,
4614
const double* vertex_coordinates,
4615
int cell_orientation,
4621
4616
const ufc::cell& c) const
4622
4617
{
4623
// Declare variables for result of evaluation.
4618
// Declare variables for result of evaluation
4624
4619
double vals[3];
4625
4620
4626
// Declare variable for physical coordinates.
4621
// Declare variable for physical coordinates
4627
4622
double y[2];
4628
const double * const * x = c.coordinates;
4629
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
4630
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
4623
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
4624
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
4631
4625
f.evaluate(vals, y, c);
4632
4626
values[0] = vals[0];
4633
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
4634
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
4627
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
4628
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
4635
4629
f.evaluate(vals, y, c);
4636
4630
values[1] = vals[1];
4637
y[0] = x[0][0];
4638
y[1] = x[0][1];
4631
y[0] = vertex_coordinates[0];
4632
y[1] = vertex_coordinates[1];
4639
4633
f.evaluate(vals, y, c);
4640
4634
values[2] = vals[2];
4641
y[0] = x[1][0];
4642
y[1] = x[1][1];
4635
y[0] = vertex_coordinates[2];
4636
y[1] = vertex_coordinates[3];
4643
4637
f.evaluate(vals, y, c);
4644
4638
values[3] = vals[2];
4645
y[0] = x[2][0];
4646
y[1] = x[2][1];
4639
y[0] = vertex_coordinates[4];
4640
y[1] = vertex_coordinates[5];
4647
4641
f.evaluate(vals, y, c);
4648
4642
values[4] = vals[2];
4649
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
4650
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
4643
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
4644
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
4651
4645
f.evaluate(vals, y, c);
4652
4646
values[5] = vals[2];
4653
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
4654
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
4647
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
4648
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
4655
4649
f.evaluate(vals, y, c);
4656
4650
values[6] = vals[2];
4657
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
4658
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
4651
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
4652
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
4659
4653
f.evaluate(vals, y, c);
4660
4654
values[7] = vals[2];
4661
4655
}
4663
4657
/// Interpolate vertex values from dof values
4664
4658
virtual void interpolate_vertex_values(double* vertex_values,
4665
4659
const double* dof_values,
4660
const double* vertex_coordinates,
4661
int cell_orientation,
4666
4662
const ufc::cell& c) const
4667
4663
{
4668
4664
// Evaluate function and change variables
4684
4680
const double* xhat,
4685
4681
const ufc::cell& c) const
4686
4682
{
4687
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
4683
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
4688
4684
}
4689
4685
4690
4686
/// Map from coordinate x in cell to coordinate xhat in reference cell
4692
4688
const double* x,
4693
4689
const ufc::cell& c) const
4694
4690
{
4695
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
4691
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
4696
4692
}
4697
4693
4698
4694
/// Return the number of sub elements (for a mixed element)
4699
virtual unsigned int num_sub_elements() const
4695
virtual std::size_t num_sub_elements() const
4700
4696
{
4701
4697
return 2;
4702
4698
}
4703
4699
4704
4700
/// Create a new finite element for sub element i (for a mixed element)
4705
virtual ufc::finite_element* create_sub_element(unsigned int i) const
4701
virtual ufc::finite_element* create_sub_element(std::size_t i) const
4706
4702
{
4707
4703
switch (i)
4708
4704
{
4750
4746
/// Return a string identifying the finite element
4751
4747
virtual const char* signature() const
4752
4748
{
4753
return "FiniteElement('Raviart-Thomas', Cell('triangle', Space(2)), 3, None)";
4749
return "FiniteElement('Raviart-Thomas', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 3, None)";
4754
4750
}
4755
4751
4756
4752
/// Return the cell shape
4760
4756
}
4761
4757
4762
4758
/// Return the topological dimension of the cell shape
4763
virtual unsigned int topological_dimension() const
4759
virtual std::size_t topological_dimension() const
4764
4760
{
4765
4761
return 2;
4766
4762
}
4767
4763
4768
4764
/// Return the geometric dimension of the cell shape
4769
virtual unsigned int geometric_dimension() const
4765
virtual std::size_t geometric_dimension() const
4770
4766
{
4771
4767
return 2;
4772
4768
}
4773
4769
4774
4770
/// Return the dimension of the finite element function space
4775
virtual unsigned int space_dimension() const
4771
virtual std::size_t space_dimension() const
4776
4772
{
4777
4773
return 15;
4778
4774
}
4779
4775
4780
4776
/// Return the rank of the value space
4781
virtual unsigned int value_rank() const
4777
virtual std::size_t value_rank() const
4782
4778
{
4783
4779
return 1;
4784
4780
}
4785
4781
4786
4782
/// Return the dimension of the value space for axis i
4787
virtual unsigned int value_dimension(unsigned int i) const
4783
virtual std::size_t value_dimension(std::size_t i) const
4788
4784
{
4789
4785
switch (i)
4790
4786
{
4798
4794
return 0;
4799
4795
}
4800
4796
4801
/// Evaluate basis function i at given point in cell
4802
virtual void evaluate_basis(unsigned int i,
4797
/// Evaluate basis function i at given point x in cell
4798
virtual void evaluate_basis(std::size_t i,
4803
4799
double* values,
4804
const double* coordinates,
4805
const ufc::cell& c) const
4800
const double* x,
4801
const double* vertex_coordinates,
4802
int cell_orientation) const
4806
4803
{
4807
// Extract vertex coordinates
4808
const double * const * x = c.coordinates;
4809
4810
// Compute Jacobian of affine map from reference cell
4811
const double J_00 = x[1][0] - x[0][0];
4812
const double J_01 = x[2][0] - x[0][0];
4813
const double J_10 = x[1][1] - x[0][1];
4814
const double J_11 = x[2][1] - x[0][1];
4815
4816
// Compute determinant of Jacobian
4817
double detJ = J_00*J_11 - J_01*J_10;
4818
4819
// Compute inverse of Jacobian
4804
// Compute Jacobian
4805
double J[4];
4806
compute_jacobian_triangle_2d(J, vertex_coordinates);
4807
4808
// Compute Jacobian inverse and determinant
4809
double K[4];
4810
double detJ;
4811
compute_jacobian_inverse_triangle_2d(K, detJ, J);
4812
4813
4820
4814
4821
4815
// Compute constants
4822
const double C0 = x[1][0] + x[2][0];
4823
const double C1 = x[1][1] + x[2][1];
4816
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
4817
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
4824
4818
4825
4819
// Get coordinates and map to the reference (FIAT) element
4826
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
4827
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
4820
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
4821
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
4828
4822
4829
// Reset values.
4823
// Reset values
4830
4824
values[0] = 0.0;
4831
4825
values[1] = 0.0;
4832
4826
switch (i)
4834
4828
case 0:
4835
4829
{
4836
4830
4837
// Array of basisvalues.
4831
// Array of basisvalues
4838
4832
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4839
4833
4840
// Declare helper variables.
4834
// Declare helper variables
4841
4835
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4842
4836
double tmp1 = (1.0 - Y)/2.0;
4843
4837
double tmp2 = tmp1*tmp1;
4844
4838
4845
// Compute basisvalues.
4839
// Compute basisvalues
4846
4840
basisvalues[0] = 1.0;
4847
4841
basisvalues[1] = tmp0;
4848
4842
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4864
4858
basisvalues[7] *= std::sqrt(10.0);
4865
4859
basisvalues[6] *= std::sqrt(14.0);
4866
4860
4867
// Table(s) of coefficients.
4861
// Table(s) of coefficients
4868
4862
static const double coefficients0[10] = \
4869
4863
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
4870
4864
4871
4865
static const double coefficients1[10] = \
4872
4866
{0.14142136, -0.038490018, 0.13333333, 0.069552071, -0.12121831, 0.089425816, 0.0, 0.06023386, -0.077761579, 0.053874802};
4873
4867
4874
// Compute value(s).
4868
// Compute value(s)
4875
4869
for (unsigned int r = 0; r < 10; r++)
4876
4870
{
4877
4871
values[0] += coefficients0[r]*basisvalues[r];
4878
4872
values[1] += coefficients1[r]*basisvalues[r];
4879
4873
}// end loop over 'r'
4880
4874
4881
// Using contravariant Piola transform to map values back to the physical element.
4875
// Using contravariant Piola transform to map values back to the physical element
4882
4876
const double tmp_ref0 = values[0];
4883
4877
const double tmp_ref1 = values[1];
4884
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
4885
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
4878
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
4879
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
4886
4880
break;
4887
4881
}
4888
4882
case 1:
4889
4883
{
4890
4884
4891
// Array of basisvalues.
4885
// Array of basisvalues
4892
4886
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4893
4887
4894
// Declare helper variables.
4888
// Declare helper variables
4895
4889
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4896
4890
double tmp1 = (1.0 - Y)/2.0;
4897
4891
double tmp2 = tmp1*tmp1;
4898
4892
4899
// Compute basisvalues.
4893
// Compute basisvalues
4900
4894
basisvalues[0] = 1.0;
4901
4895
basisvalues[1] = tmp0;
4902
4896
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4918
4912
basisvalues[7] *= std::sqrt(10.0);
4919
4913
basisvalues[6] *= std::sqrt(14.0);
4920
4914
4921
// Table(s) of coefficients.
4915
// Table(s) of coefficients
4922
4916
static const double coefficients0[10] = \
4923
4917
{-0.18856181, -0.25018512, 0.23333333, -0.10432811, 0.32324881, -0.25661321, 0.0, 0.12046772, -0.15552316, 0.1077496};
4924
4918
4925
4919
static const double coefficients1[10] = \
4926
4920
{-0.18856181, 0.076980036, -0.33333333, 0.0, 0.24243661, -0.34992711, 0.0, 0.0, 0.15552316, -0.16162441};
4927
4921
4928
// Compute value(s).
4922
// Compute value(s)
4929
4923
for (unsigned int r = 0; r < 10; r++)
4930
4924
{
4931
4925
values[0] += coefficients0[r]*basisvalues[r];
4932
4926
values[1] += coefficients1[r]*basisvalues[r];
4933
4927
}// end loop over 'r'
4934
4928
4935
// Using contravariant Piola transform to map values back to the physical element.
4929
// Using contravariant Piola transform to map values back to the physical element
4936
4930
const double tmp_ref0 = values[0];
4937
4931
const double tmp_ref1 = values[1];
4938
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
4939
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
4932
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
4933
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
4940
4934
break;
4941
4935
}
4942
4936
case 2:
4943
4937
{
4944
4938
4945
// Array of basisvalues.
4939
// Array of basisvalues
4946
4940
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4947
4941
4948
// Declare helper variables.
4942
// Declare helper variables
4949
4943
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4950
4944
double tmp1 = (1.0 - Y)/2.0;
4951
4945
double tmp2 = tmp1*tmp1;
4952
4946
4953
// Compute basisvalues.
4947
// Compute basisvalues
4954
4948
basisvalues[0] = 1.0;
4955
4949
basisvalues[1] = tmp0;
4956
4950
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4972
4966
basisvalues[7] *= std::sqrt(10.0);
4973
4967
basisvalues[6] *= std::sqrt(14.0);
4974
4968
4975
// Table(s) of coefficients.
4969
// Table(s) of coefficients
4976
4970
static const double coefficients0[10] = \
4977
4971
{0.14142136, 0.096225045, -0.1, 0.0, -0.067343503, 0.15163508, 0.0, 0.0, 0.077761579, -0.080812204};
4978
4972
4979
4973
static const double coefficients1[10] = \
4980
4974
{0.18856181, 0.0, 0.33333333, 0.0, 0.0, 0.34992711, 0.0, 0.0, 0.0, 0.16162441};
4981
4975
4982
// Compute value(s).
4976
// Compute value(s)
4983
4977
for (unsigned int r = 0; r < 10; r++)
4984
4978
{
4985
4979
values[0] += coefficients0[r]*basisvalues[r];
4986
4980
values[1] += coefficients1[r]*basisvalues[r];
4987
4981
}// end loop over 'r'
4988
4982
4989
// Using contravariant Piola transform to map values back to the physical element.
4983
// Using contravariant Piola transform to map values back to the physical element
4990
4984
const double tmp_ref0 = values[0];
4991
4985
const double tmp_ref1 = values[1];
4992
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
4993
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
4986
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
4987
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
4994
4988
break;
4995
4989
}
4996
4990
case 3:
4997
4991
{
4998
4992
4999
// Array of basisvalues.
4993
// Array of basisvalues
5000
4994
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5001
4995
5002
// Declare helper variables.
4996
// Declare helper variables
5003
4997
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5004
4998
double tmp1 = (1.0 - Y)/2.0;
5005
4999
double tmp2 = tmp1*tmp1;
5006
5000
5007
// Compute basisvalues.
5001
// Compute basisvalues
5008
5002
basisvalues[0] = 1.0;
5009
5003
basisvalues[1] = tmp0;
5010
5004
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5026
5020
basisvalues[7] *= std::sqrt(10.0);
5027
5021
basisvalues[6] *= std::sqrt(14.0);
5028
5022
5029
// Table(s) of coefficients.
5023
// Table(s) of coefficients
5030
5024
static const double coefficients0[10] = \
5031
5025
{0.32998316, -0.25018512, -0.033333333, 0.33037234, 0.32324881, 0.20606818, -0.1069045, -0.03011693, 0.0077761579, 0.013468701};
5032
5026
5033
5027
static const double coefficients1[10] = \
5034
5028
{-0.14142136, -0.038490018, -0.13333333, -0.069552071, -0.12121831, -0.089425816, 0.0, -0.06023386, -0.077761579, -0.053874802};
5035
5029
5036
// Compute value(s).
5030
// Compute value(s)
5037
5031
for (unsigned int r = 0; r < 10; r++)
5038
5032
{
5039
5033
values[0] += coefficients0[r]*basisvalues[r];
5040
5034
values[1] += coefficients1[r]*basisvalues[r];
5041
5035
}// end loop over 'r'
5042
5036
5043
// Using contravariant Piola transform to map values back to the physical element.
5037
// Using contravariant Piola transform to map values back to the physical element
5044
5038
const double tmp_ref0 = values[0];
5045
5039
const double tmp_ref1 = values[1];
5046
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5047
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5040
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5041
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5048
5042
break;
5049
5043
}
5050
5044
case 4:
5051
5045
{
5052
5046
5053
// Array of basisvalues.
5047
// Array of basisvalues
5054
5048
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5055
5049
5056
// Declare helper variables.
5050
// Declare helper variables
5057
5051
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5058
5052
double tmp1 = (1.0 - Y)/2.0;
5059
5053
double tmp2 = tmp1*tmp1;
5060
5054
5061
// Compute basisvalues.
5055
// Compute basisvalues
5062
5056
basisvalues[0] = 1.0;
5063
5057
basisvalues[1] = tmp0;
5064
5058
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5080
5074
basisvalues[7] *= std::sqrt(10.0);
5081
5075
basisvalues[6] *= std::sqrt(14.0);
5082
5076
5083
// Table(s) of coefficients.
5077
// Table(s) of coefficients
5084
5078
static const double coefficients0[10] = \
5085
5079
{-0.37712362, 0.17320508, -0.1, -0.10432811, -0.56568542, -0.60654032, 0.0, 0.12046772, 0.0, -0.053874802};
5086
5080
5087
5081
static const double coefficients1[10] = \
5088
5082
{0.18856181, 0.076980036, 0.33333333, 0.0, 0.24243661, 0.34992711, 0.0, 0.0, 0.15552316, 0.16162441};
5089
5083
5090
// Compute value(s).
5084
// Compute value(s)
5091
5085
for (unsigned int r = 0; r < 10; r++)
5092
5086
{
5093
5087
values[0] += coefficients0[r]*basisvalues[r];
5094
5088
values[1] += coefficients1[r]*basisvalues[r];
5095
5089
}// end loop over 'r'
5096
5090
5097
// Using contravariant Piola transform to map values back to the physical element.
5091
// Using contravariant Piola transform to map values back to the physical element
5098
5092
const double tmp_ref0 = values[0];
5099
5093
const double tmp_ref1 = values[1];
5100
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5101
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5094
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5095
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5102
5096
break;
5103
5097
}
5104
5098
case 5:
5105
5099
{
5106
5100
5107
// Array of basisvalues.
5101
// Array of basisvalues
5108
5102
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5109
5103
5110
// Declare helper variables.
5104
// Declare helper variables
5111
5105
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5112
5106
double tmp1 = (1.0 - Y)/2.0;
5113
5107
double tmp2 = tmp1*tmp1;
5114
5108
5115
// Compute basisvalues.
5109
// Compute basisvalues
5116
5110
basisvalues[0] = 1.0;
5117
5111
basisvalues[1] = tmp0;
5118
5112
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5134
5128
basisvalues[7] *= std::sqrt(10.0);
5135
5129
basisvalues[6] *= std::sqrt(14.0);
5136
5130
5137
// Table(s) of coefficients.
5131
// Table(s) of coefficients
5138
5132
static const double coefficients0[10] = \
5139
5133
{0.32998316, -0.096225045, 0.23333333, 0.0, 0.067343503, 0.50156219, 0.0, 0.0, -0.077761579, 0.080812204};
5140
5134
5141
5135
static const double coefficients1[10] = \
5142
5136
{-0.18856181, 0.0, -0.33333333, 0.0, 0.0, -0.34992711, 0.0, 0.0, 0.0, -0.16162441};
5143
5137
5144
// Compute value(s).
5138
// Compute value(s)
5145
5139
for (unsigned int r = 0; r < 10; r++)
5146
5140
{
5147
5141
values[0] += coefficients0[r]*basisvalues[r];
5148
5142
values[1] += coefficients1[r]*basisvalues[r];
5149
5143
}// end loop over 'r'
5150
5144
5151
// Using contravariant Piola transform to map values back to the physical element.
5145
// Using contravariant Piola transform to map values back to the physical element
5152
5146
const double tmp_ref0 = values[0];
5153
5147
const double tmp_ref1 = values[1];
5154
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5155
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5148
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5149
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5156
5150
break;
5157
5151
}
5158
5152
case 6:
5159
5153
{
5160
5154
5161
// Array of basisvalues.
5155
// Array of basisvalues
5162
5156
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5163
5157
5164
// Declare helper variables.
5158
// Declare helper variables
5165
5159
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5166
5160
double tmp1 = (1.0 - Y)/2.0;
5167
5161
double tmp2 = tmp1*tmp1;
5168
5162
5169
// Compute basisvalues.
5163
// Compute basisvalues
5170
5164
basisvalues[0] = 1.0;
5171
5165
basisvalues[1] = tmp0;
5172
5166
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5188
5182
basisvalues[7] *= std::sqrt(10.0);
5189
5183
basisvalues[6] *= std::sqrt(14.0);
5190
5184
5191
// Table(s) of coefficients.
5185
// Table(s) of coefficients
5192
5186
static const double coefficients0[10] = \
5193
5187
{0.14142136, 0.13471506, -0.033333333, 0.15649216, 0.053874802, 0.011664237, 0.1069045, 0.03011693, -0.0077761579, -0.013468701};
5194
5188
5195
5189
static const double coefficients1[10] = \
5196
5190
{-0.32998316, 0.15396007, 0.2, -0.41731242, -0.25590531, -0.12830661, 0.0, 0.06023386, 0.077761579, 0.053874802};
5197
5191
5198
// Compute value(s).
5192
// Compute value(s)
5199
5193
for (unsigned int r = 0; r < 10; r++)
5200
5194
{
5201
5195
values[0] += coefficients0[r]*basisvalues[r];
5202
5196
values[1] += coefficients1[r]*basisvalues[r];
5203
5197
}// end loop over 'r'
5204
5198
5205
// Using contravariant Piola transform to map values back to the physical element.
5199
// Using contravariant Piola transform to map values back to the physical element
5206
5200
const double tmp_ref0 = values[0];
5207
5201
const double tmp_ref1 = values[1];
5208
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5209
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5202
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5203
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5210
5204
break;
5211
5205
}
5212
5206
case 7:
5213
5207
{
5214
5208
5215
// Array of basisvalues.
5209
// Array of basisvalues
5216
5210
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5217
5211
5218
// Declare helper variables.
5212
// Declare helper variables
5219
5213
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5220
5214
double tmp1 = (1.0 - Y)/2.0;
5221
5215
double tmp2 = tmp1*tmp1;
5222
5216
5223
// Compute basisvalues.
5217
// Compute basisvalues
5224
5218
basisvalues[0] = 1.0;
5225
5219
basisvalues[1] = tmp0;
5226
5220
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5242
5236
basisvalues[7] *= std::sqrt(10.0);
5243
5237
basisvalues[6] *= std::sqrt(14.0);
5244
5238
5245
// Table(s) of coefficients.
5239
// Table(s) of coefficients
5246
5240
static const double coefficients0[10] = \
5247
5241
{-0.18856181, -0.32716515, 0.1, -0.41731242, 0.080812204, 0.023328474, -0.21380899, 0.06023386, 0.015552316, -0.026937401};
5248
5242
5249
5243
static const double coefficients1[10] = \
5250
5244
{0.37712362, 0.0, -0.2, 0.83462485, 0.0, -0.046656947, 0.0, -0.12046772, 0.0, 0.053874802};
5251
5245
5252
// Compute value(s).
5246
// Compute value(s)
5253
5247
for (unsigned int r = 0; r < 10; r++)
5254
5248
{
5255
5249
values[0] += coefficients0[r]*basisvalues[r];
5256
5250
values[1] += coefficients1[r]*basisvalues[r];
5257
5251
}// end loop over 'r'
5258
5252
5259
// Using contravariant Piola transform to map values back to the physical element.
5253
// Using contravariant Piola transform to map values back to the physical element
5260
5254
const double tmp_ref0 = values[0];
5261
5255
const double tmp_ref1 = values[1];
5262
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5263
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5256
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5257
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5264
5258
break;
5265
5259
}
5266
5260
case 8:
5267
5261
{
5268
5262
5269
// Array of basisvalues.
5263
// Array of basisvalues
5270
5264
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5271
5265
5272
// Declare helper variables.
5266
// Declare helper variables
5273
5267
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5274
5268
double tmp1 = (1.0 - Y)/2.0;
5275
5269
double tmp2 = tmp1*tmp1;
5276
5270
5277
// Compute basisvalues.
5271
// Compute basisvalues
5278
5272
basisvalues[0] = 1.0;
5279
5273
basisvalues[1] = tmp0;
5280
5274
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5296
5290
basisvalues[7] *= std::sqrt(10.0);
5297
5291
basisvalues[6] *= std::sqrt(14.0);
5298
5292
5299
// Table(s) of coefficients.
5293
// Table(s) of coefficients
5300
5294
static const double coefficients0[10] = \
5301
5295
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
5302
5296
5303
5297
static const double coefficients1[10] = \
5304
5298
{-0.32998316, -0.15396007, 0.2, -0.41731242, 0.25590531, -0.12830661, 0.0, 0.06023386, -0.077761579, 0.053874802};
5305
5299
5306
// Compute value(s).
5300
// Compute value(s)
5307
5301
for (unsigned int r = 0; r < 10; r++)
5308
5302
{
5309
5303
values[0] += coefficients0[r]*basisvalues[r];
5310
5304
values[1] += coefficients1[r]*basisvalues[r];
5311
5305
}// end loop over 'r'
5312
5306
5313
// Using contravariant Piola transform to map values back to the physical element.
5307
// Using contravariant Piola transform to map values back to the physical element
5314
5308
const double tmp_ref0 = values[0];
5315
5309
const double tmp_ref1 = values[1];
5316
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5317
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5310
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5311
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5318
5312
break;
5319
5313
}
5320
5314
case 9:
5321
5315
{
5322
5316
5323
// Array of basisvalues.
5317
// Array of basisvalues
5324
5318
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5325
5319
5326
// Declare helper variables.
5320
// Declare helper variables
5327
5321
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5328
5322
double tmp1 = (1.0 - Y)/2.0;
5329
5323
double tmp2 = tmp1*tmp1;
5330
5324
5331
// Compute basisvalues.
5325
// Compute basisvalues
5332
5326
basisvalues[0] = 1.0;
5333
5327
basisvalues[1] = tmp0;
5334
5328
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5350
5344
basisvalues[7] *= std::sqrt(10.0);
5351
5345
basisvalues[6] *= std::sqrt(14.0);
5352
5346
5353
// Table(s) of coefficients.
5347
// Table(s) of coefficients
5354
5348
static const double coefficients0[10] = \
5355
5349
{0.32998316, -0.69282032, -0.53333333, -0.39992441, -0.026937401, 0.20606818, 0.32071349, -0.03011693, -0.023328474, 0.013468701};
5356
5350
5357
5351
static const double coefficients1[10] = \
5358
5352
{0.23570226, 0.038490018, 0.066666667, 0.20865621, 0.12121831, -0.081649658, 0.0, 0.18070158, 0.077761579, 0.0};
5359
5353
5360
// Compute value(s).
5354
// Compute value(s)
5361
5355
for (unsigned int r = 0; r < 10; r++)
5362
5356
{
5363
5357
values[0] += coefficients0[r]*basisvalues[r];
5364
5358
values[1] += coefficients1[r]*basisvalues[r];
5365
5359
}// end loop over 'r'
5366
5360
5367
// Using contravariant Piola transform to map values back to the physical element.
5361
// Using contravariant Piola transform to map values back to the physical element
5368
5362
const double tmp_ref0 = values[0];
5369
5363
const double tmp_ref1 = values[1];
5370
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5371
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5364
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5365
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5372
5366
break;
5373
5367
}
5374
5368
case 10:
5375
5369
{
5376
5370
5377
// Array of basisvalues.
5371
// Array of basisvalues
5378
5372
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5379
5373
5380
// Declare helper variables.
5374
// Declare helper variables
5381
5375
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5382
5376
double tmp1 = (1.0 - Y)/2.0;
5383
5377
double tmp2 = tmp1*tmp1;
5384
5378
5385
// Compute basisvalues.
5379
// Compute basisvalues
5386
5380
basisvalues[0] = 1.0;
5387
5381
basisvalues[1] = tmp0;
5388
5382
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5404
5398
basisvalues[7] *= std::sqrt(10.0);
5405
5399
basisvalues[6] *= std::sqrt(14.0);
5406
5400
5407
// Table(s) of coefficients.
5401
// Table(s) of coefficients
5408
5402
static const double coefficients0[10] = \
5409
5403
{0.56568542, 0.65433031, -0.46666667, -0.19126819, -0.094280904, 0.12441853, -0.32071349, 0.15058465, -0.054433105, 0.013468701};
5410
5404
5411
5405
static const double coefficients1[10] = \
5412
5406
{-0.23570226, 0.038490018, -0.066666667, -0.20865621, 0.12121831, 0.081649658, 0.0, -0.18070158, 0.077761579, 0.0};
5413
5407
5414
// Compute value(s).
5408
// Compute value(s)
5415
5409
for (unsigned int r = 0; r < 10; r++)
5416
5410
{
5417
5411
values[0] += coefficients0[r]*basisvalues[r];
5418
5412
values[1] += coefficients1[r]*basisvalues[r];
5419
5413
}// end loop over 'r'
5420
5414
5421
// Using contravariant Piola transform to map values back to the physical element.
5415
// Using contravariant Piola transform to map values back to the physical element
5422
5416
const double tmp_ref0 = values[0];
5423
5417
const double tmp_ref1 = values[1];
5424
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5425
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5418
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5419
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5426
5420
break;
5427
5421
}
5428
5422
case 11:
5429
5423
{
5430
5424
5431
// Array of basisvalues.
5425
// Array of basisvalues
5432
5426
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5433
5427
5434
// Declare helper variables.
5428
// Declare helper variables
5435
5429
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5436
5430
double tmp1 = (1.0 - Y)/2.0;
5437
5431
double tmp2 = tmp1*tmp1;
5438
5432
5439
// Compute basisvalues.
5433
// Compute basisvalues
5440
5434
basisvalues[0] = 1.0;
5441
5435
basisvalues[1] = tmp0;
5442
5436
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5458
5452
basisvalues[7] *= std::sqrt(10.0);
5459
5453
basisvalues[6] *= std::sqrt(14.0);
5460
5454
5461
// Table(s) of coefficients.
5455
// Table(s) of coefficients
5462
5456
static const double coefficients0[10] = \
5463
5457
{0.094280904, 0.076980036, 0.93333333, 0.20865621, 0.24243661, -0.443241, 0.0, -0.24093544, 0.15552316, -0.053874802};
5464
5458
5465
5459
static const double coefficients1[10] = \
5466
5460
{0.0, -0.15396007, 0.0, 0.0, -0.48487322, 0.0, 0.0, 0.0, -0.31104632, 0.0};
5467
5461
5468
// Compute value(s).
5462
// Compute value(s)
5469
5463
for (unsigned int r = 0; r < 10; r++)
5470
5464
{
5471
5465
values[0] += coefficients0[r]*basisvalues[r];
5472
5466
values[1] += coefficients1[r]*basisvalues[r];
5473
5467
}// end loop over 'r'
5474
5468
5475
// Using contravariant Piola transform to map values back to the physical element.
5469
// Using contravariant Piola transform to map values back to the physical element
5476
5470
const double tmp_ref0 = values[0];
5477
5471
const double tmp_ref1 = values[1];
5478
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5479
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5472
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5473
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5480
5474
break;
5481
5475
}
5482
5476
case 12:
5483
5477
{
5484
5478
5485
// Array of basisvalues.
5479
// Array of basisvalues
5486
5480
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5487
5481
5488
// Declare helper variables.
5482
// Declare helper variables
5489
5483
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5490
5484
double tmp1 = (1.0 - Y)/2.0;
5491
5485
double tmp2 = tmp1*tmp1;
5492
5486
5493
// Compute basisvalues.
5487
// Compute basisvalues
5494
5488
basisvalues[0] = 1.0;
5495
5489
basisvalues[1] = tmp0;
5496
5490
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5512
5506
basisvalues[7] *= std::sqrt(10.0);
5513
5507
basisvalues[6] *= std::sqrt(14.0);
5514
5508
5515
// Table(s) of coefficients.
5509
// Table(s) of coefficients
5516
5510
static const double coefficients0[10] = \
5517
5511
{0.23570226, 0.076980036, 0.0, 0.052164053, 0.24243661, 0.058321184, 0.1069045, 0.15058465, -0.0077761579, -0.067343503};
5518
5512
5519
5513
static const double coefficients1[10] = \
5520
5514
{0.32998316, -0.80829038, -0.33333333, 0.069552071, -0.39059232, -0.21384434, 0.0, 0.06023386, 0.23328474, 0.21549921};
5521
5515
5522
// Compute value(s).
5516
// Compute value(s)
5523
5517
for (unsigned int r = 0; r < 10; r++)
5524
5518
{
5525
5519
values[0] += coefficients0[r]*basisvalues[r];
5526
5520
values[1] += coefficients1[r]*basisvalues[r];
5527
5521
}// end loop over 'r'
5528
5522
5529
// Using contravariant Piola transform to map values back to the physical element.
5523
// Using contravariant Piola transform to map values back to the physical element
5530
5524
const double tmp_ref0 = values[0];
5531
5525
const double tmp_ref1 = values[1];
5532
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5533
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5526
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5527
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5534
5528
break;
5535
5529
}
5536
5530
case 13:
5537
5531
{
5538
5532
5539
// Array of basisvalues.
5533
// Array of basisvalues
5540
5534
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5541
5535
5542
// Declare helper variables.
5536
// Declare helper variables
5543
5537
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5544
5538
double tmp1 = (1.0 - Y)/2.0;
5545
5539
double tmp2 = tmp1*tmp1;
5546
5540
5547
// Compute basisvalues.
5541
// Compute basisvalues
5548
5542
basisvalues[0] = 1.0;
5549
5543
basisvalues[1] = tmp0;
5550
5544
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5566
5560
basisvalues[7] *= std::sqrt(10.0);
5567
5561
basisvalues[6] *= std::sqrt(14.0);
5568
5562
5569
// Table(s) of coefficients.
5563
// Table(s) of coefficients
5570
5564
static const double coefficients0[10] = \
5571
5565
{0.0, -0.076980036, -0.13333333, -0.31298432, -0.24243661, 0.27994168, -0.21380899, -0.06023386, 0.17107547, -0.13468701};
5572
5566
5573
5567
static const double coefficients1[10] = \
5574
5568
{0.094280904, 0.84678039, -0.4, -0.13910414, 0.51181062, -0.13219468, 0.0, -0.12046772, -0.15552316, 0.21549921};
5575
5569
5576
// Compute value(s).
5570
// Compute value(s)
5577
5571
for (unsigned int r = 0; r < 10; r++)
5578
5572
{
5579
5573
values[0] += coefficients0[r]*basisvalues[r];
5580
5574
values[1] += coefficients1[r]*basisvalues[r];
5581
5575
}// end loop over 'r'
5582
5576
5583
// Using contravariant Piola transform to map values back to the physical element.
5577
// Using contravariant Piola transform to map values back to the physical element
5584
5578
const double tmp_ref0 = values[0];
5585
5579
const double tmp_ref1 = values[1];
5586
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5587
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5580
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5581
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5588
5582
break;
5589
5583
}
5590
5584
case 14:
5591
5585
{
5592
5586
5593
// Array of basisvalues.
5587
// Array of basisvalues
5594
5588
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5595
5589
5596
// Declare helper variables.
5590
// Declare helper variables
5597
5591
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5598
5592
double tmp1 = (1.0 - Y)/2.0;
5599
5593
double tmp2 = tmp1*tmp1;
5600
5594
5601
// Compute basisvalues.
5595
// Compute basisvalues
5602
5596
basisvalues[0] = 1.0;
5603
5597
basisvalues[1] = tmp0;
5604
5598
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5620
5614
basisvalues[7] *= std::sqrt(10.0);
5621
5615
basisvalues[6] *= std::sqrt(14.0);
5622
5616
5623
// Table(s) of coefficients.
5617
// Table(s) of coefficients
5624
5618
static const double coefficients0[10] = \
5625
5619
{-0.23570226, -0.038490018, 0.066666667, 0.10432811, -0.12121831, -0.19829203, 0.0, -0.12046772, -0.077761579, 0.13468701};
5626
5620
5627
5621
static const double coefficients1[10] = \
5628
5622
{0.56568542, -0.076980036, 0.8, 0.0, -0.24243661, -0.046656947, 0.0, 0.0, -0.15552316, -0.32324881};
5629
5623
5630
// Compute value(s).
5624
// Compute value(s)
5631
5625
for (unsigned int r = 0; r < 10; r++)
5632
5626
{
5633
5627
values[0] += coefficients0[r]*basisvalues[r];
5634
5628
values[1] += coefficients1[r]*basisvalues[r];
5635
5629
}// end loop over 'r'
5636
5630
5637
// Using contravariant Piola transform to map values back to the physical element.
5631
// Using contravariant Piola transform to map values back to the physical element
5638
5632
const double tmp_ref0 = values[0];
5639
5633
const double tmp_ref1 = values[1];
5640
values[0] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5641
values[1] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5634
values[0] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5635
values[1] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5642
5636
break;
5643
5637
}
5644
5638
}
5645
5639
5646
5640
}
5647
5641
5648
/// Evaluate all basis functions at given point in cell
5642
/// Evaluate all basis functions at given point x in cell
5649
5643
virtual void evaluate_basis_all(double* values,
5650
const double* coordinates,
5651
const ufc::cell& c) const
5644
const double* x,
5645
const double* vertex_coordinates,
5646
int cell_orientation) const
5652
5647
{
5653
5648
// Helper variable to hold values of a single dof.
5654
5649
double dof_values[2] = {0.0, 0.0};
5655
5650
5656
// Loop dofs and call evaluate_basis.
5651
// Loop dofs and call evaluate_basis
5657
5652
for (unsigned int r = 0; r < 15; r++)
5658
5653
{
5659
evaluate_basis(r, dof_values, coordinates, c);
5654
evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
5660
5655
for (unsigned int s = 0; s < 2; s++)
5661
5656
{
5662
5657
values[r*2 + s] = dof_values[s];
5664
5659
}// end loop over 'r'
5665
5660
}
5666
5661
5667
/// Evaluate order n derivatives of basis function i at given point in cell
5668
virtual void evaluate_basis_derivatives(unsigned int i,
5669
unsigned int n,
5662
/// Evaluate order n derivatives of basis function i at given point x in cell
5663
virtual void evaluate_basis_derivatives(std::size_t i,
5664
std::size_t n,
5670
5665
double* values,
5671
const double* coordinates,
5672
const ufc::cell& c) const
5666
const double* x,
5667
const double* vertex_coordinates,
5668
int cell_orientation) const
5673
5669
{
5674
// Extract vertex coordinates
5675
const double * const * x = c.coordinates;
5676
5677
// Compute Jacobian of affine map from reference cell
5678
const double J_00 = x[1][0] - x[0][0];
5679
const double J_01 = x[2][0] - x[0][0];
5680
const double J_10 = x[1][1] - x[0][1];
5681
const double J_11 = x[2][1] - x[0][1];
5682
5683
// Compute determinant of Jacobian
5684
double detJ = J_00*J_11 - J_01*J_10;
5685
5686
// Compute inverse of Jacobian
5687
const double K_00 = J_11 / detJ;
5688
const double K_01 = -J_01 / detJ;
5689
const double K_10 = -J_10 / detJ;
5690
const double K_11 = J_00 / detJ;
5670
// Compute Jacobian
5671
double J[4];
5672
compute_jacobian_triangle_2d(J, vertex_coordinates);
5673
5674
// Compute Jacobian inverse and determinant
5675
double K[4];
5676
double detJ;
5677
compute_jacobian_inverse_triangle_2d(K, detJ, J);
5678
5679
5691
5680
5692
5681
// Compute constants
5693
const double C0 = x[1][0] + x[2][0];
5694
const double C1 = x[1][1] + x[2][1];
5682
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
5683
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
5695
5684
5696
5685
// Get coordinates and map to the reference (FIAT) element
5697
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
5698
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
5686
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
5687
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
5699
5688
5700
5689
// Compute number of derivatives.
5701
5690
unsigned int num_derivatives = 1;
5732
5721
}
5733
5722
5734
5723
// Compute inverse of Jacobian
5735
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
5724
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
5736
5725
5737
5726
// Declare transformation matrix
5738
5727
// Declare pointer to two dimensional array and initialise
5766
5755
case 0:
5767
5756
{
5768
5757
5769
// Array of basisvalues.
5758
// Array of basisvalues
5770
5759
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5771
5760
5772
// Declare helper variables.
5761
// Declare helper variables
5773
5762
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5774
5763
double tmp1 = (1.0 - Y)/2.0;
5775
5764
double tmp2 = tmp1*tmp1;
5776
5765
5777
// Compute basisvalues.
5766
// Compute basisvalues
5778
5767
basisvalues[0] = 1.0;
5779
5768
basisvalues[1] = tmp0;
5780
5769
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5796
5785
basisvalues[7] *= std::sqrt(10.0);
5797
5786
basisvalues[6] *= std::sqrt(14.0);
5798
5787
5799
// Table(s) of coefficients.
5788
// Table(s) of coefficients
5800
5789
static const double coefficients0[10] = \
5801
5790
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
5802
5791
5836
5825
derivatives[r] = 0.0;
5837
5826
}// end loop over 'r'
5838
5827
5828
// Declare pointer to array of reference derivatives on physical element.
5829
double *derivatives_p = new double[2*num_derivatives];
5830
for (unsigned int r = 0; r < 2*num_derivatives; r++)
5831
{
5832
derivatives_p[r] = 0.0;
5833
}// end loop over 'r'
5834
5839
5835
// Declare derivative matrix (of polynomial basis).
5840
5836
double dmats[10][10] = \
5841
5837
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
5934
5930
// Using contravariant Piola transform to map values back to the physical element.
5935
5931
const double tmp_ref0 = derivatives[r];
5936
5932
const double tmp_ref1 = derivatives[num_derivatives + r];
5937
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
5938
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
5933
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
5934
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
5939
5935
}// end loop over 'r'
5940
5936
5941
5937
// Transform derivatives back to physical element
5943
5939
{
5944
5940
for (unsigned int s = 0; s < num_derivatives; s++)
5945
5941
{
5946
values[r] += transform[r][s]*derivatives[s];
5947
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
5942
values[r] += transform[r][s]*derivatives_p[s];
5943
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
5948
5944
}// end loop over 's'
5949
5945
}// end loop over 'r'
5950
5946
5951
5947
// Delete pointer to array of derivatives on FIAT element
5952
5948
delete [] derivatives;
5953
5949
5950
// Delete pointer to array of reference derivatives on physical element.
5951
delete [] derivatives_p;
5952
5954
5953
// Delete pointer to array of combinations of derivatives and transform
5955
5954
for (unsigned int r = 0; r < num_derivatives; r++)
5956
5955
{
5967
5966
case 1:
5968
5967
{
5969
5968
5970
// Array of basisvalues.
5969
// Array of basisvalues
5971
5970
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5972
5971
5973
// Declare helper variables.
5972
// Declare helper variables
5974
5973
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5975
5974
double tmp1 = (1.0 - Y)/2.0;
5976
5975
double tmp2 = tmp1*tmp1;
5977
5976
5978
// Compute basisvalues.
5977
// Compute basisvalues
5979
5978
basisvalues[0] = 1.0;
5980
5979
basisvalues[1] = tmp0;
5981
5980
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
5997
5996
basisvalues[7] *= std::sqrt(10.0);
5998
5997
basisvalues[6] *= std::sqrt(14.0);
5999
5998
6000
// Table(s) of coefficients.
5999
// Table(s) of coefficients
6001
6000
static const double coefficients0[10] = \
6002
6001
{-0.18856181, -0.25018512, 0.23333333, -0.10432811, 0.32324881, -0.25661321, 0.0, 0.12046772, -0.15552316, 0.1077496};
6003
6002
6037
6036
derivatives[r] = 0.0;
6038
6037
}// end loop over 'r'
6039
6038
6039
// Declare pointer to array of reference derivatives on physical element.
6040
double *derivatives_p = new double[2*num_derivatives];
6041
for (unsigned int r = 0; r < 2*num_derivatives; r++)
6042
{
6043
derivatives_p[r] = 0.0;
6044
}// end loop over 'r'
6045
6040
6046
// Declare derivative matrix (of polynomial basis).
6041
6047
double dmats[10][10] = \
6042
6048
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
6135
6141
// Using contravariant Piola transform to map values back to the physical element.
6136
6142
const double tmp_ref0 = derivatives[r];
6137
6143
const double tmp_ref1 = derivatives[num_derivatives + r];
6138
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
6139
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
6144
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
6145
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
6140
6146
}// end loop over 'r'
6141
6147
6142
6148
// Transform derivatives back to physical element
6144
6150
{
6145
6151
for (unsigned int s = 0; s < num_derivatives; s++)
6146
6152
{
6147
values[r] += transform[r][s]*derivatives[s];
6148
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
6153
values[r] += transform[r][s]*derivatives_p[s];
6154
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
6149
6155
}// end loop over 's'
6150
6156
}// end loop over 'r'
6151
6157
6152
6158
// Delete pointer to array of derivatives on FIAT element
6153
6159
delete [] derivatives;
6154
6160
6161
// Delete pointer to array of reference derivatives on physical element.
6162
delete [] derivatives_p;
6163
6155
6164
// Delete pointer to array of combinations of derivatives and transform
6156
6165
for (unsigned int r = 0; r < num_derivatives; r++)
6157
6166
{
6168
6177
case 2:
6169
6178
{
6170
6179
6171
// Array of basisvalues.
6180
// Array of basisvalues
6172
6181
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6173
6182
6174
// Declare helper variables.
6183
// Declare helper variables
6175
6184
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
6176
6185
double tmp1 = (1.0 - Y)/2.0;
6177
6186
double tmp2 = tmp1*tmp1;
6178
6187
6179
// Compute basisvalues.
6188
// Compute basisvalues
6180
6189
basisvalues[0] = 1.0;
6181
6190
basisvalues[1] = tmp0;
6182
6191
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
6198
6207
basisvalues[7] *= std::sqrt(10.0);
6199
6208
basisvalues[6] *= std::sqrt(14.0);
6200
6209
6201
// Table(s) of coefficients.
6210
// Table(s) of coefficients
6202
6211
static const double coefficients0[10] = \
6203
6212
{0.14142136, 0.096225045, -0.1, 0.0, -0.067343503, 0.15163508, 0.0, 0.0, 0.077761579, -0.080812204};
6204
6213
6238
6247
derivatives[r] = 0.0;
6239
6248
}// end loop over 'r'
6240
6249
6250
// Declare pointer to array of reference derivatives on physical element.
6251
double *derivatives_p = new double[2*num_derivatives];
6252
for (unsigned int r = 0; r < 2*num_derivatives; r++)
6253
{
6254
derivatives_p[r] = 0.0;
6255
}// end loop over 'r'
6256
6241
6257
// Declare derivative matrix (of polynomial basis).
6242
6258
double dmats[10][10] = \
6243
6259
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
6336
6352
// Using contravariant Piola transform to map values back to the physical element.
6337
6353
const double tmp_ref0 = derivatives[r];
6338
6354
const double tmp_ref1 = derivatives[num_derivatives + r];
6339
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
6340
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
6355
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
6356
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
6341
6357
}// end loop over 'r'
6342
6358
6343
6359
// Transform derivatives back to physical element
6345
6361
{
6346
6362
for (unsigned int s = 0; s < num_derivatives; s++)
6347
6363
{
6348
values[r] += transform[r][s]*derivatives[s];
6349
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
6364
values[r] += transform[r][s]*derivatives_p[s];
6365
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
6350
6366
}// end loop over 's'
6351
6367
}// end loop over 'r'
6352
6368
6353
6369
// Delete pointer to array of derivatives on FIAT element
6354
6370
delete [] derivatives;
6355
6371
6372
// Delete pointer to array of reference derivatives on physical element.
6373
delete [] derivatives_p;
6374
6356
6375
// Delete pointer to array of combinations of derivatives and transform
6357
6376
for (unsigned int r = 0; r < num_derivatives; r++)
6358
6377
{
6369
6388
case 3:
6370
6389
{
6371
6390
6372
// Array of basisvalues.
6391
// Array of basisvalues
6373
6392
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6374
6393
6375
// Declare helper variables.
6394
// Declare helper variables
6376
6395
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
6377
6396
double tmp1 = (1.0 - Y)/2.0;
6378
6397
double tmp2 = tmp1*tmp1;
6379
6398
6380
// Compute basisvalues.
6399
// Compute basisvalues
6381
6400
basisvalues[0] = 1.0;
6382
6401
basisvalues[1] = tmp0;
6383
6402
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
6399
6418
basisvalues[7] *= std::sqrt(10.0);
6400
6419
basisvalues[6] *= std::sqrt(14.0);
6401
6420
6402
// Table(s) of coefficients.
6421
// Table(s) of coefficients
6403
6422
static const double coefficients0[10] = \
6404
6423
{0.32998316, -0.25018512, -0.033333333, 0.33037234, 0.32324881, 0.20606818, -0.1069045, -0.03011693, 0.0077761579, 0.013468701};
6405
6424
6439
6458
derivatives[r] = 0.0;
6440
6459
}// end loop over 'r'
6441
6460
6461
// Declare pointer to array of reference derivatives on physical element.
6462
double *derivatives_p = new double[2*num_derivatives];
6463
for (unsigned int r = 0; r < 2*num_derivatives; r++)
6464
{
6465
derivatives_p[r] = 0.0;
6466
}// end loop over 'r'
6467
6442
6468
// Declare derivative matrix (of polynomial basis).
6443
6469
double dmats[10][10] = \
6444
6470
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
6537
6563
// Using contravariant Piola transform to map values back to the physical element.
6538
6564
const double tmp_ref0 = derivatives[r];
6539
6565
const double tmp_ref1 = derivatives[num_derivatives + r];
6540
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
6541
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
6566
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
6567
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
6542
6568
}// end loop over 'r'
6543
6569
6544
6570
// Transform derivatives back to physical element
6546
6572
{
6547
6573
for (unsigned int s = 0; s < num_derivatives; s++)
6548
6574
{
6549
values[r] += transform[r][s]*derivatives[s];
6550
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
6575
values[r] += transform[r][s]*derivatives_p[s];
6576
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
6551
6577
}// end loop over 's'
6552
6578
}// end loop over 'r'
6553
6579
6554
6580
// Delete pointer to array of derivatives on FIAT element
6555
6581
delete [] derivatives;
6556
6582
6583
// Delete pointer to array of reference derivatives on physical element.
6584
delete [] derivatives_p;
6585
6557
6586
// Delete pointer to array of combinations of derivatives and transform
6558
6587
for (unsigned int r = 0; r < num_derivatives; r++)
6559
6588
{
6570
6599
case 4:
6571
6600
{
6572
6601
6573
// Array of basisvalues.
6602
// Array of basisvalues
6574
6603
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6575
6604
6576
// Declare helper variables.
6605
// Declare helper variables
6577
6606
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
6578
6607
double tmp1 = (1.0 - Y)/2.0;
6579
6608
double tmp2 = tmp1*tmp1;
6580
6609
6581
// Compute basisvalues.
6610
// Compute basisvalues
6582
6611
basisvalues[0] = 1.0;
6583
6612
basisvalues[1] = tmp0;
6584
6613
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
6600
6629
basisvalues[7] *= std::sqrt(10.0);
6601
6630
basisvalues[6] *= std::sqrt(14.0);
6602
6631
6603
// Table(s) of coefficients.
6632
// Table(s) of coefficients
6604
6633
static const double coefficients0[10] = \
6605
6634
{-0.37712362, 0.17320508, -0.1, -0.10432811, -0.56568542, -0.60654032, 0.0, 0.12046772, 0.0, -0.053874802};
6606
6635
6640
6669
derivatives[r] = 0.0;
6641
6670
}// end loop over 'r'
6642
6671
6672
// Declare pointer to array of reference derivatives on physical element.
6673
double *derivatives_p = new double[2*num_derivatives];
6674
for (unsigned int r = 0; r < 2*num_derivatives; r++)
6675
{
6676
derivatives_p[r] = 0.0;
6677
}// end loop over 'r'
6678
6643
6679
// Declare derivative matrix (of polynomial basis).
6644
6680
double dmats[10][10] = \
6645
6681
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
6738
6774
// Using contravariant Piola transform to map values back to the physical element.
6739
6775
const double tmp_ref0 = derivatives[r];
6740
6776
const double tmp_ref1 = derivatives[num_derivatives + r];
6741
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
6742
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
6777
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
6778
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
6743
6779
}// end loop over 'r'
6744
6780
6745
6781
// Transform derivatives back to physical element
6747
6783
{
6748
6784
for (unsigned int s = 0; s < num_derivatives; s++)
6749
6785
{
6750
values[r] += transform[r][s]*derivatives[s];
6751
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
6786
values[r] += transform[r][s]*derivatives_p[s];
6787
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
6752
6788
}// end loop over 's'
6753
6789
}// end loop over 'r'
6754
6790
6755
6791
// Delete pointer to array of derivatives on FIAT element
6756
6792
delete [] derivatives;
6757
6793
6794
// Delete pointer to array of reference derivatives on physical element.
6795
delete [] derivatives_p;
6796
6758
6797
// Delete pointer to array of combinations of derivatives and transform
6759
6798
for (unsigned int r = 0; r < num_derivatives; r++)
6760
6799
{
6771
6810
case 5:
6772
6811
{
6773
6812
6774
// Array of basisvalues.
6813
// Array of basisvalues
6775
6814
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6776
6815
6777
// Declare helper variables.
6816
// Declare helper variables
6778
6817
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
6779
6818
double tmp1 = (1.0 - Y)/2.0;
6780
6819
double tmp2 = tmp1*tmp1;
6781
6820
6782
// Compute basisvalues.
6821
// Compute basisvalues
6783
6822
basisvalues[0] = 1.0;
6784
6823
basisvalues[1] = tmp0;
6785
6824
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
6801
6840
basisvalues[7] *= std::sqrt(10.0);
6802
6841
basisvalues[6] *= std::sqrt(14.0);
6803
6842
6804
// Table(s) of coefficients.
6843
// Table(s) of coefficients
6805
6844
static const double coefficients0[10] = \
6806
6845
{0.32998316, -0.096225045, 0.23333333, 0.0, 0.067343503, 0.50156219, 0.0, 0.0, -0.077761579, 0.080812204};
6807
6846
6841
6880
derivatives[r] = 0.0;
6842
6881
}// end loop over 'r'
6843
6882
6883
// Declare pointer to array of reference derivatives on physical element.
6884
double *derivatives_p = new double[2*num_derivatives];
6885
for (unsigned int r = 0; r < 2*num_derivatives; r++)
6886
{
6887
derivatives_p[r] = 0.0;
6888
}// end loop over 'r'
6889
6844
6890
// Declare derivative matrix (of polynomial basis).
6845
6891
double dmats[10][10] = \
6846
6892
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
6939
6985
// Using contravariant Piola transform to map values back to the physical element.
6940
6986
const double tmp_ref0 = derivatives[r];
6941
6987
const double tmp_ref1 = derivatives[num_derivatives + r];
6942
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
6943
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
6988
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
6989
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
6944
6990
}// end loop over 'r'
6945
6991
6946
6992
// Transform derivatives back to physical element
6948
6994
{
6949
6995
for (unsigned int s = 0; s < num_derivatives; s++)
6950
6996
{
6951
values[r] += transform[r][s]*derivatives[s];
6952
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
6997
values[r] += transform[r][s]*derivatives_p[s];
6998
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
6953
6999
}// end loop over 's'
6954
7000
}// end loop over 'r'
6955
7001
6956
7002
// Delete pointer to array of derivatives on FIAT element
6957
7003
delete [] derivatives;
6958
7004
7005
// Delete pointer to array of reference derivatives on physical element.
7006
delete [] derivatives_p;
7007
6959
7008
// Delete pointer to array of combinations of derivatives and transform
6960
7009
for (unsigned int r = 0; r < num_derivatives; r++)
6961
7010
{
6972
7021
case 6:
6973
7022
{
6974
7023
6975
// Array of basisvalues.
7024
// Array of basisvalues
6976
7025
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6977
7026
6978
// Declare helper variables.
7027
// Declare helper variables
6979
7028
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
6980
7029
double tmp1 = (1.0 - Y)/2.0;
6981
7030
double tmp2 = tmp1*tmp1;
6982
7031
6983
// Compute basisvalues.
7032
// Compute basisvalues
6984
7033
basisvalues[0] = 1.0;
6985
7034
basisvalues[1] = tmp0;
6986
7035
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
7002
7051
basisvalues[7] *= std::sqrt(10.0);
7003
7052
basisvalues[6] *= std::sqrt(14.0);
7004
7053
7005
// Table(s) of coefficients.
7054
// Table(s) of coefficients
7006
7055
static const double coefficients0[10] = \
7007
7056
{0.14142136, 0.13471506, -0.033333333, 0.15649216, 0.053874802, 0.011664237, 0.1069045, 0.03011693, -0.0077761579, -0.013468701};
7008
7057
7042
7091
derivatives[r] = 0.0;
7043
7092
}// end loop over 'r'
7044
7093
7094
// Declare pointer to array of reference derivatives on physical element.
7095
double *derivatives_p = new double[2*num_derivatives];
7096
for (unsigned int r = 0; r < 2*num_derivatives; r++)
7097
{
7098
derivatives_p[r] = 0.0;
7099
}// end loop over 'r'
7100
7045
7101
// Declare derivative matrix (of polynomial basis).
7046
7102
double dmats[10][10] = \
7047
7103
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
7140
7196
// Using contravariant Piola transform to map values back to the physical element.
7141
7197
const double tmp_ref0 = derivatives[r];
7142
7198
const double tmp_ref1 = derivatives[num_derivatives + r];
7143
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
7144
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
7199
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
7200
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
7145
7201
}// end loop over 'r'
7146
7202
7147
7203
// Transform derivatives back to physical element
7149
7205
{
7150
7206
for (unsigned int s = 0; s < num_derivatives; s++)
7151
7207
{
7152
values[r] += transform[r][s]*derivatives[s];
7153
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
7208
values[r] += transform[r][s]*derivatives_p[s];
7209
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
7154
7210
}// end loop over 's'
7155
7211
}// end loop over 'r'
7156
7212
7157
7213
// Delete pointer to array of derivatives on FIAT element
7158
7214
delete [] derivatives;
7159
7215
7216
// Delete pointer to array of reference derivatives on physical element.
7217
delete [] derivatives_p;
7218
7160
7219
// Delete pointer to array of combinations of derivatives and transform
7161
7220
for (unsigned int r = 0; r < num_derivatives; r++)
7162
7221
{
7173
7232
case 7:
7174
7233
{
7175
7234
7176
// Array of basisvalues.
7235
// Array of basisvalues
7177
7236
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7178
7237
7179
// Declare helper variables.
7238
// Declare helper variables
7180
7239
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
7181
7240
double tmp1 = (1.0 - Y)/2.0;
7182
7241
double tmp2 = tmp1*tmp1;
7183
7242
7184
// Compute basisvalues.
7243
// Compute basisvalues
7185
7244
basisvalues[0] = 1.0;
7186
7245
basisvalues[1] = tmp0;
7187
7246
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
7203
7262
basisvalues[7] *= std::sqrt(10.0);
7204
7263
basisvalues[6] *= std::sqrt(14.0);
7205
7264
7206
// Table(s) of coefficients.
7265
// Table(s) of coefficients
7207
7266
static const double coefficients0[10] = \
7208
7267
{-0.18856181, -0.32716515, 0.1, -0.41731242, 0.080812204, 0.023328474, -0.21380899, 0.06023386, 0.015552316, -0.026937401};
7209
7268
7243
7302
derivatives[r] = 0.0;
7244
7303
}// end loop over 'r'
7245
7304
7305
// Declare pointer to array of reference derivatives on physical element.
7306
double *derivatives_p = new double[2*num_derivatives];
7307
for (unsigned int r = 0; r < 2*num_derivatives; r++)
7308
{
7309
derivatives_p[r] = 0.0;
7310
}// end loop over 'r'
7311
7246
7312
// Declare derivative matrix (of polynomial basis).
7247
7313
double dmats[10][10] = \
7248
7314
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
7341
7407
// Using contravariant Piola transform to map values back to the physical element.
7342
7408
const double tmp_ref0 = derivatives[r];
7343
7409
const double tmp_ref1 = derivatives[num_derivatives + r];
7344
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
7345
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
7410
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
7411
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
7346
7412
}// end loop over 'r'
7347
7413
7348
7414
// Transform derivatives back to physical element
7350
7416
{
7351
7417
for (unsigned int s = 0; s < num_derivatives; s++)
7352
7418
{
7353
values[r] += transform[r][s]*derivatives[s];
7354
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
7419
values[r] += transform[r][s]*derivatives_p[s];
7420
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
7355
7421
}// end loop over 's'
7356
7422
}// end loop over 'r'
7357
7423
7358
7424
// Delete pointer to array of derivatives on FIAT element
7359
7425
delete [] derivatives;
7360
7426
7427
// Delete pointer to array of reference derivatives on physical element.
7428
delete [] derivatives_p;
7429
7361
7430
// Delete pointer to array of combinations of derivatives and transform
7362
7431
for (unsigned int r = 0; r < num_derivatives; r++)
7363
7432
{
7374
7443
case 8:
7375
7444
{
7376
7445
7377
// Array of basisvalues.
7446
// Array of basisvalues
7378
7447
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7379
7448
7380
// Declare helper variables.
7449
// Declare helper variables
7381
7450
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
7382
7451
double tmp1 = (1.0 - Y)/2.0;
7383
7452
double tmp2 = tmp1*tmp1;
7384
7453
7385
// Compute basisvalues.
7454
// Compute basisvalues
7386
7455
basisvalues[0] = 1.0;
7387
7456
basisvalues[1] = tmp0;
7388
7457
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
7404
7473
basisvalues[7] *= std::sqrt(10.0);
7405
7474
basisvalues[6] *= std::sqrt(14.0);
7406
7475
7407
// Table(s) of coefficients.
7476
// Table(s) of coefficients
7408
7477
static const double coefficients0[10] = \
7409
7478
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
7410
7479
7444
7513
derivatives[r] = 0.0;
7445
7514
}// end loop over 'r'
7446
7515
7516
// Declare pointer to array of reference derivatives on physical element.
7517
double *derivatives_p = new double[2*num_derivatives];
7518
for (unsigned int r = 0; r < 2*num_derivatives; r++)
7519
{
7520
derivatives_p[r] = 0.0;
7521
}// end loop over 'r'
7522
7447
7523
// Declare derivative matrix (of polynomial basis).
7448
7524
double dmats[10][10] = \
7449
7525
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
7542
7618
// Using contravariant Piola transform to map values back to the physical element.
7543
7619
const double tmp_ref0 = derivatives[r];
7544
7620
const double tmp_ref1 = derivatives[num_derivatives + r];
7545
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
7546
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
7621
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
7622
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
7547
7623
}// end loop over 'r'
7548
7624
7549
7625
// Transform derivatives back to physical element
7551
7627
{
7552
7628
for (unsigned int s = 0; s < num_derivatives; s++)
7553
7629
{
7554
values[r] += transform[r][s]*derivatives[s];
7555
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
7630
values[r] += transform[r][s]*derivatives_p[s];
7631
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
7556
7632
}// end loop over 's'
7557
7633
}// end loop over 'r'
7558
7634
7559
7635
// Delete pointer to array of derivatives on FIAT element
7560
7636
delete [] derivatives;
7561
7637
7638
// Delete pointer to array of reference derivatives on physical element.
7639
delete [] derivatives_p;
7640
7562
7641
// Delete pointer to array of combinations of derivatives and transform
7563
7642
for (unsigned int r = 0; r < num_derivatives; r++)
7564
7643
{
7575
7654
case 9:
7576
7655
{
7577
7656
7578
// Array of basisvalues.
7657
// Array of basisvalues
7579
7658
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7580
7659
7581
// Declare helper variables.
7660
// Declare helper variables
7582
7661
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
7583
7662
double tmp1 = (1.0 - Y)/2.0;
7584
7663
double tmp2 = tmp1*tmp1;
7585
7664
7586
// Compute basisvalues.
7665
// Compute basisvalues
7587
7666
basisvalues[0] = 1.0;
7588
7667
basisvalues[1] = tmp0;
7589
7668
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
7605
7684
basisvalues[7] *= std::sqrt(10.0);
7606
7685
basisvalues[6] *= std::sqrt(14.0);
7607
7686
7608
// Table(s) of coefficients.
7687
// Table(s) of coefficients
7609
7688
static const double coefficients0[10] = \
7610
7689
{0.32998316, -0.69282032, -0.53333333, -0.39992441, -0.026937401, 0.20606818, 0.32071349, -0.03011693, -0.023328474, 0.013468701};
7611
7690
7645
7724
derivatives[r] = 0.0;
7646
7725
}// end loop over 'r'
7647
7726
7727
// Declare pointer to array of reference derivatives on physical element.
7728
double *derivatives_p = new double[2*num_derivatives];
7729
for (unsigned int r = 0; r < 2*num_derivatives; r++)
7730
{
7731
derivatives_p[r] = 0.0;
7732
}// end loop over 'r'
7733
7648
7734
// Declare derivative matrix (of polynomial basis).
7649
7735
double dmats[10][10] = \
7650
7736
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
7743
7829
// Using contravariant Piola transform to map values back to the physical element.
7744
7830
const double tmp_ref0 = derivatives[r];
7745
7831
const double tmp_ref1 = derivatives[num_derivatives + r];
7746
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
7747
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
7832
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
7833
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
7748
7834
}// end loop over 'r'
7749
7835
7750
7836
// Transform derivatives back to physical element
7752
7838
{
7753
7839
for (unsigned int s = 0; s < num_derivatives; s++)
7754
7840
{
7755
values[r] += transform[r][s]*derivatives[s];
7756
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
7841
values[r] += transform[r][s]*derivatives_p[s];
7842
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
7757
7843
}// end loop over 's'
7758
7844
}// end loop over 'r'
7759
7845
7760
7846
// Delete pointer to array of derivatives on FIAT element
7761
7847
delete [] derivatives;
7762
7848
7849
// Delete pointer to array of reference derivatives on physical element.
7850
delete [] derivatives_p;
7851
7763
7852
// Delete pointer to array of combinations of derivatives and transform
7764
7853
for (unsigned int r = 0; r < num_derivatives; r++)
7765
7854
{
7776
7865
case 10:
7777
7866
{
7778
7867
7779
// Array of basisvalues.
7868
// Array of basisvalues
7780
7869
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7781
7870
7782
// Declare helper variables.
7871
// Declare helper variables
7783
7872
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
7784
7873
double tmp1 = (1.0 - Y)/2.0;
7785
7874
double tmp2 = tmp1*tmp1;
7786
7875
7787
// Compute basisvalues.
7876
// Compute basisvalues
7788
7877
basisvalues[0] = 1.0;
7789
7878
basisvalues[1] = tmp0;
7790
7879
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
7806
7895
basisvalues[7] *= std::sqrt(10.0);
7807
7896
basisvalues[6] *= std::sqrt(14.0);
7808
7897
7809
// Table(s) of coefficients.
7898
// Table(s) of coefficients
7810
7899
static const double coefficients0[10] = \
7811
7900
{0.56568542, 0.65433031, -0.46666667, -0.19126819, -0.094280904, 0.12441853, -0.32071349, 0.15058465, -0.054433105, 0.013468701};
7812
7901
7846
7935
derivatives[r] = 0.0;
7847
7936
}// end loop over 'r'
7848
7937
7938
// Declare pointer to array of reference derivatives on physical element.
7939
double *derivatives_p = new double[2*num_derivatives];
7940
for (unsigned int r = 0; r < 2*num_derivatives; r++)
7941
{
7942
derivatives_p[r] = 0.0;
7943
}// end loop over 'r'
7944
7849
7945
// Declare derivative matrix (of polynomial basis).
7850
7946
double dmats[10][10] = \
7851
7947
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
7944
8040
// Using contravariant Piola transform to map values back to the physical element.
7945
8041
const double tmp_ref0 = derivatives[r];
7946
8042
const double tmp_ref1 = derivatives[num_derivatives + r];
7947
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
7948
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
8043
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
8044
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
7949
8045
}// end loop over 'r'
7950
8046
7951
8047
// Transform derivatives back to physical element
7953
8049
{
7954
8050
for (unsigned int s = 0; s < num_derivatives; s++)
7955
8051
{
7956
values[r] += transform[r][s]*derivatives[s];
7957
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
8052
values[r] += transform[r][s]*derivatives_p[s];
8053
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
7958
8054
}// end loop over 's'
7959
8055
}// end loop over 'r'
7960
8056
7961
8057
// Delete pointer to array of derivatives on FIAT element
7962
8058
delete [] derivatives;
7963
8059
8060
// Delete pointer to array of reference derivatives on physical element.
8061
delete [] derivatives_p;
8062
7964
8063
// Delete pointer to array of combinations of derivatives and transform
7965
8064
for (unsigned int r = 0; r < num_derivatives; r++)
7966
8065
{
7977
8076
case 11:
7978
8077
{
7979
8078
7980
// Array of basisvalues.
8079
// Array of basisvalues
7981
8080
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7982
8081
7983
// Declare helper variables.
8082
// Declare helper variables
7984
8083
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
7985
8084
double tmp1 = (1.0 - Y)/2.0;
7986
8085
double tmp2 = tmp1*tmp1;
7987
8086
7988
// Compute basisvalues.
8087
// Compute basisvalues
7989
8088
basisvalues[0] = 1.0;
7990
8089
basisvalues[1] = tmp0;
7991
8090
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
8007
8106
basisvalues[7] *= std::sqrt(10.0);
8008
8107
basisvalues[6] *= std::sqrt(14.0);
8009
8108
8010
// Table(s) of coefficients.
8109
// Table(s) of coefficients
8011
8110
static const double coefficients0[10] = \
8012
8111
{0.094280904, 0.076980036, 0.93333333, 0.20865621, 0.24243661, -0.443241, 0.0, -0.24093544, 0.15552316, -0.053874802};
8013
8112
8047
8146
derivatives[r] = 0.0;
8048
8147
}// end loop over 'r'
8049
8148
8149
// Declare pointer to array of reference derivatives on physical element.
8150
double *derivatives_p = new double[2*num_derivatives];
8151
for (unsigned int r = 0; r < 2*num_derivatives; r++)
8152
{
8153
derivatives_p[r] = 0.0;
8154
}// end loop over 'r'
8155
8050
8156
// Declare derivative matrix (of polynomial basis).
8051
8157
double dmats[10][10] = \
8052
8158
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
8145
8251
// Using contravariant Piola transform to map values back to the physical element.
8146
8252
const double tmp_ref0 = derivatives[r];
8147
8253
const double tmp_ref1 = derivatives[num_derivatives + r];
8148
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
8149
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
8254
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
8255
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
8150
8256
}// end loop over 'r'
8151
8257
8152
8258
// Transform derivatives back to physical element
8154
8260
{
8155
8261
for (unsigned int s = 0; s < num_derivatives; s++)
8156
8262
{
8157
values[r] += transform[r][s]*derivatives[s];
8158
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
8263
values[r] += transform[r][s]*derivatives_p[s];
8264
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
8159
8265
}// end loop over 's'
8160
8266
}// end loop over 'r'
8161
8267
8162
8268
// Delete pointer to array of derivatives on FIAT element
8163
8269
delete [] derivatives;
8164
8270
8271
// Delete pointer to array of reference derivatives on physical element.
8272
delete [] derivatives_p;
8273
8165
8274
// Delete pointer to array of combinations of derivatives and transform
8166
8275
for (unsigned int r = 0; r < num_derivatives; r++)
8167
8276
{
8178
8287
case 12:
8179
8288
{
8180
8289
8181
// Array of basisvalues.
8290
// Array of basisvalues
8182
8291
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8183
8292
8184
// Declare helper variables.
8293
// Declare helper variables
8185
8294
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
8186
8295
double tmp1 = (1.0 - Y)/2.0;
8187
8296
double tmp2 = tmp1*tmp1;
8188
8297
8189
// Compute basisvalues.
8298
// Compute basisvalues
8190
8299
basisvalues[0] = 1.0;
8191
8300
basisvalues[1] = tmp0;
8192
8301
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
8208
8317
basisvalues[7] *= std::sqrt(10.0);
8209
8318
basisvalues[6] *= std::sqrt(14.0);
8210
8319
8211
// Table(s) of coefficients.
8320
// Table(s) of coefficients
8212
8321
static const double coefficients0[10] = \
8213
8322
{0.23570226, 0.076980036, 0.0, 0.052164053, 0.24243661, 0.058321184, 0.1069045, 0.15058465, -0.0077761579, -0.067343503};
8214
8323
8248
8357
derivatives[r] = 0.0;
8249
8358
}// end loop over 'r'
8250
8359
8360
// Declare pointer to array of reference derivatives on physical element.
8361
double *derivatives_p = new double[2*num_derivatives];
8362
for (unsigned int r = 0; r < 2*num_derivatives; r++)
8363
{
8364
derivatives_p[r] = 0.0;
8365
}// end loop over 'r'
8366
8251
8367
// Declare derivative matrix (of polynomial basis).
8252
8368
double dmats[10][10] = \
8253
8369
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
8346
8462
// Using contravariant Piola transform to map values back to the physical element.
8347
8463
const double tmp_ref0 = derivatives[r];
8348
8464
const double tmp_ref1 = derivatives[num_derivatives + r];
8349
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
8350
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
8465
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
8466
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
8351
8467
}// end loop over 'r'
8352
8468
8353
8469
// Transform derivatives back to physical element
8355
8471
{
8356
8472
for (unsigned int s = 0; s < num_derivatives; s++)
8357
8473
{
8358
values[r] += transform[r][s]*derivatives[s];
8359
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
8474
values[r] += transform[r][s]*derivatives_p[s];
8475
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
8360
8476
}// end loop over 's'
8361
8477
}// end loop over 'r'
8362
8478
8363
8479
// Delete pointer to array of derivatives on FIAT element
8364
8480
delete [] derivatives;
8365
8481
8482
// Delete pointer to array of reference derivatives on physical element.
8483
delete [] derivatives_p;
8484
8366
8485
// Delete pointer to array of combinations of derivatives and transform
8367
8486
for (unsigned int r = 0; r < num_derivatives; r++)
8368
8487
{
8379
8498
case 13:
8380
8499
{
8381
8500
8382
// Array of basisvalues.
8501
// Array of basisvalues
8383
8502
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8384
8503
8385
// Declare helper variables.
8504
// Declare helper variables
8386
8505
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
8387
8506
double tmp1 = (1.0 - Y)/2.0;
8388
8507
double tmp2 = tmp1*tmp1;
8389
8508
8390
// Compute basisvalues.
8509
// Compute basisvalues
8391
8510
basisvalues[0] = 1.0;
8392
8511
basisvalues[1] = tmp0;
8393
8512
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
8409
8528
basisvalues[7] *= std::sqrt(10.0);
8410
8529
basisvalues[6] *= std::sqrt(14.0);
8411
8530
8412
// Table(s) of coefficients.
8531
// Table(s) of coefficients
8413
8532
static const double coefficients0[10] = \
8414
8533
{0.0, -0.076980036, -0.13333333, -0.31298432, -0.24243661, 0.27994168, -0.21380899, -0.06023386, 0.17107547, -0.13468701};
8415
8534
8449
8568
derivatives[r] = 0.0;
8450
8569
}// end loop over 'r'
8451
8570
8571
// Declare pointer to array of reference derivatives on physical element.
8572
double *derivatives_p = new double[2*num_derivatives];
8573
for (unsigned int r = 0; r < 2*num_derivatives; r++)
8574
{
8575
derivatives_p[r] = 0.0;
8576
}// end loop over 'r'
8577
8452
8578
// Declare derivative matrix (of polynomial basis).
8453
8579
double dmats[10][10] = \
8454
8580
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
8547
8673
// Using contravariant Piola transform to map values back to the physical element.
8548
8674
const double tmp_ref0 = derivatives[r];
8549
8675
const double tmp_ref1 = derivatives[num_derivatives + r];
8550
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
8551
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
8676
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
8677
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
8552
8678
}// end loop over 'r'
8553
8679
8554
8680
// Transform derivatives back to physical element
8556
8682
{
8557
8683
for (unsigned int s = 0; s < num_derivatives; s++)
8558
8684
{
8559
values[r] += transform[r][s]*derivatives[s];
8560
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
8685
values[r] += transform[r][s]*derivatives_p[s];
8686
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
8561
8687
}// end loop over 's'
8562
8688
}// end loop over 'r'
8563
8689
8564
8690
// Delete pointer to array of derivatives on FIAT element
8565
8691
delete [] derivatives;
8566
8692
8693
// Delete pointer to array of reference derivatives on physical element.
8694
delete [] derivatives_p;
8695
8567
8696
// Delete pointer to array of combinations of derivatives and transform
8568
8697
for (unsigned int r = 0; r < num_derivatives; r++)
8569
8698
{
8580
8709
case 14:
8581
8710
{
8582
8711
8583
// Array of basisvalues.
8712
// Array of basisvalues
8584
8713
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8585
8714
8586
// Declare helper variables.
8715
// Declare helper variables
8587
8716
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
8588
8717
double tmp1 = (1.0 - Y)/2.0;
8589
8718
double tmp2 = tmp1*tmp1;
8590
8719
8591
// Compute basisvalues.
8720
// Compute basisvalues
8592
8721
basisvalues[0] = 1.0;
8593
8722
basisvalues[1] = tmp0;
8594
8723
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
8610
8739
basisvalues[7] *= std::sqrt(10.0);
8611
8740
basisvalues[6] *= std::sqrt(14.0);
8612
8741
8613
// Table(s) of coefficients.
8742
// Table(s) of coefficients
8614
8743
static const double coefficients0[10] = \
8615
8744
{-0.23570226, -0.038490018, 0.066666667, 0.10432811, -0.12121831, -0.19829203, 0.0, -0.12046772, -0.077761579, 0.13468701};
8616
8745
8650
8779
derivatives[r] = 0.0;
8651
8780
}// end loop over 'r'
8652
8781
8782
// Declare pointer to array of reference derivatives on physical element.
8783
double *derivatives_p = new double[2*num_derivatives];
8784
for (unsigned int r = 0; r < 2*num_derivatives; r++)
8785
{
8786
derivatives_p[r] = 0.0;
8787
}// end loop over 'r'
8788
8653
8789
// Declare derivative matrix (of polynomial basis).
8654
8790
double dmats[10][10] = \
8655
8791
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
8748
8884
// Using contravariant Piola transform to map values back to the physical element.
8749
8885
const double tmp_ref0 = derivatives[r];
8750
8886
const double tmp_ref1 = derivatives[num_derivatives + r];
8751
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
8752
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
8887
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
8888
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
8753
8889
}// end loop over 'r'
8754
8890
8755
8891
// Transform derivatives back to physical element
8757
8893
{
8758
8894
for (unsigned int s = 0; s < num_derivatives; s++)
8759
8895
{
8760
values[r] += transform[r][s]*derivatives[s];
8761
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
8896
values[r] += transform[r][s]*derivatives_p[s];
8897
values[num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
8762
8898
}// end loop over 's'
8763
8899
}// end loop over 'r'
8764
8900
8765
8901
// Delete pointer to array of derivatives on FIAT element
8766
8902
delete [] derivatives;
8767
8903
8904
// Delete pointer to array of reference derivatives on physical element.
8905
delete [] derivatives_p;
8906
8768
8907
// Delete pointer to array of combinations of derivatives and transform
8769
8908
for (unsigned int r = 0; r < num_derivatives; r++)
8770
8909
{
8782
8921
8783
8922
}
8784
8923
8785
/// Evaluate order n derivatives of all basis functions at given point in cell
8786
virtual void evaluate_basis_derivatives_all(unsigned int n,
8924
/// Evaluate order n derivatives of all basis functions at given point x in cell
8925
virtual void evaluate_basis_derivatives_all(std::size_t n,
8787
8926
double* values,
8788
const double* coordinates,
8789
const ufc::cell& c) const
8927
const double* x,
8928
const double* vertex_coordinates,
8929
int cell_orientation) const
8790
8930
{
8791
8931
// Compute number of derivatives.
8792
8932
unsigned int num_derivatives = 1;
8805
8945
// Loop dofs and call evaluate_basis_derivatives.
8806
8946
for (unsigned int r = 0; r < 15; r++)
8807
8947
{
8808
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
8948
evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
8809
8949
for (unsigned int s = 0; s < 2*num_derivatives; s++)
8810
8950
{
8811
8951
values[r*2*num_derivatives + s] = dof_values[s];
8817
8957
}
8818
8958
8819
8959
/// Evaluate linear functional for dof i on the function f
8820
virtual double evaluate_dof(unsigned int i,
8960
virtual double evaluate_dof(std::size_t i,
8821
8961
const ufc::function& f,
8962
const double* vertex_coordinates,
8963
int cell_orientation,
8822
8964
const ufc::cell& c) const
8823
8965
{
8824
// Declare variables for result of evaluation.
8966
// Declare variables for result of evaluation
8825
8967
double vals[2];
8826
8968
8827
// Declare variable for physical coordinates.
8969
// Declare variable for physical coordinates
8828
8970
double y[2];
8971
8829
8972
double result;
8830
// Extract vertex coordinates
8831
const double * const * x = c.coordinates;
8832
8833
// Compute Jacobian of affine map from reference cell
8834
const double J_00 = x[1][0] - x[0][0];
8835
const double J_01 = x[2][0] - x[0][0];
8836
const double J_10 = x[1][1] - x[0][1];
8837
const double J_11 = x[2][1] - x[0][1];
8838
8839
// Compute determinant of Jacobian
8840
double detJ = J_00*J_11 - J_01*J_10;
8841
8842
// Compute inverse of Jacobian
8843
const double K_00 = J_11 / detJ;
8844
const double K_01 = -J_01 / detJ;
8845
const double K_10 = -J_10 / detJ;
8846
const double K_11 = J_00 / detJ;switch (i)
8973
// Compute Jacobian
8974
double J[4];
8975
compute_jacobian_triangle_2d(J, vertex_coordinates);
8976
8977
8978
// Compute Jacobian inverse and determinant
8979
double K[4];
8980
double detJ;
8981
compute_jacobian_inverse_triangle_2d(K, detJ, J);
8982
8983
8984
switch (i)
8847
8985
{
8848
8986
case 0:
8849
8987
{
8850
y[0] = 0.75*x[1][0] + 0.25*x[2][0];
8851
y[1] = 0.75*x[1][1] + 0.25*x[2][1];
8988
y[0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
8989
y[1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
8852
8990
f.evaluate(vals, y, c);
8853
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
8991
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8854
8992
return result;
8855
8993
break;
8856
8994
}
8857
8995
case 1:
8858
8996
{
8859
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
8860
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
8997
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
8998
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
8861
8999
f.evaluate(vals, y, c);
8862
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
9000
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8863
9001
return result;
8864
9002
break;
8865
9003
}
8866
9004
case 2:
8867
9005
{
8868
y[0] = 0.25*x[1][0] + 0.75*x[2][0];
8869
y[1] = 0.25*x[1][1] + 0.75*x[2][1];
9006
y[0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
9007
y[1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
8870
9008
f.evaluate(vals, y, c);
8871
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
9009
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8872
9010
return result;
8873
9011
break;
8874
9012
}
8875
9013
case 3:
8876
9014
{
8877
y[0] = 0.75*x[0][0] + 0.25*x[2][0];
8878
y[1] = 0.75*x[0][1] + 0.25*x[2][1];
9015
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
9016
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
8879
9017
f.evaluate(vals, y, c);
8880
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9018
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8881
9019
return result;
8882
9020
break;
8883
9021
}
8884
9022
case 4:
8885
9023
{
8886
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
8887
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
9024
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
9025
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
8888
9026
f.evaluate(vals, y, c);
8889
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9027
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8890
9028
return result;
8891
9029
break;
8892
9030
}
8893
9031
case 5:
8894
9032
{
8895
y[0] = 0.25*x[0][0] + 0.75*x[2][0];
8896
y[1] = 0.25*x[0][1] + 0.75*x[2][1];
9033
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
9034
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
8897
9035
f.evaluate(vals, y, c);
8898
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9036
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8899
9037
return result;
8900
9038
break;
8901
9039
}
8902
9040
case 6:
8903
9041
{
8904
y[0] = 0.75*x[0][0] + 0.25*x[1][0];
8905
y[1] = 0.75*x[0][1] + 0.25*x[1][1];
9042
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
9043
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
8906
9044
f.evaluate(vals, y, c);
8907
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9045
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
8908
9046
return result;
8909
9047
break;
8910
9048
}
8911
9049
case 7:
8912
9050
{
8913
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
8914
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
9051
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
9052
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
8915
9053
f.evaluate(vals, y, c);
8916
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9054
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
8917
9055
return result;
8918
9056
break;
8919
9057
}
8920
9058
case 8:
8921
9059
{
8922
y[0] = 0.25*x[0][0] + 0.75*x[1][0];
8923
y[1] = 0.25*x[0][1] + 0.75*x[1][1];
9060
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
9061
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
8924
9062
f.evaluate(vals, y, c);
8925
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9063
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
8926
9064
return result;
8927
9065
break;
8928
9066
}
8929
9067
case 9:
8930
9068
{
8931
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
8932
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
9069
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9070
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
8933
9071
f.evaluate(vals, y, c);
8934
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9072
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8935
9073
return result;
8936
9074
break;
8937
9075
}
8938
9076
case 10:
8939
9077
{
8940
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
8941
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
9078
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9079
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
8942
9080
f.evaluate(vals, y, c);
8943
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9081
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8944
9082
return result;
8945
9083
break;
8946
9084
}
8947
9085
case 11:
8948
9086
{
8949
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
8950
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
9087
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
9088
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
8951
9089
f.evaluate(vals, y, c);
8952
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9090
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
8953
9091
return result;
8954
9092
break;
8955
9093
}
8956
9094
case 12:
8957
9095
{
8958
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
8959
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
9096
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9097
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
8960
9098
f.evaluate(vals, y, c);
8961
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9099
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8962
9100
return result;
8963
9101
break;
8964
9102
}
8965
9103
case 13:
8966
9104
{
8967
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
8968
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
9105
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9106
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
8969
9107
f.evaluate(vals, y, c);
8970
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9108
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8971
9109
return result;
8972
9110
break;
8973
9111
}
8974
9112
case 14:
8975
9113
{
8976
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
8977
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
9114
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
9115
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
8978
9116
f.evaluate(vals, y, c);
8979
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9117
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
8980
9118
return result;
8981
9119
break;
8982
9120
}
8988
9126
/// Evaluate linear functionals for all dofs on the function f
8989
9127
virtual void evaluate_dofs(double* values,
8990
9128
const ufc::function& f,
9129
const double* vertex_coordinates,
9130
int cell_orientation,
8991
9131
const ufc::cell& c) const
8992
9132
{
8993
// Declare variables for result of evaluation.
9133
// Declare variables for result of evaluation
8994
9134
double vals[2];
8995
9135
8996
// Declare variable for physical coordinates.
9136
// Declare variable for physical coordinates
8997
9137
double y[2];
9138
8998
9139
double result;
8999
// Extract vertex coordinates
9000
const double * const * x = c.coordinates;
9001
9002
// Compute Jacobian of affine map from reference cell
9003
const double J_00 = x[1][0] - x[0][0];
9004
const double J_01 = x[2][0] - x[0][0];
9005
const double J_10 = x[1][1] - x[0][1];
9006
const double J_11 = x[2][1] - x[0][1];
9007
9008
// Compute determinant of Jacobian
9009
double detJ = J_00*J_11 - J_01*J_10;
9010
9011
// Compute inverse of Jacobian
9012
const double K_00 = J_11 / detJ;
9013
const double K_01 = -J_01 / detJ;
9014
const double K_10 = -J_10 / detJ;
9015
const double K_11 = J_00 / detJ;y[0] = 0.75*x[1][0] + 0.25*x[2][0];
9016
y[1] = 0.75*x[1][1] + 0.25*x[2][1];
9140
// Compute Jacobian
9141
double J[4];
9142
compute_jacobian_triangle_2d(J, vertex_coordinates);
9143
9144
9145
// Compute Jacobian inverse and determinant
9146
double K[4];
9147
double detJ;
9148
compute_jacobian_inverse_triangle_2d(K, detJ, J);
9149
9150
9151
y[0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9152
y[1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
9017
9153
f.evaluate(vals, y, c);
9018
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
9154
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9019
9155
values[0] = result;
9020
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
9021
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
9156
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
9157
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
9022
9158
f.evaluate(vals, y, c);
9023
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
9159
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9024
9160
values[1] = result;
9025
y[0] = 0.25*x[1][0] + 0.75*x[2][0];
9026
y[1] = 0.25*x[1][1] + 0.75*x[2][1];
9161
y[0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
9162
y[1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
9027
9163
f.evaluate(vals, y, c);
9028
result = (detJ*(K_00*vals[0] + K_01*vals[1])) + (detJ*(K_10*vals[0] + K_11*vals[1]));
9164
result = (detJ*(K[0]*vals[0] + K[1]*vals[1])) + (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9029
9165
values[2] = result;
9030
y[0] = 0.75*x[0][0] + 0.25*x[2][0];
9031
y[1] = 0.75*x[0][1] + 0.25*x[2][1];
9166
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
9167
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
9032
9168
f.evaluate(vals, y, c);
9033
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9169
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9034
9170
values[3] = result;
9035
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
9036
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
9171
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
9172
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
9037
9173
f.evaluate(vals, y, c);
9038
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9174
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9039
9175
values[4] = result;
9040
y[0] = 0.25*x[0][0] + 0.75*x[2][0];
9041
y[1] = 0.25*x[0][1] + 0.75*x[2][1];
9176
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
9177
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
9042
9178
f.evaluate(vals, y, c);
9043
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9179
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9044
9180
values[5] = result;
9045
y[0] = 0.75*x[0][0] + 0.25*x[1][0];
9046
y[1] = 0.75*x[0][1] + 0.25*x[1][1];
9181
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
9182
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
9047
9183
f.evaluate(vals, y, c);
9048
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9184
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
9049
9185
values[6] = result;
9050
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
9051
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
9186
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
9187
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
9052
9188
f.evaluate(vals, y, c);
9053
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9189
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
9054
9190
values[7] = result;
9055
y[0] = 0.25*x[0][0] + 0.75*x[1][0];
9056
y[1] = 0.25*x[0][1] + 0.75*x[1][1];
9191
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
9192
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
9057
9193
f.evaluate(vals, y, c);
9058
result = (-1.0)*(detJ*(K_10*vals[0] + K_11*vals[1]));
9194
result = (-1.0)*(detJ*(K[2]*vals[0] + K[3]*vals[1]));
9059
9195
values[8] = result;
9060
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
9061
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
9196
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9197
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
9062
9198
f.evaluate(vals, y, c);
9063
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9199
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9064
9200
values[9] = result;
9065
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
9066
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
9201
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9202
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
9067
9203
f.evaluate(vals, y, c);
9068
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9204
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9069
9205
values[10] = result;
9070
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
9071
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
9206
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
9207
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
9072
9208
f.evaluate(vals, y, c);
9073
result = (detJ*(K_00*vals[0] + K_01*vals[1]));
9209
result = (detJ*(K[0]*vals[0] + K[1]*vals[1]));
9074
9210
values[11] = result;
9075
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
9076
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
9211
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9212
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
9077
9213
f.evaluate(vals, y, c);
9078
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9214
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9079
9215
values[12] = result;
9080
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
9081
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
9216
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
9217
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
9082
9218
f.evaluate(vals, y, c);
9083
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9219
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9084
9220
values[13] = result;
9085
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
9086
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
9221
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
9222
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
9087
9223
f.evaluate(vals, y, c);
9088
result = (detJ*(K_10*vals[0] + K_11*vals[1]));
9224
result = (detJ*(K[2]*vals[0] + K[3]*vals[1]));
9089
9225
values[14] = result;
9090
9226
}
9091
9227
9092
9228
/// Interpolate vertex values from dof values
9093
9229
virtual void interpolate_vertex_values(double* vertex_values,
9094
9230
const double* dof_values,
9231
const double* vertex_coordinates,
9232
int cell_orientation,
9095
9233
const ufc::cell& c) const
9096
9234
{
9097
// Extract vertex coordinates
9098
const double * const * x = c.coordinates;
9099
9100
// Compute Jacobian of affine map from reference cell
9101
const double J_00 = x[1][0] - x[0][0];
9102
const double J_01 = x[2][0] - x[0][0];
9103
const double J_10 = x[1][1] - x[0][1];
9104
const double J_11 = x[2][1] - x[0][1];
9105
9106
// Compute determinant of Jacobian
9107
double detJ = J_00*J_11 - J_01*J_10;
9108
9109
// Compute inverse of Jacobian
9235
// Compute Jacobian
9236
double J[4];
9237
compute_jacobian_triangle_2d(J, vertex_coordinates);
9238
9239
9240
// Compute Jacobian inverse and determinant
9241
double K[4];
9242
double detJ;
9243
compute_jacobian_inverse_triangle_2d(K, detJ, J);
9244
9245
9246
9110
9247
// Evaluate function and change variables
9111
vertex_values[0] = dof_values[3]*(1.0/detJ)*J_00*3.0 + dof_values[4]*((1.0/detJ)*(J_00*(-3.0))) + dof_values[5]*(1.0/detJ)*J_00 + dof_values[6]*((1.0/detJ)*(J_01*(-3.0))) + dof_values[7]*(1.0/detJ)*J_01*3.0 + dof_values[8]*((1.0/detJ)*(J_01*(-1.0)));
9112
vertex_values[2] = dof_values[0]*(1.0/detJ)*J_00*3.0 + dof_values[1]*((1.0/detJ)*(J_00*(-3.0))) + dof_values[2]*(1.0/detJ)*J_00 + dof_values[6]*((1.0/detJ)*(J_00 + J_01*(-1.0))) + dof_values[7]*((1.0/detJ)*(J_00*(-3.0) + J_01*3.0)) + dof_values[8]*((1.0/detJ)*(J_00*3.0 + J_01*(-3.0)));
9113
vertex_values[4] = dof_values[0]*(1.0/detJ)*J_01 + dof_values[1]*((1.0/detJ)*(J_01*(-3.0))) + dof_values[2]*(1.0/detJ)*J_01*3.0 + dof_values[3]*((1.0/detJ)*(J_00 + J_01*(-1.0))) + dof_values[4]*((1.0/detJ)*(J_00*(-3.0) + J_01*3.0)) + dof_values[5]*((1.0/detJ)*(J_00*3.0 + J_01*(-3.0)));
9114
vertex_values[1] = dof_values[3]*(1.0/detJ)*J_10*3.0 + dof_values[4]*((1.0/detJ)*(J_10*(-3.0))) + dof_values[5]*(1.0/detJ)*J_10 + dof_values[6]*((1.0/detJ)*(J_11*(-3.0))) + dof_values[7]*(1.0/detJ)*J_11*3.0 + dof_values[8]*((1.0/detJ)*(J_11*(-1.0)));
9115
vertex_values[3] = dof_values[0]*(1.0/detJ)*J_10*3.0 + dof_values[1]*((1.0/detJ)*(J_10*(-3.0))) + dof_values[2]*(1.0/detJ)*J_10 + dof_values[6]*((1.0/detJ)*(J_10 + J_11*(-1.0))) + dof_values[7]*((1.0/detJ)*(J_10*(-3.0) + J_11*3.0)) + dof_values[8]*((1.0/detJ)*(J_10*3.0 + J_11*(-3.0)));
9116
vertex_values[5] = dof_values[0]*(1.0/detJ)*J_11 + dof_values[1]*((1.0/detJ)*(J_11*(-3.0))) + dof_values[2]*(1.0/detJ)*J_11*3.0 + dof_values[3]*((1.0/detJ)*(J_10 + J_11*(-1.0))) + dof_values[4]*((1.0/detJ)*(J_10*(-3.0) + J_11*3.0)) + dof_values[5]*((1.0/detJ)*(J_10*3.0 + J_11*(-3.0)));
9248
vertex_values[0] = dof_values[3]*(1.0/detJ)*J[0]*3.0 + dof_values[4]*((1.0/detJ)*(J[0]*(-3.0))) + dof_values[5]*(1.0/detJ)*J[0] + dof_values[6]*((1.0/detJ)*(J[1]*(-3.0))) + dof_values[7]*(1.0/detJ)*J[1]*3.0 + dof_values[8]*((1.0/detJ)*(J[1]*(-1.0)));
9249
vertex_values[2] = dof_values[0]*(1.0/detJ)*J[0]*3.0 + dof_values[1]*((1.0/detJ)*(J[0]*(-3.0))) + dof_values[2]*(1.0/detJ)*J[0] + dof_values[6]*((1.0/detJ)*(J[0] + J[1]*(-1.0))) + dof_values[7]*((1.0/detJ)*(J[0]*(-3.0) + J[1]*3.0)) + dof_values[8]*((1.0/detJ)*(J[0]*3.0 + J[1]*(-3.0)));
9250
vertex_values[4] = dof_values[0]*(1.0/detJ)*J[1] + dof_values[1]*((1.0/detJ)*(J[1]*(-3.0))) + dof_values[2]*(1.0/detJ)*J[1]*3.0 + dof_values[3]*((1.0/detJ)*(J[0] + J[1]*(-1.0))) + dof_values[4]*((1.0/detJ)*(J[0]*(-3.0) + J[1]*3.0)) + dof_values[5]*((1.0/detJ)*(J[0]*3.0 + J[1]*(-3.0)));
9251
vertex_values[1] = dof_values[3]*(1.0/detJ)*J[2]*3.0 + dof_values[4]*((1.0/detJ)*(J[2]*(-3.0))) + dof_values[5]*(1.0/detJ)*J[2] + dof_values[6]*((1.0/detJ)*(J[3]*(-3.0))) + dof_values[7]*(1.0/detJ)*J[3]*3.0 + dof_values[8]*((1.0/detJ)*(J[3]*(-1.0)));
9252
vertex_values[3] = dof_values[0]*(1.0/detJ)*J[2]*3.0 + dof_values[1]*((1.0/detJ)*(J[2]*(-3.0))) + dof_values[2]*(1.0/detJ)*J[2] + dof_values[6]*((1.0/detJ)*(J[2] + J[3]*(-1.0))) + dof_values[7]*((1.0/detJ)*(J[2]*(-3.0) + J[3]*3.0)) + dof_values[8]*((1.0/detJ)*(J[2]*3.0 + J[3]*(-3.0)));
9253
vertex_values[5] = dof_values[0]*(1.0/detJ)*J[3] + dof_values[1]*((1.0/detJ)*(J[3]*(-3.0))) + dof_values[2]*(1.0/detJ)*J[3]*3.0 + dof_values[3]*((1.0/detJ)*(J[2] + J[3]*(-1.0))) + dof_values[4]*((1.0/detJ)*(J[2]*(-3.0) + J[3]*3.0)) + dof_values[5]*((1.0/detJ)*(J[2]*3.0 + J[3]*(-3.0)));
9117
9254
}
9118
9255
9119
9256
/// Map coordinate xhat from reference cell to coordinate x in cell
9121
9258
const double* xhat,
9122
9259
const ufc::cell& c) const
9123
9260
{
9124
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
9261
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
9125
9262
}
9126
9263
9127
9264
/// Map from coordinate x in cell to coordinate xhat in reference cell
9129
9266
const double* x,
9130
9267
const ufc::cell& c) const
9131
9268
{
9132
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
9269
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
9133
9270
}
9134
9271
9135
9272
/// Return the number of sub elements (for a mixed element)
9136
virtual unsigned int num_sub_elements() const
9273
virtual std::size_t num_sub_elements() const
9137
9274
{
9138
9275
return 0;
9139
9276
}
9140
9277
9141
9278
/// Create a new finite element for sub element i (for a mixed element)
9142
virtual ufc::finite_element* create_sub_element(unsigned int i) const
9279
virtual ufc::finite_element* create_sub_element(std::size_t i) const
9143
9280
{
9144
9281
return 0;
9145
9282
}
9173
9310
/// Return a string identifying the finite element
9174
9311
virtual const char* signature() const
9175
9312
{
9176
return "MixedElement(*[MixedElement(*[VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None), FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)], **{'value_shape': (3,) }), FiniteElement('Raviart-Thomas', Cell('triangle', Space(2)), 3, None)], **{'value_shape': (5,) })";
9313
return "MixedElement(*[MixedElement(*[VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None), FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)], **{'value_shape': (3,) }), FiniteElement('Raviart-Thomas', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 3, None)], **{'value_shape': (5,) })";
9177
9314
}
9178
9315
9179
9316
/// Return the cell shape
9183
9320
}
9184
9321
9185
9322
/// Return the topological dimension of the cell shape
9186
virtual unsigned int topological_dimension() const
9323
virtual std::size_t topological_dimension() const
9187
9324
{
9188
9325
return 2;
9189
9326
}
9190
9327
9191
9328
/// Return the geometric dimension of the cell shape
9192
virtual unsigned int geometric_dimension() const
9329
virtual std::size_t geometric_dimension() const
9193
9330
{
9194
9331
return 2;
9195
9332
}
9196
9333
9197
9334
/// Return the dimension of the finite element function space
9198
virtual unsigned int space_dimension() const
9335
virtual std::size_t space_dimension() const
9199
9336
{
9200
9337
return 23;
9201
9338
}
9202
9339
9203
9340
/// Return the rank of the value space
9204
virtual unsigned int value_rank() const
9341
virtual std::size_t value_rank() const
9205
9342
{
9206
9343
return 1;
9207
9344
}
9208
9345
9209
9346
/// Return the dimension of the value space for axis i
9210
virtual unsigned int value_dimension(unsigned int i) const
9347
virtual std::size_t value_dimension(std::size_t i) const
9211
9348
{
9212
9349
switch (i)
9213
9350
{
9221
9358
return 0;
9222
9359
}
9223
9360
9224
/// Evaluate basis function i at given point in cell
9225
virtual void evaluate_basis(unsigned int i,
9361
/// Evaluate basis function i at given point x in cell
9362
virtual void evaluate_basis(std::size_t i,
9226
9363
double* values,
9227
const double* coordinates,
9228
const ufc::cell& c) const
9364
const double* x,
9365
const double* vertex_coordinates,
9366
int cell_orientation) const
9229
9367
{
9230
// Extract vertex coordinates
9231
const double * const * x = c.coordinates;
9232
9233
// Compute Jacobian of affine map from reference cell
9234
const double J_00 = x[1][0] - x[0][0];
9235
const double J_01 = x[2][0] - x[0][0];
9236
const double J_10 = x[1][1] - x[0][1];
9237
const double J_11 = x[2][1] - x[0][1];
9238
9239
// Compute determinant of Jacobian
9240
double detJ = J_00*J_11 - J_01*J_10;
9241
9242
// Compute inverse of Jacobian
9368
// Compute Jacobian
9369
double J[4];
9370
compute_jacobian_triangle_2d(J, vertex_coordinates);
9371
9372
// Compute Jacobian inverse and determinant
9373
double K[4];
9374
double detJ;
9375
compute_jacobian_inverse_triangle_2d(K, detJ, J);
9376
9377
9243
9378
9244
9379
// Compute constants
9245
const double C0 = x[1][0] + x[2][0];
9246
const double C1 = x[1][1] + x[2][1];
9380
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
9381
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
9247
9382
9248
9383
// Get coordinates and map to the reference (FIAT) element
9249
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
9250
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
9384
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
9385
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
9251
9386
9252
// Reset values.
9387
// Reset values
9253
9388
values[0] = 0.0;
9254
9389
values[1] = 0.0;
9255
9390
values[2] = 0.0;
9260
9395
case 0:
9261
9396
{
9262
9397
9263
// Array of basisvalues.
9398
// Array of basisvalues
9264
9399
double basisvalues[1] = {0.0};
9265
9400
9266
// Declare helper variables.
9401
// Declare helper variables
9267
9402
9268
// Compute basisvalues.
9403
// Compute basisvalues
9269
9404
basisvalues[0] = 1.0;
9270
9405
9271
// Table(s) of coefficients.
9406
// Table(s) of coefficients
9272
9407
static const double coefficients0[1] = \
9273
9408
{1.0};
9274
9409
9275
// Compute value(s).
9410
// Compute value(s)
9276
9411
for (unsigned int r = 0; r < 1; r++)
9277
9412
{
9278
9413
values[0] += coefficients0[r]*basisvalues[r];
9282
9417
case 1:
9283
9418
{
9284
9419
9285
// Array of basisvalues.
9420
// Array of basisvalues
9286
9421
double basisvalues[1] = {0.0};
9287
9422
9288
// Declare helper variables.
9423
// Declare helper variables
9289
9424
9290
// Compute basisvalues.
9425
// Compute basisvalues
9291
9426
basisvalues[0] = 1.0;
9292
9427
9293
// Table(s) of coefficients.
9428
// Table(s) of coefficients
9294
9429
static const double coefficients0[1] = \
9295
9430
{1.0};
9296
9431
9297
// Compute value(s).
9432
// Compute value(s)
9298
9433
for (unsigned int r = 0; r < 1; r++)
9299
9434
{
9300
9435
values[1] += coefficients0[r]*basisvalues[r];
9304
9439
case 2:
9305
9440
{
9306
9441
9307
// Array of basisvalues.
9442
// Array of basisvalues
9308
9443
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9309
9444
9310
// Declare helper variables.
9445
// Declare helper variables
9311
9446
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9312
9447
double tmp1 = (1.0 - Y)/2.0;
9313
9448
double tmp2 = tmp1*tmp1;
9314
9449
9315
// Compute basisvalues.
9450
// Compute basisvalues
9316
9451
basisvalues[0] = 1.0;
9317
9452
basisvalues[1] = tmp0;
9318
9453
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9326
9461
basisvalues[4] *= std::sqrt(4.5);
9327
9462
basisvalues[3] *= std::sqrt(7.5);
9328
9463
9329
// Table(s) of coefficients.
9464
// Table(s) of coefficients
9330
9465
static const double coefficients0[6] = \
9331
9466
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
9332
9467
9333
// Compute value(s).
9468
// Compute value(s)
9334
9469
for (unsigned int r = 0; r < 6; r++)
9335
9470
{
9336
9471
values[2] += coefficients0[r]*basisvalues[r];
9340
9475
case 3:
9341
9476
{
9342
9477
9343
// Array of basisvalues.
9478
// Array of basisvalues
9344
9479
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9345
9480
9346
// Declare helper variables.
9481
// Declare helper variables
9347
9482
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9348
9483
double tmp1 = (1.0 - Y)/2.0;
9349
9484
double tmp2 = tmp1*tmp1;
9350
9485
9351
// Compute basisvalues.
9486
// Compute basisvalues
9352
9487
basisvalues[0] = 1.0;
9353
9488
basisvalues[1] = tmp0;
9354
9489
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9362
9497
basisvalues[4] *= std::sqrt(4.5);
9363
9498
basisvalues[3] *= std::sqrt(7.5);
9364
9499
9365
// Table(s) of coefficients.
9500
// Table(s) of coefficients
9366
9501
static const double coefficients0[6] = \
9367
9502
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
9368
9503
9369
// Compute value(s).
9504
// Compute value(s)
9370
9505
for (unsigned int r = 0; r < 6; r++)
9371
9506
{
9372
9507
values[2] += coefficients0[r]*basisvalues[r];
9376
9511
case 4:
9377
9512
{
9378
9513
9379
// Array of basisvalues.
9514
// Array of basisvalues
9380
9515
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9381
9516
9382
// Declare helper variables.
9517
// Declare helper variables
9383
9518
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9384
9519
double tmp1 = (1.0 - Y)/2.0;
9385
9520
double tmp2 = tmp1*tmp1;
9386
9521
9387
// Compute basisvalues.
9522
// Compute basisvalues
9388
9523
basisvalues[0] = 1.0;
9389
9524
basisvalues[1] = tmp0;
9390
9525
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9398
9533
basisvalues[4] *= std::sqrt(4.5);
9399
9534
basisvalues[3] *= std::sqrt(7.5);
9400
9535
9401
// Table(s) of coefficients.
9536
// Table(s) of coefficients
9402
9537
static const double coefficients0[6] = \
9403
9538
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
9404
9539
9405
// Compute value(s).
9540
// Compute value(s)
9406
9541
for (unsigned int r = 0; r < 6; r++)
9407
9542
{
9408
9543
values[2] += coefficients0[r]*basisvalues[r];
9412
9547
case 5:
9413
9548
{
9414
9549
9415
// Array of basisvalues.
9550
// Array of basisvalues
9416
9551
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9417
9552
9418
// Declare helper variables.
9553
// Declare helper variables
9419
9554
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9420
9555
double tmp1 = (1.0 - Y)/2.0;
9421
9556
double tmp2 = tmp1*tmp1;
9422
9557
9423
// Compute basisvalues.
9558
// Compute basisvalues
9424
9559
basisvalues[0] = 1.0;
9425
9560
basisvalues[1] = tmp0;
9426
9561
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9434
9569
basisvalues[4] *= std::sqrt(4.5);
9435
9570
basisvalues[3] *= std::sqrt(7.5);
9436
9571
9437
// Table(s) of coefficients.
9572
// Table(s) of coefficients
9438
9573
static const double coefficients0[6] = \
9439
9574
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
9440
9575
9441
// Compute value(s).
9576
// Compute value(s)
9442
9577
for (unsigned int r = 0; r < 6; r++)
9443
9578
{
9444
9579
values[2] += coefficients0[r]*basisvalues[r];
9448
9583
case 6:
9449
9584
{
9450
9585
9451
// Array of basisvalues.
9586
// Array of basisvalues
9452
9587
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9453
9588
9454
// Declare helper variables.
9589
// Declare helper variables
9455
9590
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9456
9591
double tmp1 = (1.0 - Y)/2.0;
9457
9592
double tmp2 = tmp1*tmp1;
9458
9593
9459
// Compute basisvalues.
9594
// Compute basisvalues
9460
9595
basisvalues[0] = 1.0;
9461
9596
basisvalues[1] = tmp0;
9462
9597
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9470
9605
basisvalues[4] *= std::sqrt(4.5);
9471
9606
basisvalues[3] *= std::sqrt(7.5);
9472
9607
9473
// Table(s) of coefficients.
9608
// Table(s) of coefficients
9474
9609
static const double coefficients0[6] = \
9475
9610
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
9476
9611
9477
// Compute value(s).
9612
// Compute value(s)
9478
9613
for (unsigned int r = 0; r < 6; r++)
9479
9614
{
9480
9615
values[2] += coefficients0[r]*basisvalues[r];
9484
9619
case 7:
9485
9620
{
9486
9621
9487
// Array of basisvalues.
9622
// Array of basisvalues
9488
9623
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9489
9624
9490
// Declare helper variables.
9625
// Declare helper variables
9491
9626
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9492
9627
double tmp1 = (1.0 - Y)/2.0;
9493
9628
double tmp2 = tmp1*tmp1;
9494
9629
9495
// Compute basisvalues.
9630
// Compute basisvalues
9496
9631
basisvalues[0] = 1.0;
9497
9632
basisvalues[1] = tmp0;
9498
9633
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9506
9641
basisvalues[4] *= std::sqrt(4.5);
9507
9642
basisvalues[3] *= std::sqrt(7.5);
9508
9643
9509
// Table(s) of coefficients.
9644
// Table(s) of coefficients
9510
9645
static const double coefficients0[6] = \
9511
9646
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
9512
9647
9513
// Compute value(s).
9648
// Compute value(s)
9514
9649
for (unsigned int r = 0; r < 6; r++)
9515
9650
{
9516
9651
values[2] += coefficients0[r]*basisvalues[r];
9520
9655
case 8:
9521
9656
{
9522
9657
9523
// Array of basisvalues.
9658
// Array of basisvalues
9524
9659
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9525
9660
9526
// Declare helper variables.
9661
// Declare helper variables
9527
9662
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9528
9663
double tmp1 = (1.0 - Y)/2.0;
9529
9664
double tmp2 = tmp1*tmp1;
9530
9665
9531
// Compute basisvalues.
9666
// Compute basisvalues
9532
9667
basisvalues[0] = 1.0;
9533
9668
basisvalues[1] = tmp0;
9534
9669
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9550
9685
basisvalues[7] *= std::sqrt(10.0);
9551
9686
basisvalues[6] *= std::sqrt(14.0);
9552
9687
9553
// Table(s) of coefficients.
9688
// Table(s) of coefficients
9554
9689
static const double coefficients0[10] = \
9555
9690
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
9556
9691
9557
9692
static const double coefficients1[10] = \
9558
9693
{0.14142136, -0.038490018, 0.13333333, 0.069552071, -0.12121831, 0.089425816, 0.0, 0.06023386, -0.077761579, 0.053874802};
9559
9694
9560
// Compute value(s).
9695
// Compute value(s)
9561
9696
for (unsigned int r = 0; r < 10; r++)
9562
9697
{
9563
9698
values[3] += coefficients0[r]*basisvalues[r];
9564
9699
values[4] += coefficients1[r]*basisvalues[r];
9565
9700
}// end loop over 'r'
9566
9701
9567
// Using contravariant Piola transform to map values back to the physical element.
9702
// Using contravariant Piola transform to map values back to the physical element
9568
9703
const double tmp_ref0 = values[3];
9569
9704
const double tmp_ref1 = values[4];
9570
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9571
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9705
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9706
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9572
9707
break;
9573
9708
}
9574
9709
case 9:
9575
9710
{
9576
9711
9577
// Array of basisvalues.
9712
// Array of basisvalues
9578
9713
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9579
9714
9580
// Declare helper variables.
9715
// Declare helper variables
9581
9716
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9582
9717
double tmp1 = (1.0 - Y)/2.0;
9583
9718
double tmp2 = tmp1*tmp1;
9584
9719
9585
// Compute basisvalues.
9720
// Compute basisvalues
9586
9721
basisvalues[0] = 1.0;
9587
9722
basisvalues[1] = tmp0;
9588
9723
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9604
9739
basisvalues[7] *= std::sqrt(10.0);
9605
9740
basisvalues[6] *= std::sqrt(14.0);
9606
9741
9607
// Table(s) of coefficients.
9742
// Table(s) of coefficients
9608
9743
static const double coefficients0[10] = \
9609
9744
{-0.18856181, -0.25018512, 0.23333333, -0.10432811, 0.32324881, -0.25661321, 0.0, 0.12046772, -0.15552316, 0.1077496};
9610
9745
9611
9746
static const double coefficients1[10] = \
9612
9747
{-0.18856181, 0.076980036, -0.33333333, 0.0, 0.24243661, -0.34992711, 0.0, 0.0, 0.15552316, -0.16162441};
9613
9748
9614
// Compute value(s).
9749
// Compute value(s)
9615
9750
for (unsigned int r = 0; r < 10; r++)
9616
9751
{
9617
9752
values[3] += coefficients0[r]*basisvalues[r];
9618
9753
values[4] += coefficients1[r]*basisvalues[r];
9619
9754
}// end loop over 'r'
9620
9755
9621
// Using contravariant Piola transform to map values back to the physical element.
9756
// Using contravariant Piola transform to map values back to the physical element
9622
9757
const double tmp_ref0 = values[3];
9623
9758
const double tmp_ref1 = values[4];
9624
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9625
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9759
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9760
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9626
9761
break;
9627
9762
}
9628
9763
case 10:
9629
9764
{
9630
9765
9631
// Array of basisvalues.
9766
// Array of basisvalues
9632
9767
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9633
9768
9634
// Declare helper variables.
9769
// Declare helper variables
9635
9770
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9636
9771
double tmp1 = (1.0 - Y)/2.0;
9637
9772
double tmp2 = tmp1*tmp1;
9638
9773
9639
// Compute basisvalues.
9774
// Compute basisvalues
9640
9775
basisvalues[0] = 1.0;
9641
9776
basisvalues[1] = tmp0;
9642
9777
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9658
9793
basisvalues[7] *= std::sqrt(10.0);
9659
9794
basisvalues[6] *= std::sqrt(14.0);
9660
9795
9661
// Table(s) of coefficients.
9796
// Table(s) of coefficients
9662
9797
static const double coefficients0[10] = \
9663
9798
{0.14142136, 0.096225045, -0.1, 0.0, -0.067343503, 0.15163508, 0.0, 0.0, 0.077761579, -0.080812204};
9664
9799
9665
9800
static const double coefficients1[10] = \
9666
9801
{0.18856181, 0.0, 0.33333333, 0.0, 0.0, 0.34992711, 0.0, 0.0, 0.0, 0.16162441};
9667
9802
9668
// Compute value(s).
9803
// Compute value(s)
9669
9804
for (unsigned int r = 0; r < 10; r++)
9670
9805
{
9671
9806
values[3] += coefficients0[r]*basisvalues[r];
9672
9807
values[4] += coefficients1[r]*basisvalues[r];
9673
9808
}// end loop over 'r'
9674
9809
9675
// Using contravariant Piola transform to map values back to the physical element.
9810
// Using contravariant Piola transform to map values back to the physical element
9676
9811
const double tmp_ref0 = values[3];
9677
9812
const double tmp_ref1 = values[4];
9678
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9679
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9813
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9814
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9680
9815
break;
9681
9816
}
9682
9817
case 11:
9683
9818
{
9684
9819
9685
// Array of basisvalues.
9820
// Array of basisvalues
9686
9821
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9687
9822
9688
// Declare helper variables.
9823
// Declare helper variables
9689
9824
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9690
9825
double tmp1 = (1.0 - Y)/2.0;
9691
9826
double tmp2 = tmp1*tmp1;
9692
9827
9693
// Compute basisvalues.
9828
// Compute basisvalues
9694
9829
basisvalues[0] = 1.0;
9695
9830
basisvalues[1] = tmp0;
9696
9831
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9712
9847
basisvalues[7] *= std::sqrt(10.0);
9713
9848
basisvalues[6] *= std::sqrt(14.0);
9714
9849
9715
// Table(s) of coefficients.
9850
// Table(s) of coefficients
9716
9851
static const double coefficients0[10] = \
9717
9852
{0.32998316, -0.25018512, -0.033333333, 0.33037234, 0.32324881, 0.20606818, -0.1069045, -0.03011693, 0.0077761579, 0.013468701};
9718
9853
9719
9854
static const double coefficients1[10] = \
9720
9855
{-0.14142136, -0.038490018, -0.13333333, -0.069552071, -0.12121831, -0.089425816, 0.0, -0.06023386, -0.077761579, -0.053874802};
9721
9856
9722
// Compute value(s).
9857
// Compute value(s)
9723
9858
for (unsigned int r = 0; r < 10; r++)
9724
9859
{
9725
9860
values[3] += coefficients0[r]*basisvalues[r];
9726
9861
values[4] += coefficients1[r]*basisvalues[r];
9727
9862
}// end loop over 'r'
9728
9863
9729
// Using contravariant Piola transform to map values back to the physical element.
9864
// Using contravariant Piola transform to map values back to the physical element
9730
9865
const double tmp_ref0 = values[3];
9731
9866
const double tmp_ref1 = values[4];
9732
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9733
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9867
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9868
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9734
9869
break;
9735
9870
}
9736
9871
case 12:
9737
9872
{
9738
9873
9739
// Array of basisvalues.
9874
// Array of basisvalues
9740
9875
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9741
9876
9742
// Declare helper variables.
9877
// Declare helper variables
9743
9878
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9744
9879
double tmp1 = (1.0 - Y)/2.0;
9745
9880
double tmp2 = tmp1*tmp1;
9746
9881
9747
// Compute basisvalues.
9882
// Compute basisvalues
9748
9883
basisvalues[0] = 1.0;
9749
9884
basisvalues[1] = tmp0;
9750
9885
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9766
9901
basisvalues[7] *= std::sqrt(10.0);
9767
9902
basisvalues[6] *= std::sqrt(14.0);
9768
9903
9769
// Table(s) of coefficients.
9904
// Table(s) of coefficients
9770
9905
static const double coefficients0[10] = \
9771
9906
{-0.37712362, 0.17320508, -0.1, -0.10432811, -0.56568542, -0.60654032, 0.0, 0.12046772, 0.0, -0.053874802};
9772
9907
9773
9908
static const double coefficients1[10] = \
9774
9909
{0.18856181, 0.076980036, 0.33333333, 0.0, 0.24243661, 0.34992711, 0.0, 0.0, 0.15552316, 0.16162441};
9775
9910
9776
// Compute value(s).
9911
// Compute value(s)
9777
9912
for (unsigned int r = 0; r < 10; r++)
9778
9913
{
9779
9914
values[3] += coefficients0[r]*basisvalues[r];
9780
9915
values[4] += coefficients1[r]*basisvalues[r];
9781
9916
}// end loop over 'r'
9782
9917
9783
// Using contravariant Piola transform to map values back to the physical element.
9918
// Using contravariant Piola transform to map values back to the physical element
9784
9919
const double tmp_ref0 = values[3];
9785
9920
const double tmp_ref1 = values[4];
9786
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9787
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9921
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9922
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9788
9923
break;
9789
9924
}
9790
9925
case 13:
9791
9926
{
9792
9927
9793
// Array of basisvalues.
9928
// Array of basisvalues
9794
9929
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9795
9930
9796
// Declare helper variables.
9931
// Declare helper variables
9797
9932
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9798
9933
double tmp1 = (1.0 - Y)/2.0;
9799
9934
double tmp2 = tmp1*tmp1;
9800
9935
9801
// Compute basisvalues.
9936
// Compute basisvalues
9802
9937
basisvalues[0] = 1.0;
9803
9938
basisvalues[1] = tmp0;
9804
9939
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9820
9955
basisvalues[7] *= std::sqrt(10.0);
9821
9956
basisvalues[6] *= std::sqrt(14.0);
9822
9957
9823
// Table(s) of coefficients.
9958
// Table(s) of coefficients
9824
9959
static const double coefficients0[10] = \
9825
9960
{0.32998316, -0.096225045, 0.23333333, 0.0, 0.067343503, 0.50156219, 0.0, 0.0, -0.077761579, 0.080812204};
9826
9961
9827
9962
static const double coefficients1[10] = \
9828
9963
{-0.18856181, 0.0, -0.33333333, 0.0, 0.0, -0.34992711, 0.0, 0.0, 0.0, -0.16162441};
9829
9964
9830
// Compute value(s).
9965
// Compute value(s)
9831
9966
for (unsigned int r = 0; r < 10; r++)
9832
9967
{
9833
9968
values[3] += coefficients0[r]*basisvalues[r];
9834
9969
values[4] += coefficients1[r]*basisvalues[r];
9835
9970
}// end loop over 'r'
9836
9971
9837
// Using contravariant Piola transform to map values back to the physical element.
9972
// Using contravariant Piola transform to map values back to the physical element
9838
9973
const double tmp_ref0 = values[3];
9839
9974
const double tmp_ref1 = values[4];
9840
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9841
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
9975
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
9976
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9842
9977
break;
9843
9978
}
9844
9979
case 14:
9845
9980
{
9846
9981
9847
// Array of basisvalues.
9982
// Array of basisvalues
9848
9983
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9849
9984
9850
// Declare helper variables.
9985
// Declare helper variables
9851
9986
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9852
9987
double tmp1 = (1.0 - Y)/2.0;
9853
9988
double tmp2 = tmp1*tmp1;
9854
9989
9855
// Compute basisvalues.
9990
// Compute basisvalues
9856
9991
basisvalues[0] = 1.0;
9857
9992
basisvalues[1] = tmp0;
9858
9993
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9874
10009
basisvalues[7] *= std::sqrt(10.0);
9875
10010
basisvalues[6] *= std::sqrt(14.0);
9876
10011
9877
// Table(s) of coefficients.
10012
// Table(s) of coefficients
9878
10013
static const double coefficients0[10] = \
9879
10014
{0.14142136, 0.13471506, -0.033333333, 0.15649216, 0.053874802, 0.011664237, 0.1069045, 0.03011693, -0.0077761579, -0.013468701};
9880
10015
9881
10016
static const double coefficients1[10] = \
9882
10017
{-0.32998316, 0.15396007, 0.2, -0.41731242, -0.25590531, -0.12830661, 0.0, 0.06023386, 0.077761579, 0.053874802};
9883
10018
9884
// Compute value(s).
10019
// Compute value(s)
9885
10020
for (unsigned int r = 0; r < 10; r++)
9886
10021
{
9887
10022
values[3] += coefficients0[r]*basisvalues[r];
9888
10023
values[4] += coefficients1[r]*basisvalues[r];
9889
10024
}// end loop over 'r'
9890
10025
9891
// Using contravariant Piola transform to map values back to the physical element.
10026
// Using contravariant Piola transform to map values back to the physical element
9892
10027
const double tmp_ref0 = values[3];
9893
10028
const double tmp_ref1 = values[4];
9894
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9895
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10029
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10030
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9896
10031
break;
9897
10032
}
9898
10033
case 15:
9899
10034
{
9900
10035
9901
// Array of basisvalues.
10036
// Array of basisvalues
9902
10037
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9903
10038
9904
// Declare helper variables.
10039
// Declare helper variables
9905
10040
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9906
10041
double tmp1 = (1.0 - Y)/2.0;
9907
10042
double tmp2 = tmp1*tmp1;
9908
10043
9909
// Compute basisvalues.
10044
// Compute basisvalues
9910
10045
basisvalues[0] = 1.0;
9911
10046
basisvalues[1] = tmp0;
9912
10047
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9928
10063
basisvalues[7] *= std::sqrt(10.0);
9929
10064
basisvalues[6] *= std::sqrt(14.0);
9930
10065
9931
// Table(s) of coefficients.
10066
// Table(s) of coefficients
9932
10067
static const double coefficients0[10] = \
9933
10068
{-0.18856181, -0.32716515, 0.1, -0.41731242, 0.080812204, 0.023328474, -0.21380899, 0.06023386, 0.015552316, -0.026937401};
9934
10069
9935
10070
static const double coefficients1[10] = \
9936
10071
{0.37712362, 0.0, -0.2, 0.83462485, 0.0, -0.046656947, 0.0, -0.12046772, 0.0, 0.053874802};
9937
10072
9938
// Compute value(s).
10073
// Compute value(s)
9939
10074
for (unsigned int r = 0; r < 10; r++)
9940
10075
{
9941
10076
values[3] += coefficients0[r]*basisvalues[r];
9942
10077
values[4] += coefficients1[r]*basisvalues[r];
9943
10078
}// end loop over 'r'
9944
10079
9945
// Using contravariant Piola transform to map values back to the physical element.
10080
// Using contravariant Piola transform to map values back to the physical element
9946
10081
const double tmp_ref0 = values[3];
9947
10082
const double tmp_ref1 = values[4];
9948
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
9949
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10083
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10084
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
9950
10085
break;
9951
10086
}
9952
10087
case 16:
9953
10088
{
9954
10089
9955
// Array of basisvalues.
10090
// Array of basisvalues
9956
10091
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9957
10092
9958
// Declare helper variables.
10093
// Declare helper variables
9959
10094
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
9960
10095
double tmp1 = (1.0 - Y)/2.0;
9961
10096
double tmp2 = tmp1*tmp1;
9962
10097
9963
// Compute basisvalues.
10098
// Compute basisvalues
9964
10099
basisvalues[0] = 1.0;
9965
10100
basisvalues[1] = tmp0;
9966
10101
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
9982
10117
basisvalues[7] *= std::sqrt(10.0);
9983
10118
basisvalues[6] *= std::sqrt(14.0);
9984
10119
9985
// Table(s) of coefficients.
10120
// Table(s) of coefficients
9986
10121
static const double coefficients0[10] = \
9987
10122
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
9988
10123
9989
10124
static const double coefficients1[10] = \
9990
10125
{-0.32998316, -0.15396007, 0.2, -0.41731242, 0.25590531, -0.12830661, 0.0, 0.06023386, -0.077761579, 0.053874802};
9991
10126
9992
// Compute value(s).
10127
// Compute value(s)
9993
10128
for (unsigned int r = 0; r < 10; r++)
9994
10129
{
9995
10130
values[3] += coefficients0[r]*basisvalues[r];
9996
10131
values[4] += coefficients1[r]*basisvalues[r];
9997
10132
}// end loop over 'r'
9998
10133
9999
// Using contravariant Piola transform to map values back to the physical element.
10134
// Using contravariant Piola transform to map values back to the physical element
10000
10135
const double tmp_ref0 = values[3];
10001
10136
const double tmp_ref1 = values[4];
10002
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10003
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10137
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10138
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10004
10139
break;
10005
10140
}
10006
10141
case 17:
10007
10142
{
10008
10143
10009
// Array of basisvalues.
10144
// Array of basisvalues
10010
10145
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10011
10146
10012
// Declare helper variables.
10147
// Declare helper variables
10013
10148
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10014
10149
double tmp1 = (1.0 - Y)/2.0;
10015
10150
double tmp2 = tmp1*tmp1;
10016
10151
10017
// Compute basisvalues.
10152
// Compute basisvalues
10018
10153
basisvalues[0] = 1.0;
10019
10154
basisvalues[1] = tmp0;
10020
10155
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10036
10171
basisvalues[7] *= std::sqrt(10.0);
10037
10172
basisvalues[6] *= std::sqrt(14.0);
10038
10173
10039
// Table(s) of coefficients.
10174
// Table(s) of coefficients
10040
10175
static const double coefficients0[10] = \
10041
10176
{0.32998316, -0.69282032, -0.53333333, -0.39992441, -0.026937401, 0.20606818, 0.32071349, -0.03011693, -0.023328474, 0.013468701};
10042
10177
10043
10178
static const double coefficients1[10] = \
10044
10179
{0.23570226, 0.038490018, 0.066666667, 0.20865621, 0.12121831, -0.081649658, 0.0, 0.18070158, 0.077761579, 0.0};
10045
10180
10046
// Compute value(s).
10181
// Compute value(s)
10047
10182
for (unsigned int r = 0; r < 10; r++)
10048
10183
{
10049
10184
values[3] += coefficients0[r]*basisvalues[r];
10050
10185
values[4] += coefficients1[r]*basisvalues[r];
10051
10186
}// end loop over 'r'
10052
10187
10053
// Using contravariant Piola transform to map values back to the physical element.
10188
// Using contravariant Piola transform to map values back to the physical element
10054
10189
const double tmp_ref0 = values[3];
10055
10190
const double tmp_ref1 = values[4];
10056
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10057
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10191
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10192
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10058
10193
break;
10059
10194
}
10060
10195
case 18:
10061
10196
{
10062
10197
10063
// Array of basisvalues.
10198
// Array of basisvalues
10064
10199
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10065
10200
10066
// Declare helper variables.
10201
// Declare helper variables
10067
10202
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10068
10203
double tmp1 = (1.0 - Y)/2.0;
10069
10204
double tmp2 = tmp1*tmp1;
10070
10205
10071
// Compute basisvalues.
10206
// Compute basisvalues
10072
10207
basisvalues[0] = 1.0;
10073
10208
basisvalues[1] = tmp0;
10074
10209
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10090
10225
basisvalues[7] *= std::sqrt(10.0);
10091
10226
basisvalues[6] *= std::sqrt(14.0);
10092
10227
10093
// Table(s) of coefficients.
10228
// Table(s) of coefficients
10094
10229
static const double coefficients0[10] = \
10095
10230
{0.56568542, 0.65433031, -0.46666667, -0.19126819, -0.094280904, 0.12441853, -0.32071349, 0.15058465, -0.054433105, 0.013468701};
10096
10231
10097
10232
static const double coefficients1[10] = \
10098
10233
{-0.23570226, 0.038490018, -0.066666667, -0.20865621, 0.12121831, 0.081649658, 0.0, -0.18070158, 0.077761579, 0.0};
10099
10234
10100
// Compute value(s).
10235
// Compute value(s)
10101
10236
for (unsigned int r = 0; r < 10; r++)
10102
10237
{
10103
10238
values[3] += coefficients0[r]*basisvalues[r];
10104
10239
values[4] += coefficients1[r]*basisvalues[r];
10105
10240
}// end loop over 'r'
10106
10241
10107
// Using contravariant Piola transform to map values back to the physical element.
10242
// Using contravariant Piola transform to map values back to the physical element
10108
10243
const double tmp_ref0 = values[3];
10109
10244
const double tmp_ref1 = values[4];
10110
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10111
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10245
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10246
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10112
10247
break;
10113
10248
}
10114
10249
case 19:
10115
10250
{
10116
10251
10117
// Array of basisvalues.
10252
// Array of basisvalues
10118
10253
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10119
10254
10120
// Declare helper variables.
10255
// Declare helper variables
10121
10256
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10122
10257
double tmp1 = (1.0 - Y)/2.0;
10123
10258
double tmp2 = tmp1*tmp1;
10124
10259
10125
// Compute basisvalues.
10260
// Compute basisvalues
10126
10261
basisvalues[0] = 1.0;
10127
10262
basisvalues[1] = tmp0;
10128
10263
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10144
10279
basisvalues[7] *= std::sqrt(10.0);
10145
10280
basisvalues[6] *= std::sqrt(14.0);
10146
10281
10147
// Table(s) of coefficients.
10282
// Table(s) of coefficients
10148
10283
static const double coefficients0[10] = \
10149
10284
{0.094280904, 0.076980036, 0.93333333, 0.20865621, 0.24243661, -0.443241, 0.0, -0.24093544, 0.15552316, -0.053874802};
10150
10285
10151
10286
static const double coefficients1[10] = \
10152
10287
{0.0, -0.15396007, 0.0, 0.0, -0.48487322, 0.0, 0.0, 0.0, -0.31104632, 0.0};
10153
10288
10154
// Compute value(s).
10289
// Compute value(s)
10155
10290
for (unsigned int r = 0; r < 10; r++)
10156
10291
{
10157
10292
values[3] += coefficients0[r]*basisvalues[r];
10158
10293
values[4] += coefficients1[r]*basisvalues[r];
10159
10294
}// end loop over 'r'
10160
10295
10161
// Using contravariant Piola transform to map values back to the physical element.
10296
// Using contravariant Piola transform to map values back to the physical element
10162
10297
const double tmp_ref0 = values[3];
10163
10298
const double tmp_ref1 = values[4];
10164
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10165
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10299
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10300
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10166
10301
break;
10167
10302
}
10168
10303
case 20:
10169
10304
{
10170
10305
10171
// Array of basisvalues.
10306
// Array of basisvalues
10172
10307
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10173
10308
10174
// Declare helper variables.
10309
// Declare helper variables
10175
10310
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10176
10311
double tmp1 = (1.0 - Y)/2.0;
10177
10312
double tmp2 = tmp1*tmp1;
10178
10313
10179
// Compute basisvalues.
10314
// Compute basisvalues
10180
10315
basisvalues[0] = 1.0;
10181
10316
basisvalues[1] = tmp0;
10182
10317
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10198
10333
basisvalues[7] *= std::sqrt(10.0);
10199
10334
basisvalues[6] *= std::sqrt(14.0);
10200
10335
10201
// Table(s) of coefficients.
10336
// Table(s) of coefficients
10202
10337
static const double coefficients0[10] = \
10203
10338
{0.23570226, 0.076980036, 0.0, 0.052164053, 0.24243661, 0.058321184, 0.1069045, 0.15058465, -0.0077761579, -0.067343503};
10204
10339
10205
10340
static const double coefficients1[10] = \
10206
10341
{0.32998316, -0.80829038, -0.33333333, 0.069552071, -0.39059232, -0.21384434, 0.0, 0.06023386, 0.23328474, 0.21549921};
10207
10342
10208
// Compute value(s).
10343
// Compute value(s)
10209
10344
for (unsigned int r = 0; r < 10; r++)
10210
10345
{
10211
10346
values[3] += coefficients0[r]*basisvalues[r];
10212
10347
values[4] += coefficients1[r]*basisvalues[r];
10213
10348
}// end loop over 'r'
10214
10349
10215
// Using contravariant Piola transform to map values back to the physical element.
10350
// Using contravariant Piola transform to map values back to the physical element
10216
10351
const double tmp_ref0 = values[3];
10217
10352
const double tmp_ref1 = values[4];
10218
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10219
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10353
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10354
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10220
10355
break;
10221
10356
}
10222
10357
case 21:
10223
10358
{
10224
10359
10225
// Array of basisvalues.
10360
// Array of basisvalues
10226
10361
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10227
10362
10228
// Declare helper variables.
10363
// Declare helper variables
10229
10364
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10230
10365
double tmp1 = (1.0 - Y)/2.0;
10231
10366
double tmp2 = tmp1*tmp1;
10232
10367
10233
// Compute basisvalues.
10368
// Compute basisvalues
10234
10369
basisvalues[0] = 1.0;
10235
10370
basisvalues[1] = tmp0;
10236
10371
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10252
10387
basisvalues[7] *= std::sqrt(10.0);
10253
10388
basisvalues[6] *= std::sqrt(14.0);
10254
10389
10255
// Table(s) of coefficients.
10390
// Table(s) of coefficients
10256
10391
static const double coefficients0[10] = \
10257
10392
{0.0, -0.076980036, -0.13333333, -0.31298432, -0.24243661, 0.27994168, -0.21380899, -0.06023386, 0.17107547, -0.13468701};
10258
10393
10259
10394
static const double coefficients1[10] = \
10260
10395
{0.094280904, 0.84678039, -0.4, -0.13910414, 0.51181062, -0.13219468, 0.0, -0.12046772, -0.15552316, 0.21549921};
10261
10396
10262
// Compute value(s).
10397
// Compute value(s)
10263
10398
for (unsigned int r = 0; r < 10; r++)
10264
10399
{
10265
10400
values[3] += coefficients0[r]*basisvalues[r];
10266
10401
values[4] += coefficients1[r]*basisvalues[r];
10267
10402
}// end loop over 'r'
10268
10403
10269
// Using contravariant Piola transform to map values back to the physical element.
10404
// Using contravariant Piola transform to map values back to the physical element
10270
10405
const double tmp_ref0 = values[3];
10271
10406
const double tmp_ref1 = values[4];
10272
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10273
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10407
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10408
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10274
10409
break;
10275
10410
}
10276
10411
case 22:
10277
10412
{
10278
10413
10279
// Array of basisvalues.
10414
// Array of basisvalues
10280
10415
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10281
10416
10282
// Declare helper variables.
10417
// Declare helper variables
10283
10418
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10284
10419
double tmp1 = (1.0 - Y)/2.0;
10285
10420
double tmp2 = tmp1*tmp1;
10286
10421
10287
// Compute basisvalues.
10422
// Compute basisvalues
10288
10423
basisvalues[0] = 1.0;
10289
10424
basisvalues[1] = tmp0;
10290
10425
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10306
10441
basisvalues[7] *= std::sqrt(10.0);
10307
10442
basisvalues[6] *= std::sqrt(14.0);
10308
10443
10309
// Table(s) of coefficients.
10444
// Table(s) of coefficients
10310
10445
static const double coefficients0[10] = \
10311
10446
{-0.23570226, -0.038490018, 0.066666667, 0.10432811, -0.12121831, -0.19829203, 0.0, -0.12046772, -0.077761579, 0.13468701};
10312
10447
10313
10448
static const double coefficients1[10] = \
10314
10449
{0.56568542, -0.076980036, 0.8, 0.0, -0.24243661, -0.046656947, 0.0, 0.0, -0.15552316, -0.32324881};
10315
10450
10316
// Compute value(s).
10451
// Compute value(s)
10317
10452
for (unsigned int r = 0; r < 10; r++)
10318
10453
{
10319
10454
values[3] += coefficients0[r]*basisvalues[r];
10320
10455
values[4] += coefficients1[r]*basisvalues[r];
10321
10456
}// end loop over 'r'
10322
10457
10323
// Using contravariant Piola transform to map values back to the physical element.
10458
// Using contravariant Piola transform to map values back to the physical element
10324
10459
const double tmp_ref0 = values[3];
10325
10460
const double tmp_ref1 = values[4];
10326
values[3] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
10327
values[4] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
10461
values[3] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
10462
values[4] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
10328
10463
break;
10329
10464
}
10330
10465
}
10331
10466
10332
10467
}
10333
10468
10334
/// Evaluate all basis functions at given point in cell
10469
/// Evaluate all basis functions at given point x in cell
10335
10470
virtual void evaluate_basis_all(double* values,
10336
const double* coordinates,
10337
const ufc::cell& c) const
10471
const double* x,
10472
const double* vertex_coordinates,
10473
int cell_orientation) const
10338
10474
{
10339
10475
// Helper variable to hold values of a single dof.
10340
10476
double dof_values[5] = {0.0, 0.0, 0.0, 0.0, 0.0};
10341
10477
10342
// Loop dofs and call evaluate_basis.
10478
// Loop dofs and call evaluate_basis
10343
10479
for (unsigned int r = 0; r < 23; r++)
10344
10480
{
10345
evaluate_basis(r, dof_values, coordinates, c);
10481
evaluate_basis(r, dof_values, x, vertex_coordinates, cell_orientation);
10346
10482
for (unsigned int s = 0; s < 5; s++)
10347
10483
{
10348
10484
values[r*5 + s] = dof_values[s];
10350
10486
}// end loop over 'r'
10351
10487
}
10352
10488
10353
/// Evaluate order n derivatives of basis function i at given point in cell
10354
virtual void evaluate_basis_derivatives(unsigned int i,
10355
unsigned int n,
10489
/// Evaluate order n derivatives of basis function i at given point x in cell
10490
virtual void evaluate_basis_derivatives(std::size_t i,
10491
std::size_t n,
10356
10492
double* values,
10357
const double* coordinates,
10358
const ufc::cell& c) const
10493
const double* x,
10494
const double* vertex_coordinates,
10495
int cell_orientation) const
10359
10496
{
10360
// Extract vertex coordinates
10361
const double * const * x = c.coordinates;
10362
10363
// Compute Jacobian of affine map from reference cell
10364
const double J_00 = x[1][0] - x[0][0];
10365
const double J_01 = x[2][0] - x[0][0];
10366
const double J_10 = x[1][1] - x[0][1];
10367
const double J_11 = x[2][1] - x[0][1];
10368
10369
// Compute determinant of Jacobian
10370
double detJ = J_00*J_11 - J_01*J_10;
10371
10372
// Compute inverse of Jacobian
10373
const double K_00 = J_11 / detJ;
10374
const double K_01 = -J_01 / detJ;
10375
const double K_10 = -J_10 / detJ;
10376
const double K_11 = J_00 / detJ;
10497
// Compute Jacobian
10498
double J[4];
10499
compute_jacobian_triangle_2d(J, vertex_coordinates);
10500
10501
// Compute Jacobian inverse and determinant
10502
double K[4];
10503
double detJ;
10504
compute_jacobian_inverse_triangle_2d(K, detJ, J);
10505
10506
10377
10507
10378
10508
// Compute constants
10379
const double C0 = x[1][0] + x[2][0];
10380
const double C1 = x[1][1] + x[2][1];
10509
const double C0 = vertex_coordinates[2] + vertex_coordinates[4];
10510
const double C1 = vertex_coordinates[3] + vertex_coordinates[5];
10381
10511
10382
10512
// Get coordinates and map to the reference (FIAT) element
10383
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
10384
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
10513
double X = (J[1]*(C1 - 2.0*x[1]) + J[3]*(2.0*x[0] - C0)) / detJ;
10514
double Y = (J[0]*(2.0*x[1] - C1) + J[2]*(C0 - 2.0*x[0])) / detJ;
10385
10515
10386
10516
// Compute number of derivatives.
10387
10517
unsigned int num_derivatives = 1;
10418
10548
}
10419
10549
10420
10550
// Compute inverse of Jacobian
10421
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
10551
const double Jinv[2][2] = {{K[0], K[1]}, {K[2], K[3]}};
10422
10552
10423
10553
// Declare transformation matrix
10424
10554
// Declare pointer to two dimensional array and initialise
10452
10582
case 0:
10453
10583
{
10454
10584
10455
// Array of basisvalues.
10585
// Array of basisvalues
10456
10586
double basisvalues[1] = {0.0};
10457
10587
10458
// Declare helper variables.
10588
// Declare helper variables
10459
10589
10460
// Compute basisvalues.
10590
// Compute basisvalues
10461
10591
basisvalues[0] = 1.0;
10462
10592
10463
// Table(s) of coefficients.
10593
// Table(s) of coefficients
10464
10594
static const double coefficients0[1] = \
10465
10595
{1.0};
10466
10596
10584
10714
case 1:
10585
10715
{
10586
10716
10587
// Array of basisvalues.
10717
// Array of basisvalues
10588
10718
double basisvalues[1] = {0.0};
10589
10719
10590
// Declare helper variables.
10720
// Declare helper variables
10591
10721
10592
// Compute basisvalues.
10722
// Compute basisvalues
10593
10723
basisvalues[0] = 1.0;
10594
10724
10595
// Table(s) of coefficients.
10725
// Table(s) of coefficients
10596
10726
static const double coefficients0[1] = \
10597
10727
{1.0};
10598
10728
10716
10846
case 2:
10717
10847
{
10718
10848
10719
// Array of basisvalues.
10849
// Array of basisvalues
10720
10850
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10721
10851
10722
// Declare helper variables.
10852
// Declare helper variables
10723
10853
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10724
10854
double tmp1 = (1.0 - Y)/2.0;
10725
10855
double tmp2 = tmp1*tmp1;
10726
10856
10727
// Compute basisvalues.
10857
// Compute basisvalues
10728
10858
basisvalues[0] = 1.0;
10729
10859
basisvalues[1] = tmp0;
10730
10860
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10738
10868
basisvalues[4] *= std::sqrt(4.5);
10739
10869
basisvalues[3] *= std::sqrt(7.5);
10740
10870
10741
// Table(s) of coefficients.
10871
// Table(s) of coefficients
10742
10872
static const double coefficients0[6] = \
10743
10873
{0.0, -0.17320508, -0.1, 0.12171612, 0.094280904, 0.054433105};
10744
10874
10882
11012
case 3:
10883
11013
{
10884
11014
10885
// Array of basisvalues.
11015
// Array of basisvalues
10886
11016
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10887
11017
10888
// Declare helper variables.
11018
// Declare helper variables
10889
11019
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
10890
11020
double tmp1 = (1.0 - Y)/2.0;
10891
11021
double tmp2 = tmp1*tmp1;
10892
11022
10893
// Compute basisvalues.
11023
// Compute basisvalues
10894
11024
basisvalues[0] = 1.0;
10895
11025
basisvalues[1] = tmp0;
10896
11026
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
10904
11034
basisvalues[4] *= std::sqrt(4.5);
10905
11035
basisvalues[3] *= std::sqrt(7.5);
10906
11036
10907
// Table(s) of coefficients.
11037
// Table(s) of coefficients
10908
11038
static const double coefficients0[6] = \
10909
11039
{0.0, 0.17320508, -0.1, 0.12171612, -0.094280904, 0.054433105};
10910
11040
11048
11178
case 4:
11049
11179
{
11050
11180
11051
// Array of basisvalues.
11181
// Array of basisvalues
11052
11182
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11053
11183
11054
// Declare helper variables.
11184
// Declare helper variables
11055
11185
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11056
11186
double tmp1 = (1.0 - Y)/2.0;
11057
11187
double tmp2 = tmp1*tmp1;
11058
11188
11059
// Compute basisvalues.
11189
// Compute basisvalues
11060
11190
basisvalues[0] = 1.0;
11061
11191
basisvalues[1] = tmp0;
11062
11192
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11070
11200
basisvalues[4] *= std::sqrt(4.5);
11071
11201
basisvalues[3] *= std::sqrt(7.5);
11072
11202
11073
// Table(s) of coefficients.
11203
// Table(s) of coefficients
11074
11204
static const double coefficients0[6] = \
11075
11205
{0.0, 0.0, 0.2, 0.0, 0.0, 0.16329932};
11076
11206
11214
11344
case 5:
11215
11345
{
11216
11346
11217
// Array of basisvalues.
11347
// Array of basisvalues
11218
11348
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11219
11349
11220
// Declare helper variables.
11350
// Declare helper variables
11221
11351
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11222
11352
double tmp1 = (1.0 - Y)/2.0;
11223
11353
double tmp2 = tmp1*tmp1;
11224
11354
11225
// Compute basisvalues.
11355
// Compute basisvalues
11226
11356
basisvalues[0] = 1.0;
11227
11357
basisvalues[1] = tmp0;
11228
11358
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11236
11366
basisvalues[4] *= std::sqrt(4.5);
11237
11367
basisvalues[3] *= std::sqrt(7.5);
11238
11368
11239
// Table(s) of coefficients.
11369
// Table(s) of coefficients
11240
11370
static const double coefficients0[6] = \
11241
11371
{0.47140452, 0.23094011, 0.13333333, 0.0, 0.18856181, -0.16329932};
11242
11372
11380
11510
case 6:
11381
11511
{
11382
11512
11383
// Array of basisvalues.
11513
// Array of basisvalues
11384
11514
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11385
11515
11386
// Declare helper variables.
11516
// Declare helper variables
11387
11517
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11388
11518
double tmp1 = (1.0 - Y)/2.0;
11389
11519
double tmp2 = tmp1*tmp1;
11390
11520
11391
// Compute basisvalues.
11521
// Compute basisvalues
11392
11522
basisvalues[0] = 1.0;
11393
11523
basisvalues[1] = tmp0;
11394
11524
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11402
11532
basisvalues[4] *= std::sqrt(4.5);
11403
11533
basisvalues[3] *= std::sqrt(7.5);
11404
11534
11405
// Table(s) of coefficients.
11535
// Table(s) of coefficients
11406
11536
static const double coefficients0[6] = \
11407
11537
{0.47140452, -0.23094011, 0.13333333, 0.0, -0.18856181, -0.16329932};
11408
11538
11546
11676
case 7:
11547
11677
{
11548
11678
11549
// Array of basisvalues.
11679
// Array of basisvalues
11550
11680
double basisvalues[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11551
11681
11552
// Declare helper variables.
11682
// Declare helper variables
11553
11683
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11554
11684
double tmp1 = (1.0 - Y)/2.0;
11555
11685
double tmp2 = tmp1*tmp1;
11556
11686
11557
// Compute basisvalues.
11687
// Compute basisvalues
11558
11688
basisvalues[0] = 1.0;
11559
11689
basisvalues[1] = tmp0;
11560
11690
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11568
11698
basisvalues[4] *= std::sqrt(4.5);
11569
11699
basisvalues[3] *= std::sqrt(7.5);
11570
11700
11571
// Table(s) of coefficients.
11701
// Table(s) of coefficients
11572
11702
static const double coefficients0[6] = \
11573
11703
{0.47140452, 0.0, -0.26666667, -0.24343225, 0.0, 0.054433105};
11574
11704
11712
11842
case 8:
11713
11843
{
11714
11844
11715
// Array of basisvalues.
11845
// Array of basisvalues
11716
11846
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11717
11847
11718
// Declare helper variables.
11848
// Declare helper variables
11719
11849
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11720
11850
double tmp1 = (1.0 - Y)/2.0;
11721
11851
double tmp2 = tmp1*tmp1;
11722
11852
11723
// Compute basisvalues.
11853
// Compute basisvalues
11724
11854
basisvalues[0] = 1.0;
11725
11855
basisvalues[1] = tmp0;
11726
11856
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11742
11872
basisvalues[7] *= std::sqrt(10.0);
11743
11873
basisvalues[6] *= std::sqrt(14.0);
11744
11874
11745
// Table(s) of coefficients.
11875
// Table(s) of coefficients
11746
11876
static const double coefficients0[10] = \
11747
11877
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
11748
11878
11782
11912
derivatives[r] = 0.0;
11783
11913
}// end loop over 'r'
11784
11914
11915
// Declare pointer to array of reference derivatives on physical element.
11916
double *derivatives_p = new double[2*num_derivatives];
11917
for (unsigned int r = 0; r < 2*num_derivatives; r++)
11918
{
11919
derivatives_p[r] = 0.0;
11920
}// end loop over 'r'
11921
11785
11922
// Declare derivative matrix (of polynomial basis).
11786
11923
double dmats[10][10] = \
11787
11924
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
11880
12017
// Using contravariant Piola transform to map values back to the physical element.
11881
12018
const double tmp_ref0 = derivatives[r];
11882
12019
const double tmp_ref1 = derivatives[num_derivatives + r];
11883
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
11884
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
12020
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
12021
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
11885
12022
}// end loop over 'r'
11886
12023
11887
12024
// Transform derivatives back to physical element
11889
12026
{
11890
12027
for (unsigned int s = 0; s < num_derivatives; s++)
11891
12028
{
11892
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
11893
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
12029
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
12030
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
11894
12031
}// end loop over 's'
11895
12032
}// end loop over 'r'
11896
12033
11897
12034
// Delete pointer to array of derivatives on FIAT element
11898
12035
delete [] derivatives;
11899
12036
12037
// Delete pointer to array of reference derivatives on physical element.
12038
delete [] derivatives_p;
12039
11900
12040
// Delete pointer to array of combinations of derivatives and transform
11901
12041
for (unsigned int r = 0; r < num_derivatives; r++)
11902
12042
{
11913
12053
case 9:
11914
12054
{
11915
12055
11916
// Array of basisvalues.
12056
// Array of basisvalues
11917
12057
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11918
12058
11919
// Declare helper variables.
12059
// Declare helper variables
11920
12060
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
11921
12061
double tmp1 = (1.0 - Y)/2.0;
11922
12062
double tmp2 = tmp1*tmp1;
11923
12063
11924
// Compute basisvalues.
12064
// Compute basisvalues
11925
12065
basisvalues[0] = 1.0;
11926
12066
basisvalues[1] = tmp0;
11927
12067
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
11943
12083
basisvalues[7] *= std::sqrt(10.0);
11944
12084
basisvalues[6] *= std::sqrt(14.0);
11945
12085
11946
// Table(s) of coefficients.
12086
// Table(s) of coefficients
11947
12087
static const double coefficients0[10] = \
11948
12088
{-0.18856181, -0.25018512, 0.23333333, -0.10432811, 0.32324881, -0.25661321, 0.0, 0.12046772, -0.15552316, 0.1077496};
11949
12089
11983
12123
derivatives[r] = 0.0;
11984
12124
}// end loop over 'r'
11985
12125
12126
// Declare pointer to array of reference derivatives on physical element.
12127
double *derivatives_p = new double[2*num_derivatives];
12128
for (unsigned int r = 0; r < 2*num_derivatives; r++)
12129
{
12130
derivatives_p[r] = 0.0;
12131
}// end loop over 'r'
12132
11986
12133
// Declare derivative matrix (of polynomial basis).
11987
12134
double dmats[10][10] = \
11988
12135
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
12081
12228
// Using contravariant Piola transform to map values back to the physical element.
12082
12229
const double tmp_ref0 = derivatives[r];
12083
12230
const double tmp_ref1 = derivatives[num_derivatives + r];
12084
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
12085
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
12231
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
12232
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
12086
12233
}// end loop over 'r'
12087
12234
12088
12235
// Transform derivatives back to physical element
12090
12237
{
12091
12238
for (unsigned int s = 0; s < num_derivatives; s++)
12092
12239
{
12093
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
12094
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
12240
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
12241
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
12095
12242
}// end loop over 's'
12096
12243
}// end loop over 'r'
12097
12244
12098
12245
// Delete pointer to array of derivatives on FIAT element
12099
12246
delete [] derivatives;
12100
12247
12248
// Delete pointer to array of reference derivatives on physical element.
12249
delete [] derivatives_p;
12250
12101
12251
// Delete pointer to array of combinations of derivatives and transform
12102
12252
for (unsigned int r = 0; r < num_derivatives; r++)
12103
12253
{
12114
12264
case 10:
12115
12265
{
12116
12266
12117
// Array of basisvalues.
12267
// Array of basisvalues
12118
12268
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12119
12269
12120
// Declare helper variables.
12270
// Declare helper variables
12121
12271
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
12122
12272
double tmp1 = (1.0 - Y)/2.0;
12123
12273
double tmp2 = tmp1*tmp1;
12124
12274
12125
// Compute basisvalues.
12275
// Compute basisvalues
12126
12276
basisvalues[0] = 1.0;
12127
12277
basisvalues[1] = tmp0;
12128
12278
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
12144
12294
basisvalues[7] *= std::sqrt(10.0);
12145
12295
basisvalues[6] *= std::sqrt(14.0);
12146
12296
12147
// Table(s) of coefficients.
12297
// Table(s) of coefficients
12148
12298
static const double coefficients0[10] = \
12149
12299
{0.14142136, 0.096225045, -0.1, 0.0, -0.067343503, 0.15163508, 0.0, 0.0, 0.077761579, -0.080812204};
12150
12300
12184
12334
derivatives[r] = 0.0;
12185
12335
}// end loop over 'r'
12186
12336
12337
// Declare pointer to array of reference derivatives on physical element.
12338
double *derivatives_p = new double[2*num_derivatives];
12339
for (unsigned int r = 0; r < 2*num_derivatives; r++)
12340
{
12341
derivatives_p[r] = 0.0;
12342
}// end loop over 'r'
12343
12187
12344
// Declare derivative matrix (of polynomial basis).
12188
12345
double dmats[10][10] = \
12189
12346
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
12282
12439
// Using contravariant Piola transform to map values back to the physical element.
12283
12440
const double tmp_ref0 = derivatives[r];
12284
12441
const double tmp_ref1 = derivatives[num_derivatives + r];
12285
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
12286
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
12442
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
12443
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
12287
12444
}// end loop over 'r'
12288
12445
12289
12446
// Transform derivatives back to physical element
12291
12448
{
12292
12449
for (unsigned int s = 0; s < num_derivatives; s++)
12293
12450
{
12294
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
12295
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
12451
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
12452
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
12296
12453
}// end loop over 's'
12297
12454
}// end loop over 'r'
12298
12455
12299
12456
// Delete pointer to array of derivatives on FIAT element
12300
12457
delete [] derivatives;
12301
12458
12459
// Delete pointer to array of reference derivatives on physical element.
12460
delete [] derivatives_p;
12461
12302
12462
// Delete pointer to array of combinations of derivatives and transform
12303
12463
for (unsigned int r = 0; r < num_derivatives; r++)
12304
12464
{
12315
12475
case 11:
12316
12476
{
12317
12477
12318
// Array of basisvalues.
12478
// Array of basisvalues
12319
12479
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12320
12480
12321
// Declare helper variables.
12481
// Declare helper variables
12322
12482
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
12323
12483
double tmp1 = (1.0 - Y)/2.0;
12324
12484
double tmp2 = tmp1*tmp1;
12325
12485
12326
// Compute basisvalues.
12486
// Compute basisvalues
12327
12487
basisvalues[0] = 1.0;
12328
12488
basisvalues[1] = tmp0;
12329
12489
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
12345
12505
basisvalues[7] *= std::sqrt(10.0);
12346
12506
basisvalues[6] *= std::sqrt(14.0);
12347
12507
12348
// Table(s) of coefficients.
12508
// Table(s) of coefficients
12349
12509
static const double coefficients0[10] = \
12350
12510
{0.32998316, -0.25018512, -0.033333333, 0.33037234, 0.32324881, 0.20606818, -0.1069045, -0.03011693, 0.0077761579, 0.013468701};
12351
12511
12385
12545
derivatives[r] = 0.0;
12386
12546
}// end loop over 'r'
12387
12547
12548
// Declare pointer to array of reference derivatives on physical element.
12549
double *derivatives_p = new double[2*num_derivatives];
12550
for (unsigned int r = 0; r < 2*num_derivatives; r++)
12551
{
12552
derivatives_p[r] = 0.0;
12553
}// end loop over 'r'
12554
12388
12555
// Declare derivative matrix (of polynomial basis).
12389
12556
double dmats[10][10] = \
12390
12557
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
12483
12650
// Using contravariant Piola transform to map values back to the physical element.
12484
12651
const double tmp_ref0 = derivatives[r];
12485
12652
const double tmp_ref1 = derivatives[num_derivatives + r];
12486
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
12487
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
12653
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
12654
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
12488
12655
}// end loop over 'r'
12489
12656
12490
12657
// Transform derivatives back to physical element
12492
12659
{
12493
12660
for (unsigned int s = 0; s < num_derivatives; s++)
12494
12661
{
12495
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
12496
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
12662
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
12663
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
12497
12664
}// end loop over 's'
12498
12665
}// end loop over 'r'
12499
12666
12500
12667
// Delete pointer to array of derivatives on FIAT element
12501
12668
delete [] derivatives;
12502
12669
12670
// Delete pointer to array of reference derivatives on physical element.
12671
delete [] derivatives_p;
12672
12503
12673
// Delete pointer to array of combinations of derivatives and transform
12504
12674
for (unsigned int r = 0; r < num_derivatives; r++)
12505
12675
{
12516
12686
case 12:
12517
12687
{
12518
12688
12519
// Array of basisvalues.
12689
// Array of basisvalues
12520
12690
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12521
12691
12522
// Declare helper variables.
12692
// Declare helper variables
12523
12693
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
12524
12694
double tmp1 = (1.0 - Y)/2.0;
12525
12695
double tmp2 = tmp1*tmp1;
12526
12696
12527
// Compute basisvalues.
12697
// Compute basisvalues
12528
12698
basisvalues[0] = 1.0;
12529
12699
basisvalues[1] = tmp0;
12530
12700
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
12546
12716
basisvalues[7] *= std::sqrt(10.0);
12547
12717
basisvalues[6] *= std::sqrt(14.0);
12548
12718
12549
// Table(s) of coefficients.
12719
// Table(s) of coefficients
12550
12720
static const double coefficients0[10] = \
12551
12721
{-0.37712362, 0.17320508, -0.1, -0.10432811, -0.56568542, -0.60654032, 0.0, 0.12046772, 0.0, -0.053874802};
12552
12722
12586
12756
derivatives[r] = 0.0;
12587
12757
}// end loop over 'r'
12588
12758
12759
// Declare pointer to array of reference derivatives on physical element.
12760
double *derivatives_p = new double[2*num_derivatives];
12761
for (unsigned int r = 0; r < 2*num_derivatives; r++)
12762
{
12763
derivatives_p[r] = 0.0;
12764
}// end loop over 'r'
12765
12589
12766
// Declare derivative matrix (of polynomial basis).
12590
12767
double dmats[10][10] = \
12591
12768
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
12684
12861
// Using contravariant Piola transform to map values back to the physical element.
12685
12862
const double tmp_ref0 = derivatives[r];
12686
12863
const double tmp_ref1 = derivatives[num_derivatives + r];
12687
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
12688
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
12864
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
12865
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
12689
12866
}// end loop over 'r'
12690
12867
12691
12868
// Transform derivatives back to physical element
12693
12870
{
12694
12871
for (unsigned int s = 0; s < num_derivatives; s++)
12695
12872
{
12696
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
12697
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
12873
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
12874
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
12698
12875
}// end loop over 's'
12699
12876
}// end loop over 'r'
12700
12877
12701
12878
// Delete pointer to array of derivatives on FIAT element
12702
12879
delete [] derivatives;
12703
12880
12881
// Delete pointer to array of reference derivatives on physical element.
12882
delete [] derivatives_p;
12883
12704
12884
// Delete pointer to array of combinations of derivatives and transform
12705
12885
for (unsigned int r = 0; r < num_derivatives; r++)
12706
12886
{
12717
12897
case 13:
12718
12898
{
12719
12899
12720
// Array of basisvalues.
12900
// Array of basisvalues
12721
12901
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12722
12902
12723
// Declare helper variables.
12903
// Declare helper variables
12724
12904
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
12725
12905
double tmp1 = (1.0 - Y)/2.0;
12726
12906
double tmp2 = tmp1*tmp1;
12727
12907
12728
// Compute basisvalues.
12908
// Compute basisvalues
12729
12909
basisvalues[0] = 1.0;
12730
12910
basisvalues[1] = tmp0;
12731
12911
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
12747
12927
basisvalues[7] *= std::sqrt(10.0);
12748
12928
basisvalues[6] *= std::sqrt(14.0);
12749
12929
12750
// Table(s) of coefficients.
12930
// Table(s) of coefficients
12751
12931
static const double coefficients0[10] = \
12752
12932
{0.32998316, -0.096225045, 0.23333333, 0.0, 0.067343503, 0.50156219, 0.0, 0.0, -0.077761579, 0.080812204};
12753
12933
12787
12967
derivatives[r] = 0.0;
12788
12968
}// end loop over 'r'
12789
12969
12970
// Declare pointer to array of reference derivatives on physical element.
12971
double *derivatives_p = new double[2*num_derivatives];
12972
for (unsigned int r = 0; r < 2*num_derivatives; r++)
12973
{
12974
derivatives_p[r] = 0.0;
12975
}// end loop over 'r'
12976
12790
12977
// Declare derivative matrix (of polynomial basis).
12791
12978
double dmats[10][10] = \
12792
12979
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
12885
13072
// Using contravariant Piola transform to map values back to the physical element.
12886
13073
const double tmp_ref0 = derivatives[r];
12887
13074
const double tmp_ref1 = derivatives[num_derivatives + r];
12888
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
12889
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
13075
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
13076
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
12890
13077
}// end loop over 'r'
12891
13078
12892
13079
// Transform derivatives back to physical element
12894
13081
{
12895
13082
for (unsigned int s = 0; s < num_derivatives; s++)
12896
13083
{
12897
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
12898
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
13084
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
13085
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
12899
13086
}// end loop over 's'
12900
13087
}// end loop over 'r'
12901
13088
12902
13089
// Delete pointer to array of derivatives on FIAT element
12903
13090
delete [] derivatives;
12904
13091
13092
// Delete pointer to array of reference derivatives on physical element.
13093
delete [] derivatives_p;
13094
12905
13095
// Delete pointer to array of combinations of derivatives and transform
12906
13096
for (unsigned int r = 0; r < num_derivatives; r++)
12907
13097
{
12918
13108
case 14:
12919
13109
{
12920
13110
12921
// Array of basisvalues.
13111
// Array of basisvalues
12922
13112
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12923
13113
12924
// Declare helper variables.
13114
// Declare helper variables
12925
13115
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
12926
13116
double tmp1 = (1.0 - Y)/2.0;
12927
13117
double tmp2 = tmp1*tmp1;
12928
13118
12929
// Compute basisvalues.
13119
// Compute basisvalues
12930
13120
basisvalues[0] = 1.0;
12931
13121
basisvalues[1] = tmp0;
12932
13122
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
12948
13138
basisvalues[7] *= std::sqrt(10.0);
12949
13139
basisvalues[6] *= std::sqrt(14.0);
12950
13140
12951
// Table(s) of coefficients.
13141
// Table(s) of coefficients
12952
13142
static const double coefficients0[10] = \
12953
13143
{0.14142136, 0.13471506, -0.033333333, 0.15649216, 0.053874802, 0.011664237, 0.1069045, 0.03011693, -0.0077761579, -0.013468701};
12954
13144
12988
13178
derivatives[r] = 0.0;
12989
13179
}// end loop over 'r'
12990
13180
13181
// Declare pointer to array of reference derivatives on physical element.
13182
double *derivatives_p = new double[2*num_derivatives];
13183
for (unsigned int r = 0; r < 2*num_derivatives; r++)
13184
{
13185
derivatives_p[r] = 0.0;
13186
}// end loop over 'r'
13187
12991
13188
// Declare derivative matrix (of polynomial basis).
12992
13189
double dmats[10][10] = \
12993
13190
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
13086
13283
// Using contravariant Piola transform to map values back to the physical element.
13087
13284
const double tmp_ref0 = derivatives[r];
13088
13285
const double tmp_ref1 = derivatives[num_derivatives + r];
13089
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
13090
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
13286
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
13287
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
13091
13288
}// end loop over 'r'
13092
13289
13093
13290
// Transform derivatives back to physical element
13095
13292
{
13096
13293
for (unsigned int s = 0; s < num_derivatives; s++)
13097
13294
{
13098
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
13099
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
13295
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
13296
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
13100
13297
}// end loop over 's'
13101
13298
}// end loop over 'r'
13102
13299
13103
13300
// Delete pointer to array of derivatives on FIAT element
13104
13301
delete [] derivatives;
13105
13302
13303
// Delete pointer to array of reference derivatives on physical element.
13304
delete [] derivatives_p;
13305
13106
13306
// Delete pointer to array of combinations of derivatives and transform
13107
13307
for (unsigned int r = 0; r < num_derivatives; r++)
13108
13308
{
13119
13319
case 15:
13120
13320
{
13121
13321
13122
// Array of basisvalues.
13322
// Array of basisvalues
13123
13323
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13124
13324
13125
// Declare helper variables.
13325
// Declare helper variables
13126
13326
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
13127
13327
double tmp1 = (1.0 - Y)/2.0;
13128
13328
double tmp2 = tmp1*tmp1;
13129
13329
13130
// Compute basisvalues.
13330
// Compute basisvalues
13131
13331
basisvalues[0] = 1.0;
13132
13332
basisvalues[1] = tmp0;
13133
13333
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
13149
13349
basisvalues[7] *= std::sqrt(10.0);
13150
13350
basisvalues[6] *= std::sqrt(14.0);
13151
13351
13152
// Table(s) of coefficients.
13352
// Table(s) of coefficients
13153
13353
static const double coefficients0[10] = \
13154
13354
{-0.18856181, -0.32716515, 0.1, -0.41731242, 0.080812204, 0.023328474, -0.21380899, 0.06023386, 0.015552316, -0.026937401};
13155
13355
13189
13389
derivatives[r] = 0.0;
13190
13390
}// end loop over 'r'
13191
13391
13392
// Declare pointer to array of reference derivatives on physical element.
13393
double *derivatives_p = new double[2*num_derivatives];
13394
for (unsigned int r = 0; r < 2*num_derivatives; r++)
13395
{
13396
derivatives_p[r] = 0.0;
13397
}// end loop over 'r'
13398
13192
13399
// Declare derivative matrix (of polynomial basis).
13193
13400
double dmats[10][10] = \
13194
13401
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
13287
13494
// Using contravariant Piola transform to map values back to the physical element.
13288
13495
const double tmp_ref0 = derivatives[r];
13289
13496
const double tmp_ref1 = derivatives[num_derivatives + r];
13290
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
13291
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
13497
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
13498
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
13292
13499
}// end loop over 'r'
13293
13500
13294
13501
// Transform derivatives back to physical element
13296
13503
{
13297
13504
for (unsigned int s = 0; s < num_derivatives; s++)
13298
13505
{
13299
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
13300
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
13506
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
13507
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
13301
13508
}// end loop over 's'
13302
13509
}// end loop over 'r'
13303
13510
13304
13511
// Delete pointer to array of derivatives on FIAT element
13305
13512
delete [] derivatives;
13306
13513
13514
// Delete pointer to array of reference derivatives on physical element.
13515
delete [] derivatives_p;
13516
13307
13517
// Delete pointer to array of combinations of derivatives and transform
13308
13518
for (unsigned int r = 0; r < num_derivatives; r++)
13309
13519
{
13320
13530
case 16:
13321
13531
{
13322
13532
13323
// Array of basisvalues.
13533
// Array of basisvalues
13324
13534
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13325
13535
13326
// Declare helper variables.
13536
// Declare helper variables
13327
13537
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
13328
13538
double tmp1 = (1.0 - Y)/2.0;
13329
13539
double tmp2 = tmp1*tmp1;
13330
13540
13331
// Compute basisvalues.
13541
// Compute basisvalues
13332
13542
basisvalues[0] = 1.0;
13333
13543
basisvalues[1] = tmp0;
13334
13544
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
13350
13560
basisvalues[7] *= std::sqrt(10.0);
13351
13561
basisvalues[6] *= std::sqrt(14.0);
13352
13562
13353
// Table(s) of coefficients.
13563
// Table(s) of coefficients
13354
13564
static const double coefficients0[10] = \
13355
13565
{0.18856181, 0.28867513, -0.16666667, 0.26082027, -0.20203051, 0.11664237, 0.1069045, -0.09035079, 0.069985421, -0.040406102};
13356
13566
13390
13600
derivatives[r] = 0.0;
13391
13601
}// end loop over 'r'
13392
13602
13603
// Declare pointer to array of reference derivatives on physical element.
13604
double *derivatives_p = new double[2*num_derivatives];
13605
for (unsigned int r = 0; r < 2*num_derivatives; r++)
13606
{
13607
derivatives_p[r] = 0.0;
13608
}// end loop over 'r'
13609
13393
13610
// Declare derivative matrix (of polynomial basis).
13394
13611
double dmats[10][10] = \
13395
13612
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
13488
13705
// Using contravariant Piola transform to map values back to the physical element.
13489
13706
const double tmp_ref0 = derivatives[r];
13490
13707
const double tmp_ref1 = derivatives[num_derivatives + r];
13491
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
13492
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
13708
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
13709
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
13493
13710
}// end loop over 'r'
13494
13711
13495
13712
// Transform derivatives back to physical element
13497
13714
{
13498
13715
for (unsigned int s = 0; s < num_derivatives; s++)
13499
13716
{
13500
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
13501
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
13717
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
13718
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
13502
13719
}// end loop over 's'
13503
13720
}// end loop over 'r'
13504
13721
13505
13722
// Delete pointer to array of derivatives on FIAT element
13506
13723
delete [] derivatives;
13507
13724
13725
// Delete pointer to array of reference derivatives on physical element.
13726
delete [] derivatives_p;
13727
13508
13728
// Delete pointer to array of combinations of derivatives and transform
13509
13729
for (unsigned int r = 0; r < num_derivatives; r++)
13510
13730
{
13521
13741
case 17:
13522
13742
{
13523
13743
13524
// Array of basisvalues.
13744
// Array of basisvalues
13525
13745
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13526
13746
13527
// Declare helper variables.
13747
// Declare helper variables
13528
13748
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
13529
13749
double tmp1 = (1.0 - Y)/2.0;
13530
13750
double tmp2 = tmp1*tmp1;
13531
13751
13532
// Compute basisvalues.
13752
// Compute basisvalues
13533
13753
basisvalues[0] = 1.0;
13534
13754
basisvalues[1] = tmp0;
13535
13755
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
13551
13771
basisvalues[7] *= std::sqrt(10.0);
13552
13772
basisvalues[6] *= std::sqrt(14.0);
13553
13773
13554
// Table(s) of coefficients.
13774
// Table(s) of coefficients
13555
13775
static const double coefficients0[10] = \
13556
13776
{0.32998316, -0.69282032, -0.53333333, -0.39992441, -0.026937401, 0.20606818, 0.32071349, -0.03011693, -0.023328474, 0.013468701};
13557
13777
13591
13811
derivatives[r] = 0.0;
13592
13812
}// end loop over 'r'
13593
13813
13814
// Declare pointer to array of reference derivatives on physical element.
13815
double *derivatives_p = new double[2*num_derivatives];
13816
for (unsigned int r = 0; r < 2*num_derivatives; r++)
13817
{
13818
derivatives_p[r] = 0.0;
13819
}// end loop over 'r'
13820
13594
13821
// Declare derivative matrix (of polynomial basis).
13595
13822
double dmats[10][10] = \
13596
13823
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
13689
13916
// Using contravariant Piola transform to map values back to the physical element.
13690
13917
const double tmp_ref0 = derivatives[r];
13691
13918
const double tmp_ref1 = derivatives[num_derivatives + r];
13692
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
13693
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
13919
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
13920
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
13694
13921
}// end loop over 'r'
13695
13922
13696
13923
// Transform derivatives back to physical element
13698
13925
{
13699
13926
for (unsigned int s = 0; s < num_derivatives; s++)
13700
13927
{
13701
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
13702
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
13928
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
13929
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
13703
13930
}// end loop over 's'
13704
13931
}// end loop over 'r'
13705
13932
13706
13933
// Delete pointer to array of derivatives on FIAT element
13707
13934
delete [] derivatives;
13708
13935
13936
// Delete pointer to array of reference derivatives on physical element.
13937
delete [] derivatives_p;
13938
13709
13939
// Delete pointer to array of combinations of derivatives and transform
13710
13940
for (unsigned int r = 0; r < num_derivatives; r++)
13711
13941
{
13722
13952
case 18:
13723
13953
{
13724
13954
13725
// Array of basisvalues.
13955
// Array of basisvalues
13726
13956
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13727
13957
13728
// Declare helper variables.
13958
// Declare helper variables
13729
13959
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
13730
13960
double tmp1 = (1.0 - Y)/2.0;
13731
13961
double tmp2 = tmp1*tmp1;
13732
13962
13733
// Compute basisvalues.
13963
// Compute basisvalues
13734
13964
basisvalues[0] = 1.0;
13735
13965
basisvalues[1] = tmp0;
13736
13966
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
13752
13982
basisvalues[7] *= std::sqrt(10.0);
13753
13983
basisvalues[6] *= std::sqrt(14.0);
13754
13984
13755
// Table(s) of coefficients.
13985
// Table(s) of coefficients
13756
13986
static const double coefficients0[10] = \
13757
13987
{0.56568542, 0.65433031, -0.46666667, -0.19126819, -0.094280904, 0.12441853, -0.32071349, 0.15058465, -0.054433105, 0.013468701};
13758
13988
13792
14022
derivatives[r] = 0.0;
13793
14023
}// end loop over 'r'
13794
14024
14025
// Declare pointer to array of reference derivatives on physical element.
14026
double *derivatives_p = new double[2*num_derivatives];
14027
for (unsigned int r = 0; r < 2*num_derivatives; r++)
14028
{
14029
derivatives_p[r] = 0.0;
14030
}// end loop over 'r'
14031
13795
14032
// Declare derivative matrix (of polynomial basis).
13796
14033
double dmats[10][10] = \
13797
14034
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
13890
14127
// Using contravariant Piola transform to map values back to the physical element.
13891
14128
const double tmp_ref0 = derivatives[r];
13892
14129
const double tmp_ref1 = derivatives[num_derivatives + r];
13893
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
13894
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
14130
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
14131
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
13895
14132
}// end loop over 'r'
13896
14133
13897
14134
// Transform derivatives back to physical element
13899
14136
{
13900
14137
for (unsigned int s = 0; s < num_derivatives; s++)
13901
14138
{
13902
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
13903
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
14139
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
14140
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
13904
14141
}// end loop over 's'
13905
14142
}// end loop over 'r'
13906
14143
13907
14144
// Delete pointer to array of derivatives on FIAT element
13908
14145
delete [] derivatives;
13909
14146
14147
// Delete pointer to array of reference derivatives on physical element.
14148
delete [] derivatives_p;
14149
13910
14150
// Delete pointer to array of combinations of derivatives and transform
13911
14151
for (unsigned int r = 0; r < num_derivatives; r++)
13912
14152
{
13923
14163
case 19:
13924
14164
{
13925
14165
13926
// Array of basisvalues.
14166
// Array of basisvalues
13927
14167
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13928
14168
13929
// Declare helper variables.
14169
// Declare helper variables
13930
14170
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
13931
14171
double tmp1 = (1.0 - Y)/2.0;
13932
14172
double tmp2 = tmp1*tmp1;
13933
14173
13934
// Compute basisvalues.
14174
// Compute basisvalues
13935
14175
basisvalues[0] = 1.0;
13936
14176
basisvalues[1] = tmp0;
13937
14177
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
13953
14193
basisvalues[7] *= std::sqrt(10.0);
13954
14194
basisvalues[6] *= std::sqrt(14.0);
13955
14195
13956
// Table(s) of coefficients.
14196
// Table(s) of coefficients
13957
14197
static const double coefficients0[10] = \
13958
14198
{0.094280904, 0.076980036, 0.93333333, 0.20865621, 0.24243661, -0.443241, 0.0, -0.24093544, 0.15552316, -0.053874802};
13959
14199
13993
14233
derivatives[r] = 0.0;
13994
14234
}// end loop over 'r'
13995
14235
14236
// Declare pointer to array of reference derivatives on physical element.
14237
double *derivatives_p = new double[2*num_derivatives];
14238
for (unsigned int r = 0; r < 2*num_derivatives; r++)
14239
{
14240
derivatives_p[r] = 0.0;
14241
}// end loop over 'r'
14242
13996
14243
// Declare derivative matrix (of polynomial basis).
13997
14244
double dmats[10][10] = \
13998
14245
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
14091
14338
// Using contravariant Piola transform to map values back to the physical element.
14092
14339
const double tmp_ref0 = derivatives[r];
14093
14340
const double tmp_ref1 = derivatives[num_derivatives + r];
14094
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
14095
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
14341
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
14342
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
14096
14343
}// end loop over 'r'
14097
14344
14098
14345
// Transform derivatives back to physical element
14100
14347
{
14101
14348
for (unsigned int s = 0; s < num_derivatives; s++)
14102
14349
{
14103
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
14104
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
14350
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
14351
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
14105
14352
}// end loop over 's'
14106
14353
}// end loop over 'r'
14107
14354
14108
14355
// Delete pointer to array of derivatives on FIAT element
14109
14356
delete [] derivatives;
14110
14357
14358
// Delete pointer to array of reference derivatives on physical element.
14359
delete [] derivatives_p;
14360
14111
14361
// Delete pointer to array of combinations of derivatives and transform
14112
14362
for (unsigned int r = 0; r < num_derivatives; r++)
14113
14363
{
14124
14374
case 20:
14125
14375
{
14126
14376
14127
// Array of basisvalues.
14377
// Array of basisvalues
14128
14378
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14129
14379
14130
// Declare helper variables.
14380
// Declare helper variables
14131
14381
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
14132
14382
double tmp1 = (1.0 - Y)/2.0;
14133
14383
double tmp2 = tmp1*tmp1;
14134
14384
14135
// Compute basisvalues.
14385
// Compute basisvalues
14136
14386
basisvalues[0] = 1.0;
14137
14387
basisvalues[1] = tmp0;
14138
14388
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
14154
14404
basisvalues[7] *= std::sqrt(10.0);
14155
14405
basisvalues[6] *= std::sqrt(14.0);
14156
14406
14157
// Table(s) of coefficients.
14407
// Table(s) of coefficients
14158
14408
static const double coefficients0[10] = \
14159
14409
{0.23570226, 0.076980036, 0.0, 0.052164053, 0.24243661, 0.058321184, 0.1069045, 0.15058465, -0.0077761579, -0.067343503};
14160
14410
14194
14444
derivatives[r] = 0.0;
14195
14445
}// end loop over 'r'
14196
14446
14447
// Declare pointer to array of reference derivatives on physical element.
14448
double *derivatives_p = new double[2*num_derivatives];
14449
for (unsigned int r = 0; r < 2*num_derivatives; r++)
14450
{
14451
derivatives_p[r] = 0.0;
14452
}// end loop over 'r'
14453
14197
14454
// Declare derivative matrix (of polynomial basis).
14198
14455
double dmats[10][10] = \
14199
14456
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
14292
14549
// Using contravariant Piola transform to map values back to the physical element.
14293
14550
const double tmp_ref0 = derivatives[r];
14294
14551
const double tmp_ref1 = derivatives[num_derivatives + r];
14295
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
14296
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
14552
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
14553
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
14297
14554
}// end loop over 'r'
14298
14555
14299
14556
// Transform derivatives back to physical element
14301
14558
{
14302
14559
for (unsigned int s = 0; s < num_derivatives; s++)
14303
14560
{
14304
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
14305
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
14561
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
14562
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
14306
14563
}// end loop over 's'
14307
14564
}// end loop over 'r'
14308
14565
14309
14566
// Delete pointer to array of derivatives on FIAT element
14310
14567
delete [] derivatives;
14311
14568
14569
// Delete pointer to array of reference derivatives on physical element.
14570
delete [] derivatives_p;
14571
14312
14572
// Delete pointer to array of combinations of derivatives and transform
14313
14573
for (unsigned int r = 0; r < num_derivatives; r++)
14314
14574
{
14325
14585
case 21:
14326
14586
{
14327
14587
14328
// Array of basisvalues.
14588
// Array of basisvalues
14329
14589
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14330
14590
14331
// Declare helper variables.
14591
// Declare helper variables
14332
14592
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
14333
14593
double tmp1 = (1.0 - Y)/2.0;
14334
14594
double tmp2 = tmp1*tmp1;
14335
14595
14336
// Compute basisvalues.
14596
// Compute basisvalues
14337
14597
basisvalues[0] = 1.0;
14338
14598
basisvalues[1] = tmp0;
14339
14599
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
14355
14615
basisvalues[7] *= std::sqrt(10.0);
14356
14616
basisvalues[6] *= std::sqrt(14.0);
14357
14617
14358
// Table(s) of coefficients.
14618
// Table(s) of coefficients
14359
14619
static const double coefficients0[10] = \
14360
14620
{0.0, -0.076980036, -0.13333333, -0.31298432, -0.24243661, 0.27994168, -0.21380899, -0.06023386, 0.17107547, -0.13468701};
14361
14621
14395
14655
derivatives[r] = 0.0;
14396
14656
}// end loop over 'r'
14397
14657
14658
// Declare pointer to array of reference derivatives on physical element.
14659
double *derivatives_p = new double[2*num_derivatives];
14660
for (unsigned int r = 0; r < 2*num_derivatives; r++)
14661
{
14662
derivatives_p[r] = 0.0;
14663
}// end loop over 'r'
14664
14398
14665
// Declare derivative matrix (of polynomial basis).
14399
14666
double dmats[10][10] = \
14400
14667
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
14493
14760
// Using contravariant Piola transform to map values back to the physical element.
14494
14761
const double tmp_ref0 = derivatives[r];
14495
14762
const double tmp_ref1 = derivatives[num_derivatives + r];
14496
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
14497
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
14763
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
14764
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
14498
14765
}// end loop over 'r'
14499
14766
14500
14767
// Transform derivatives back to physical element
14502
14769
{
14503
14770
for (unsigned int s = 0; s < num_derivatives; s++)
14504
14771
{
14505
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
14506
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
14772
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
14773
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
14507
14774
}// end loop over 's'
14508
14775
}// end loop over 'r'
14509
14776
14510
14777
// Delete pointer to array of derivatives on FIAT element
14511
14778
delete [] derivatives;
14512
14779
14780
// Delete pointer to array of reference derivatives on physical element.
14781
delete [] derivatives_p;
14782
14513
14783
// Delete pointer to array of combinations of derivatives and transform
14514
14784
for (unsigned int r = 0; r < num_derivatives; r++)
14515
14785
{
14526
14796
case 22:
14527
14797
{
14528
14798
14529
// Array of basisvalues.
14799
// Array of basisvalues
14530
14800
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14531
14801
14532
// Declare helper variables.
14802
// Declare helper variables
14533
14803
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
14534
14804
double tmp1 = (1.0 - Y)/2.0;
14535
14805
double tmp2 = tmp1*tmp1;
14536
14806
14537
// Compute basisvalues.
14807
// Compute basisvalues
14538
14808
basisvalues[0] = 1.0;
14539
14809
basisvalues[1] = tmp0;
14540
14810
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
14556
14826
basisvalues[7] *= std::sqrt(10.0);
14557
14827
basisvalues[6] *= std::sqrt(14.0);
14558
14828
14559
// Table(s) of coefficients.
14829
// Table(s) of coefficients
14560
14830
static const double coefficients0[10] = \
14561
14831
{-0.23570226, -0.038490018, 0.066666667, 0.10432811, -0.12121831, -0.19829203, 0.0, -0.12046772, -0.077761579, 0.13468701};
14562
14832
14596
14866
derivatives[r] = 0.0;
14597
14867
}// end loop over 'r'
14598
14868
14869
// Declare pointer to array of reference derivatives on physical element.
14870
double *derivatives_p = new double[2*num_derivatives];
14871
for (unsigned int r = 0; r < 2*num_derivatives; r++)
14872
{
14873
derivatives_p[r] = 0.0;
14874
}// end loop over 'r'
14875
14599
14876
// Declare derivative matrix (of polynomial basis).
14600
14877
double dmats[10][10] = \
14601
14878
{{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
14694
14971
// Using contravariant Piola transform to map values back to the physical element.
14695
14972
const double tmp_ref0 = derivatives[r];
14696
14973
const double tmp_ref1 = derivatives[num_derivatives + r];
14697
derivatives[r] = (1.0/detJ)*(J_00*tmp_ref0 + J_01*tmp_ref1);
14698
derivatives[num_derivatives + r] = (1.0/detJ)*(J_10*tmp_ref0 + J_11*tmp_ref1);
14974
derivatives_p[r] = (1.0/detJ)*(J[0]*tmp_ref0 + J[1]*tmp_ref1);
14975
derivatives_p[num_derivatives + r] = (1.0/detJ)*(J[2]*tmp_ref0 + J[3]*tmp_ref1);
14699
14976
}// end loop over 'r'
14700
14977
14701
14978
// Transform derivatives back to physical element
14703
14980
{
14704
14981
for (unsigned int s = 0; s < num_derivatives; s++)
14705
14982
{
14706
values[3*num_derivatives + r] += transform[r][s]*derivatives[s];
14707
values[4*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
14983
values[3*num_derivatives + r] += transform[r][s]*derivatives_p[s];
14984
values[4*num_derivatives + r] += transform[r][s]*derivatives_p[num_derivatives + s];
14708
14985
}// end loop over 's'
14709
14986
}// end loop over 'r'
14710
14987
14711
14988
// Delete pointer to array of derivatives on FIAT element
14712
14989
delete [] derivatives;
14713
14990
14991
// Delete pointer to array of reference derivatives on physical element.
14992
delete [] derivatives_p;
14993
14714
14994
// Delete pointer to array of combinations of derivatives and transform
14715
14995
for (unsigned int r = 0; r < num_derivatives; r++)
14716
14996
{
14728
15008
14729
15009
}
14730
15010
14731
/// Evaluate order n derivatives of all basis functions at given point in cell
14732
virtual void evaluate_basis_derivatives_all(unsigned int n,
15011
/// Evaluate order n derivatives of all basis functions at given point x in cell
15012
virtual void evaluate_basis_derivatives_all(std::size_t n,
14733
15013
double* values,
14734
const double* coordinates,
14735
const ufc::cell& c) const
15014
const double* x,
15015
const double* vertex_coordinates,
15016
int cell_orientation) const
14736
15017
{
14737
15018
// Compute number of derivatives.
14738
15019
unsigned int num_derivatives = 1;
14751
15032
// Loop dofs and call evaluate_basis_derivatives.
14752
15033
for (unsigned int r = 0; r < 23; r++)
14753
15034
{
14754
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
15035
evaluate_basis_derivatives(r, n, dof_values, x, vertex_coordinates, cell_orientation);
14755
15036
for (unsigned int s = 0; s < 5*num_derivatives; s++)
14756
15037
{
14757
15038
values[r*5*num_derivatives + s] = dof_values[s];
14763
15044
}
14764
15045
14765
15046
/// Evaluate linear functional for dof i on the function f
14766
virtual double evaluate_dof(unsigned int i,
15047
virtual double evaluate_dof(std::size_t i,
14767
15048
const ufc::function& f,
15049
const double* vertex_coordinates,
15050
int cell_orientation,
14768
15051
const ufc::cell& c) const
14769
15052
{
14770
// Declare variables for result of evaluation.
15053
// Declare variables for result of evaluation
14771
15054
double vals[5];
14772
15055
14773
// Declare variable for physical coordinates.
15056
// Declare variable for physical coordinates
14774
15057
double y[2];
15058
14775
15059
double result;
14776
// Extract vertex coordinates
14777
const double * const * x = c.coordinates;
14778
14779
// Compute Jacobian of affine map from reference cell
14780
const double J_00 = x[1][0] - x[0][0];
14781
const double J_01 = x[2][0] - x[0][0];
14782
const double J_10 = x[1][1] - x[0][1];
14783
const double J_11 = x[2][1] - x[0][1];
14784
14785
// Compute determinant of Jacobian
14786
double detJ = J_00*J_11 - J_01*J_10;
14787
14788
// Compute inverse of Jacobian
14789
const double K_00 = J_11 / detJ;
14790
const double K_01 = -J_01 / detJ;
14791
const double K_10 = -J_10 / detJ;
14792
const double K_11 = J_00 / detJ;switch (i)
15060
// Compute Jacobian
15061
double J[4];
15062
compute_jacobian_triangle_2d(J, vertex_coordinates);
15063
15064
15065
// Compute Jacobian inverse and determinant
15066
double K[4];
15067
double detJ;
15068
compute_jacobian_inverse_triangle_2d(K, detJ, J);
15069
15070
15071
switch (i)
14793
15072
{
14794
15073
case 0:
14795
15074
{
14796
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
14797
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15075
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15076
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
14798
15077
f.evaluate(vals, y, c);
14799
15078
return vals[0];
14800
15079
break;
14801
15080
}
14802
15081
case 1:
14803
15082
{
14804
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
14805
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15083
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15084
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
14806
15085
f.evaluate(vals, y, c);
14807
15086
return vals[1];
14808
15087
break;
14809
15088
}
14810
15089
case 2:
14811
15090
{
14812
y[0] = x[0][0];
14813
y[1] = x[0][1];
15091
y[0] = vertex_coordinates[0];
15092
y[1] = vertex_coordinates[1];
14814
15093
f.evaluate(vals, y, c);
14815
15094
return vals[2];
14816
15095
break;
14817
15096
}
14818
15097
case 3:
14819
15098
{
14820
y[0] = x[1][0];
14821
y[1] = x[1][1];
15099
y[0] = vertex_coordinates[2];
15100
y[1] = vertex_coordinates[3];
14822
15101
f.evaluate(vals, y, c);
14823
15102
return vals[2];
14824
15103
break;
14825
15104
}
14826
15105
case 4:
14827
15106
{
14828
y[0] = x[2][0];
14829
y[1] = x[2][1];
15107
y[0] = vertex_coordinates[4];
15108
y[1] = vertex_coordinates[5];
14830
15109
f.evaluate(vals, y, c);
14831
15110
return vals[2];
14832
15111
break;
14833
15112
}
14834
15113
case 5:
14835
15114
{
14836
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
14837
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
15115
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15116
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
14838
15117
f.evaluate(vals, y, c);
14839
15118
return vals[2];
14840
15119
break;
14841
15120
}
14842
15121
case 6:
14843
15122
{
14844
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
14845
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
15123
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
15124
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
14846
15125
f.evaluate(vals, y, c);
14847
15126
return vals[2];
14848
15127
break;
14849
15128
}
14850
15129
case 7:
14851
15130
{
14852
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
14853
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
15131
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
15132
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
14854
15133
f.evaluate(vals, y, c);
14855
15134
return vals[2];
14856
15135
break;
14857
15136
}
14858
15137
case 8:
14859
15138
{
14860
y[0] = 0.75*x[1][0] + 0.25*x[2][0];
14861
y[1] = 0.75*x[1][1] + 0.25*x[2][1];
15139
y[0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15140
y[1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
14862
15141
f.evaluate(vals, y, c);
14863
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15142
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14864
15143
return result;
14865
15144
break;
14866
15145
}
14867
15146
case 9:
14868
15147
{
14869
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
14870
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
15148
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15149
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
14871
15150
f.evaluate(vals, y, c);
14872
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15151
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14873
15152
return result;
14874
15153
break;
14875
15154
}
14876
15155
case 10:
14877
15156
{
14878
y[0] = 0.25*x[1][0] + 0.75*x[2][0];
14879
y[1] = 0.25*x[1][1] + 0.75*x[2][1];
15157
y[0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
15158
y[1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
14880
15159
f.evaluate(vals, y, c);
14881
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15160
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14882
15161
return result;
14883
15162
break;
14884
15163
}
14885
15164
case 11:
14886
15165
{
14887
y[0] = 0.75*x[0][0] + 0.25*x[2][0];
14888
y[1] = 0.75*x[0][1] + 0.25*x[2][1];
15166
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
15167
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
14889
15168
f.evaluate(vals, y, c);
14890
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15169
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14891
15170
return result;
14892
15171
break;
14893
15172
}
14894
15173
case 12:
14895
15174
{
14896
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
14897
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
15175
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
15176
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
14898
15177
f.evaluate(vals, y, c);
14899
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15178
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14900
15179
return result;
14901
15180
break;
14902
15181
}
14903
15182
case 13:
14904
15183
{
14905
y[0] = 0.25*x[0][0] + 0.75*x[2][0];
14906
y[1] = 0.25*x[0][1] + 0.75*x[2][1];
15184
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
15185
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
14907
15186
f.evaluate(vals, y, c);
14908
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15187
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14909
15188
return result;
14910
15189
break;
14911
15190
}
14912
15191
case 14:
14913
15192
{
14914
y[0] = 0.75*x[0][0] + 0.25*x[1][0];
14915
y[1] = 0.75*x[0][1] + 0.25*x[1][1];
15193
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
15194
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
14916
15195
f.evaluate(vals, y, c);
14917
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15196
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
14918
15197
return result;
14919
15198
break;
14920
15199
}
14921
15200
case 15:
14922
15201
{
14923
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
14924
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
15202
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
15203
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
14925
15204
f.evaluate(vals, y, c);
14926
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15205
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
14927
15206
return result;
14928
15207
break;
14929
15208
}
14930
15209
case 16:
14931
15210
{
14932
y[0] = 0.25*x[0][0] + 0.75*x[1][0];
14933
y[1] = 0.25*x[0][1] + 0.75*x[1][1];
15211
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
15212
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
14934
15213
f.evaluate(vals, y, c);
14935
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15214
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
14936
15215
return result;
14937
15216
break;
14938
15217
}
14939
15218
case 17:
14940
15219
{
14941
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
14942
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
15220
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15221
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
14943
15222
f.evaluate(vals, y, c);
14944
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15223
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14945
15224
return result;
14946
15225
break;
14947
15226
}
14948
15227
case 18:
14949
15228
{
14950
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
14951
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
15229
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15230
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
14952
15231
f.evaluate(vals, y, c);
14953
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15232
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14954
15233
return result;
14955
15234
break;
14956
15235
}
14957
15236
case 19:
14958
15237
{
14959
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
14960
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
15238
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15239
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
14961
15240
f.evaluate(vals, y, c);
14962
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15241
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
14963
15242
return result;
14964
15243
break;
14965
15244
}
14966
15245
case 20:
14967
15246
{
14968
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
14969
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
15247
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15248
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
14970
15249
f.evaluate(vals, y, c);
14971
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15250
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14972
15251
return result;
14973
15252
break;
14974
15253
}
14975
15254
case 21:
14976
15255
{
14977
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
14978
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
15256
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15257
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
14979
15258
f.evaluate(vals, y, c);
14980
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15259
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14981
15260
return result;
14982
15261
break;
14983
15262
}
14984
15263
case 22:
14985
15264
{
14986
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
14987
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
15265
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15266
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
14988
15267
f.evaluate(vals, y, c);
14989
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15268
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
14990
15269
return result;
14991
15270
break;
14992
15271
}
14998
15277
/// Evaluate linear functionals for all dofs on the function f
14999
15278
virtual void evaluate_dofs(double* values,
15000
15279
const ufc::function& f,
15280
const double* vertex_coordinates,
15281
int cell_orientation,
15001
15282
const ufc::cell& c) const
15002
15283
{
15003
// Declare variables for result of evaluation.
15284
// Declare variables for result of evaluation
15004
15285
double vals[5];
15005
15286
15006
// Declare variable for physical coordinates.
15287
// Declare variable for physical coordinates
15007
15288
double y[2];
15289
15008
15290
double result;
15009
// Extract vertex coordinates
15010
const double * const * x = c.coordinates;
15011
15012
// Compute Jacobian of affine map from reference cell
15013
const double J_00 = x[1][0] - x[0][0];
15014
const double J_01 = x[2][0] - x[0][0];
15015
const double J_10 = x[1][1] - x[0][1];
15016
const double J_11 = x[2][1] - x[0][1];
15017
15018
// Compute determinant of Jacobian
15019
double detJ = J_00*J_11 - J_01*J_10;
15020
15021
// Compute inverse of Jacobian
15022
const double K_00 = J_11 / detJ;
15023
const double K_01 = -J_01 / detJ;
15024
const double K_10 = -J_10 / detJ;
15025
const double K_11 = J_00 / detJ;y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
15026
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15291
// Compute Jacobian
15292
double J[4];
15293
compute_jacobian_triangle_2d(J, vertex_coordinates);
15294
15295
15296
// Compute Jacobian inverse and determinant
15297
double K[4];
15298
double detJ;
15299
compute_jacobian_inverse_triangle_2d(K, detJ, J);
15300
15301
15302
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15303
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
15027
15304
f.evaluate(vals, y, c);
15028
15305
values[0] = vals[0];
15029
y[0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
15030
y[1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15306
y[0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15307
y[1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
15031
15308
f.evaluate(vals, y, c);
15032
15309
values[1] = vals[1];
15033
y[0] = x[0][0];
15034
y[1] = x[0][1];
15310
y[0] = vertex_coordinates[0];
15311
y[1] = vertex_coordinates[1];
15035
15312
f.evaluate(vals, y, c);
15036
15313
values[2] = vals[2];
15037
y[0] = x[1][0];
15038
y[1] = x[1][1];
15314
y[0] = vertex_coordinates[2];
15315
y[1] = vertex_coordinates[3];
15039
15316
f.evaluate(vals, y, c);
15040
15317
values[3] = vals[2];
15041
y[0] = x[2][0];
15042
y[1] = x[2][1];
15318
y[0] = vertex_coordinates[4];
15319
y[1] = vertex_coordinates[5];
15043
15320
f.evaluate(vals, y, c);
15044
15321
values[4] = vals[2];
15045
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
15046
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
15322
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15323
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
15047
15324
f.evaluate(vals, y, c);
15048
15325
values[5] = vals[2];
15049
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
15050
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
15326
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
15327
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
15051
15328
f.evaluate(vals, y, c);
15052
15329
values[6] = vals[2];
15053
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
15054
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
15330
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
15331
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
15055
15332
f.evaluate(vals, y, c);
15056
15333
values[7] = vals[2];
15057
y[0] = 0.75*x[1][0] + 0.25*x[2][0];
15058
y[1] = 0.75*x[1][1] + 0.25*x[2][1];
15334
y[0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15335
y[1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
15059
15336
f.evaluate(vals, y, c);
15060
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15337
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15061
15338
values[8] = result;
15062
y[0] = 0.5*x[1][0] + 0.5*x[2][0];
15063
y[1] = 0.5*x[1][1] + 0.5*x[2][1];
15339
y[0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15340
y[1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
15064
15341
f.evaluate(vals, y, c);
15065
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15342
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15066
15343
values[9] = result;
15067
y[0] = 0.25*x[1][0] + 0.75*x[2][0];
15068
y[1] = 0.25*x[1][1] + 0.75*x[2][1];
15344
y[0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
15345
y[1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
15069
15346
f.evaluate(vals, y, c);
15070
result = (detJ*(K_00*vals[3] + K_01*vals[4])) + (detJ*(K_10*vals[3] + K_11*vals[4]));
15347
result = (detJ*(K[0]*vals[3] + K[1]*vals[4])) + (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15071
15348
values[10] = result;
15072
y[0] = 0.75*x[0][0] + 0.25*x[2][0];
15073
y[1] = 0.75*x[0][1] + 0.25*x[2][1];
15349
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
15350
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
15074
15351
f.evaluate(vals, y, c);
15075
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15352
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15076
15353
values[11] = result;
15077
y[0] = 0.5*x[0][0] + 0.5*x[2][0];
15078
y[1] = 0.5*x[0][1] + 0.5*x[2][1];
15354
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
15355
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
15079
15356
f.evaluate(vals, y, c);
15080
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15357
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15081
15358
values[12] = result;
15082
y[0] = 0.25*x[0][0] + 0.75*x[2][0];
15083
y[1] = 0.25*x[0][1] + 0.75*x[2][1];
15359
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
15360
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
15084
15361
f.evaluate(vals, y, c);
15085
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15362
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15086
15363
values[13] = result;
15087
y[0] = 0.75*x[0][0] + 0.25*x[1][0];
15088
y[1] = 0.75*x[0][1] + 0.25*x[1][1];
15364
y[0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
15365
y[1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
15089
15366
f.evaluate(vals, y, c);
15090
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15367
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
15091
15368
values[14] = result;
15092
y[0] = 0.5*x[0][0] + 0.5*x[1][0];
15093
y[1] = 0.5*x[0][1] + 0.5*x[1][1];
15369
y[0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
15370
y[1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
15094
15371
f.evaluate(vals, y, c);
15095
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15372
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
15096
15373
values[15] = result;
15097
y[0] = 0.25*x[0][0] + 0.75*x[1][0];
15098
y[1] = 0.25*x[0][1] + 0.75*x[1][1];
15374
y[0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
15375
y[1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
15099
15376
f.evaluate(vals, y, c);
15100
result = (-1.0)*(detJ*(K_10*vals[3] + K_11*vals[4]));
15377
result = (-1.0)*(detJ*(K[2]*vals[3] + K[3]*vals[4]));
15101
15378
values[16] = result;
15102
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
15103
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
15379
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15380
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
15104
15381
f.evaluate(vals, y, c);
15105
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15382
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15106
15383
values[17] = result;
15107
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
15108
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
15384
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15385
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
15109
15386
f.evaluate(vals, y, c);
15110
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15387
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15111
15388
values[18] = result;
15112
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
15113
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
15389
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15390
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
15114
15391
f.evaluate(vals, y, c);
15115
result = (detJ*(K_00*vals[3] + K_01*vals[4]));
15392
result = (detJ*(K[0]*vals[3] + K[1]*vals[4]));
15116
15393
values[19] = result;
15117
y[0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
15118
y[1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
15394
y[0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15395
y[1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
15119
15396
f.evaluate(vals, y, c);
15120
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15397
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15121
15398
values[20] = result;
15122
y[0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
15123
y[1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
15399
y[0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
15400
y[1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
15124
15401
f.evaluate(vals, y, c);
15125
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15402
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15126
15403
values[21] = result;
15127
y[0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
15128
y[1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
15404
y[0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
15405
y[1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
15129
15406
f.evaluate(vals, y, c);
15130
result = (detJ*(K_10*vals[3] + K_11*vals[4]));
15407
result = (detJ*(K[2]*vals[3] + K[3]*vals[4]));
15131
15408
values[22] = result;
15132
15409
}
15133
15410
15134
15411
/// Interpolate vertex values from dof values
15135
15412
virtual void interpolate_vertex_values(double* vertex_values,
15136
15413
const double* dof_values,
15414
const double* vertex_coordinates,
15415
int cell_orientation,
15137
15416
const ufc::cell& c) const
15138
15417
{
15139
// Extract vertex coordinates
15140
const double * const * x = c.coordinates;
15141
15142
// Compute Jacobian of affine map from reference cell
15143
const double J_00 = x[1][0] - x[0][0];
15144
const double J_01 = x[2][0] - x[0][0];
15145
const double J_10 = x[1][1] - x[0][1];
15146
const double J_11 = x[2][1] - x[0][1];
15147
15148
// Compute determinant of Jacobian
15149
double detJ = J_00*J_11 - J_01*J_10;
15150
15151
// Compute inverse of Jacobian
15418
// Compute Jacobian
15419
double J[4];
15420
compute_jacobian_triangle_2d(J, vertex_coordinates);
15421
15422
15423
// Compute Jacobian inverse and determinant
15424
double K[4];
15425
double detJ;
15426
compute_jacobian_inverse_triangle_2d(K, detJ, J);
15427
15428
15429
15152
15430
// Evaluate function and change variables
15153
15431
vertex_values[0] = dof_values[0];
15154
15432
vertex_values[5] = dof_values[0];
15162
15440
vertex_values[7] = dof_values[3];
15163
15441
vertex_values[12] = dof_values[4];
15164
15442
// Evaluate function and change variables
15165
vertex_values[3] = dof_values[11]*(1.0/detJ)*J_00*3.0 + dof_values[12]*((1.0/detJ)*(J_00*(-3.0))) + dof_values[13]*(1.0/detJ)*J_00 + dof_values[14]*((1.0/detJ)*(J_01*(-3.0))) + dof_values[15]*(1.0/detJ)*J_01*3.0 + dof_values[16]*((1.0/detJ)*(J_01*(-1.0)));
15166
vertex_values[8] = dof_values[8]*(1.0/detJ)*J_00*3.0 + dof_values[9]*((1.0/detJ)*(J_00*(-3.0))) + dof_values[10]*(1.0/detJ)*J_00 + dof_values[14]*((1.0/detJ)*(J_00 + J_01*(-1.0))) + dof_values[15]*((1.0/detJ)*(J_00*(-3.0) + J_01*3.0)) + dof_values[16]*((1.0/detJ)*(J_00*3.0 + J_01*(-3.0)));
15167
vertex_values[13] = dof_values[8]*(1.0/detJ)*J_01 + dof_values[9]*((1.0/detJ)*(J_01*(-3.0))) + dof_values[10]*(1.0/detJ)*J_01*3.0 + dof_values[11]*((1.0/detJ)*(J_00 + J_01*(-1.0))) + dof_values[12]*((1.0/detJ)*(J_00*(-3.0) + J_01*3.0)) + dof_values[13]*((1.0/detJ)*(J_00*3.0 + J_01*(-3.0)));
15168
vertex_values[4] = dof_values[11]*(1.0/detJ)*J_10*3.0 + dof_values[12]*((1.0/detJ)*(J_10*(-3.0))) + dof_values[13]*(1.0/detJ)*J_10 + dof_values[14]*((1.0/detJ)*(J_11*(-3.0))) + dof_values[15]*(1.0/detJ)*J_11*3.0 + dof_values[16]*((1.0/detJ)*(J_11*(-1.0)));
15169
vertex_values[9] = dof_values[8]*(1.0/detJ)*J_10*3.0 + dof_values[9]*((1.0/detJ)*(J_10*(-3.0))) + dof_values[10]*(1.0/detJ)*J_10 + dof_values[14]*((1.0/detJ)*(J_10 + J_11*(-1.0))) + dof_values[15]*((1.0/detJ)*(J_10*(-3.0) + J_11*3.0)) + dof_values[16]*((1.0/detJ)*(J_10*3.0 + J_11*(-3.0)));
15170
vertex_values[14] = dof_values[8]*(1.0/detJ)*J_11 + dof_values[9]*((1.0/detJ)*(J_11*(-3.0))) + dof_values[10]*(1.0/detJ)*J_11*3.0 + dof_values[11]*((1.0/detJ)*(J_10 + J_11*(-1.0))) + dof_values[12]*((1.0/detJ)*(J_10*(-3.0) + J_11*3.0)) + dof_values[13]*((1.0/detJ)*(J_10*3.0 + J_11*(-3.0)));
15443
vertex_values[3] = dof_values[11]*(1.0/detJ)*J[0]*3.0 + dof_values[12]*((1.0/detJ)*(J[0]*(-3.0))) + dof_values[13]*(1.0/detJ)*J[0] + dof_values[14]*((1.0/detJ)*(J[1]*(-3.0))) + dof_values[15]*(1.0/detJ)*J[1]*3.0 + dof_values[16]*((1.0/detJ)*(J[1]*(-1.0)));
15444
vertex_values[8] = dof_values[8]*(1.0/detJ)*J[0]*3.0 + dof_values[9]*((1.0/detJ)*(J[0]*(-3.0))) + dof_values[10]*(1.0/detJ)*J[0] + dof_values[14]*((1.0/detJ)*(J[0] + J[1]*(-1.0))) + dof_values[15]*((1.0/detJ)*(J[0]*(-3.0) + J[1]*3.0)) + dof_values[16]*((1.0/detJ)*(J[0]*3.0 + J[1]*(-3.0)));
15445
vertex_values[13] = dof_values[8]*(1.0/detJ)*J[1] + dof_values[9]*((1.0/detJ)*(J[1]*(-3.0))) + dof_values[10]*(1.0/detJ)*J[1]*3.0 + dof_values[11]*((1.0/detJ)*(J[0] + J[1]*(-1.0))) + dof_values[12]*((1.0/detJ)*(J[0]*(-3.0) + J[1]*3.0)) + dof_values[13]*((1.0/detJ)*(J[0]*3.0 + J[1]*(-3.0)));
15446
vertex_values[4] = dof_values[11]*(1.0/detJ)*J[2]*3.0 + dof_values[12]*((1.0/detJ)*(J[2]*(-3.0))) + dof_values[13]*(1.0/detJ)*J[2] + dof_values[14]*((1.0/detJ)*(J[3]*(-3.0))) + dof_values[15]*(1.0/detJ)*J[3]*3.0 + dof_values[16]*((1.0/detJ)*(J[3]*(-1.0)));
15447
vertex_values[9] = dof_values[8]*(1.0/detJ)*J[2]*3.0 + dof_values[9]*((1.0/detJ)*(J[2]*(-3.0))) + dof_values[10]*(1.0/detJ)*J[2] + dof_values[14]*((1.0/detJ)*(J[2] + J[3]*(-1.0))) + dof_values[15]*((1.0/detJ)*(J[2]*(-3.0) + J[3]*3.0)) + dof_values[16]*((1.0/detJ)*(J[2]*3.0 + J[3]*(-3.0)));
15448
vertex_values[14] = dof_values[8]*(1.0/detJ)*J[3] + dof_values[9]*((1.0/detJ)*(J[3]*(-3.0))) + dof_values[10]*(1.0/detJ)*J[3]*3.0 + dof_values[11]*((1.0/detJ)*(J[2] + J[3]*(-1.0))) + dof_values[12]*((1.0/detJ)*(J[2]*(-3.0) + J[3]*3.0)) + dof_values[13]*((1.0/detJ)*(J[2]*3.0 + J[3]*(-3.0)));
15171
15449
}
15172
15450
15173
15451
/// Map coordinate xhat from reference cell to coordinate x in cell
15175
15453
const double* xhat,
15176
15454
const ufc::cell& c) const
15177
15455
{
15178
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
15456
std::cerr << "*** FFC warning: " << "map_from_reference_cell not yet implemented." << std::endl;
15179
15457
}
15180
15458
15181
15459
/// Map from coordinate x in cell to coordinate xhat in reference cell
15183
15461
const double* x,
15184
15462
const ufc::cell& c) const
15185
15463
{
15186
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented (introduced in UFC 2.0)." << std::endl;
15464
std::cerr << "*** FFC warning: " << "map_to_reference_cell not yet implemented." << std::endl;
15187
15465
}
15188
15466
15189
15467
/// Return the number of sub elements (for a mixed element)
15190
virtual unsigned int num_sub_elements() const
15468
virtual std::size_t num_sub_elements() const
15191
15469
{
15192
15470
return 2;
15193
15471
}
15194
15472
15195
15473
/// Create a new finite element for sub element i (for a mixed element)
15196
virtual ufc::finite_element* create_sub_element(unsigned int i) const
15474
virtual ufc::finite_element* create_sub_element(std::size_t i) const
15197
15475
{
15198
15476
switch (i)
15199
15477
{
15225
15503
15226
15504
class mixedmixedelement_dofmap_0: public ufc::dofmap
15227
15505
{
15228
private:
15229
15230
unsigned int _global_dimension;
15231
15506
public:
15232
15507
15233
15508
/// Constructor
15234
15509
mixedmixedelement_dofmap_0() : ufc::dofmap()
15235
15510
{
15236
_global_dimension = 0;
15511
// Do nothing
15237
15512
}
15238
15513
15239
15514
/// Destructor
15245
15520
/// Return a string identifying the dofmap
15246
15521
virtual const char* signature() const
15247
15522
{
15248
return "FFC dofmap for FiniteElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, None)";
15523
return "FFC dofmap for FiniteElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, None)";
15249
15524
}
15250
15525
15251
15526
/// Return true iff mesh entities of topological dimension d are needed
15252
virtual bool needs_mesh_entities(unsigned int d) const
15527
virtual bool needs_mesh_entities(std::size_t d) const
15253
15528
{
15254
15529
switch (d)
15255
15530
{
15273
15548
return false;
15274
15549
}
15275
15550
15276
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
15277
virtual bool init_mesh(const ufc::mesh& m)
15278
{
15279
_global_dimension = m.num_entities[2];
15280
return false;
15281
}
15282
15283
/// Initialize dofmap for given cell
15284
virtual void init_cell(const ufc::mesh& m,
15285
const ufc::cell& c)
15286
{
15287
// Do nothing
15288
}
15289
15290
/// Finish initialization of dofmap for cells
15291
virtual void init_cell_finalize()
15292
{
15293
// Do nothing
15294
}
15295
15296
15551
/// Return the topological dimension of the associated cell shape
15297
virtual unsigned int topological_dimension() const
15552
virtual std::size_t topological_dimension() const
15298
15553
{
15299
15554
return 2;
15300
15555
}
15301
15556
15302
15557
/// Return the geometric dimension of the associated cell shape
15303
virtual unsigned int geometric_dimension() const
15558
virtual std::size_t geometric_dimension() const
15304
15559
{
15305
15560
return 2;
15306
15561
}
15307
15562
15308
15563
/// Return the dimension of the global finite element function space
15309
virtual unsigned int global_dimension() const
15564
virtual std::size_t global_dimension(const std::vector<std::size_t>&
15565
num_global_entities) const
15310
15566
{
15311
return _global_dimension;
15567
return num_global_entities[2];
15312
15568
}
15313
15569
15314
15570
/// Return the dimension of the local finite element function space for a cell
15315
virtual unsigned int local_dimension(const ufc::cell& c) const
15571
virtual std::size_t local_dimension(const ufc::cell& c) const
15316
15572
{
15317
15573
return 1;
15318
15574
}
15319
15575
15320
15576
/// Return the maximum dimension of the local finite element function space
15321
virtual unsigned int max_local_dimension() const
15577
virtual std::size_t max_local_dimension() const
15322
15578
{
15323
15579
return 1;
15324
15580
}
15325
15581
15326
15582
/// Return the number of dofs on each cell facet
15327
virtual unsigned int num_facet_dofs() const
15583
virtual std::size_t num_facet_dofs() const
15328
15584
{
15329
15585
return 0;
15330
15586
}
15331
15587
15332
15588
/// Return the number of dofs associated with each cell entity of dimension d
15333
virtual unsigned int num_entity_dofs(unsigned int d) const
15589
virtual std::size_t num_entity_dofs(std::size_t d) const
15334
15590
{
15335
15591
switch (d)
15336
15592
{
15355
15611
}
15356
15612
15357
15613
/// Tabulate the local-to-global mapping of dofs on a cell
15358
virtual void tabulate_dofs(unsigned int* dofs,
15359
const ufc::mesh& m,
15614
virtual void tabulate_dofs(std::size_t* dofs,
15615
const std::vector<std::size_t>& num_global_entities,
15360
15616
const ufc::cell& c) const
15361
15617
{
15362
15618
dofs[0] = c.entity_indices[2][0];
15363
15619
}
15364
15620
15365
15621
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
15366
virtual void tabulate_facet_dofs(unsigned int* dofs,
15367
unsigned int facet) const
15622
virtual void tabulate_facet_dofs(std::size_t* dofs,
15623
std::size_t facet) const
15368
15624
{
15369
15625
switch (facet)
15370
15626
{
15388
15644
}
15389
15645
15390
15646
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
15391
virtual void tabulate_entity_dofs(unsigned int* dofs,
15392
unsigned int d, unsigned int i) const
15647
virtual void tabulate_entity_dofs(std::size_t* dofs,
15648
std::size_t d, std::size_t i) const
15393
15649
{
15394
15650
if (d > 2)
15395
15651
{
15423
15679
}
15424
15680
15425
15681
/// Tabulate the coordinates of all dofs on a cell
15426
virtual void tabulate_coordinates(double** coordinates,
15427
const ufc::cell& c) const
15682
virtual void tabulate_coordinates(double** dof_coordinates,
15683
const double* vertex_coordinates) const
15428
15684
{
15429
const double * const * x = c.coordinates;
15430
15431
coordinates[0][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
15432
coordinates[0][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15685
dof_coordinates[0][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15686
dof_coordinates[0][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
15433
15687
}
15434
15688
15435
15689
/// Return the number of sub dofmaps (for a mixed element)
15436
virtual unsigned int num_sub_dofmaps() const
15690
virtual std::size_t num_sub_dofmaps() const
15437
15691
{
15438
15692
return 0;
15439
15693
}
15440
15694
15441
15695
/// Create a new dofmap for sub dofmap i (for a mixed element)
15442
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
15696
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
15443
15697
{
15444
15698
return 0;
15445
15699
}
15457
15711
15458
15712
class mixedmixedelement_dofmap_1: public ufc::dofmap
15459
15713
{
15460
private:
15461
15462
unsigned int _global_dimension;
15463
15714
public:
15464
15715
15465
15716
/// Constructor
15466
15717
mixedmixedelement_dofmap_1() : ufc::dofmap()
15467
15718
{
15468
_global_dimension = 0;
15719
// Do nothing
15469
15720
}
15470
15721
15471
15722
/// Destructor
15477
15728
/// Return a string identifying the dofmap
15478
15729
virtual const char* signature() const
15479
15730
{
15480
return "FFC dofmap for VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None)";
15731
return "FFC dofmap for VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None)";
15481
15732
}
15482
15733
15483
15734
/// Return true iff mesh entities of topological dimension d are needed
15484
virtual bool needs_mesh_entities(unsigned int d) const
15735
virtual bool needs_mesh_entities(std::size_t d) const
15485
15736
{
15486
15737
switch (d)
15487
15738
{
15505
15756
return false;
15506
15757
}
15507
15758
15508
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
15509
virtual bool init_mesh(const ufc::mesh& m)
15510
{
15511
_global_dimension = 2*m.num_entities[2];
15512
return false;
15513
}
15514
15515
/// Initialize dofmap for given cell
15516
virtual void init_cell(const ufc::mesh& m,
15517
const ufc::cell& c)
15518
{
15519
// Do nothing
15520
}
15521
15522
/// Finish initialization of dofmap for cells
15523
virtual void init_cell_finalize()
15524
{
15525
// Do nothing
15526
}
15527
15528
15759
/// Return the topological dimension of the associated cell shape
15529
virtual unsigned int topological_dimension() const
15760
virtual std::size_t topological_dimension() const
15530
15761
{
15531
15762
return 2;
15532
15763
}
15533
15764
15534
15765
/// Return the geometric dimension of the associated cell shape
15535
virtual unsigned int geometric_dimension() const
15766
virtual std::size_t geometric_dimension() const
15536
15767
{
15537
15768
return 2;
15538
15769
}
15539
15770
15540
15771
/// Return the dimension of the global finite element function space
15541
virtual unsigned int global_dimension() const
15772
virtual std::size_t global_dimension(const std::vector<std::size_t>&
15773
num_global_entities) const
15542
15774
{
15543
return _global_dimension;
15775
return 2*num_global_entities[2];
15544
15776
}
15545
15777
15546
15778
/// Return the dimension of the local finite element function space for a cell
15547
virtual unsigned int local_dimension(const ufc::cell& c) const
15779
virtual std::size_t local_dimension(const ufc::cell& c) const
15548
15780
{
15549
15781
return 2;
15550
15782
}
15551
15783
15552
15784
/// Return the maximum dimension of the local finite element function space
15553
virtual unsigned int max_local_dimension() const
15785
virtual std::size_t max_local_dimension() const
15554
15786
{
15555
15787
return 2;
15556
15788
}
15557
15789
15558
15790
/// Return the number of dofs on each cell facet
15559
virtual unsigned int num_facet_dofs() const
15791
virtual std::size_t num_facet_dofs() const
15560
15792
{
15561
15793
return 0;
15562
15794
}
15563
15795
15564
15796
/// Return the number of dofs associated with each cell entity of dimension d
15565
virtual unsigned int num_entity_dofs(unsigned int d) const
15797
virtual std::size_t num_entity_dofs(std::size_t d) const
15566
15798
{
15567
15799
switch (d)
15568
15800
{
15587
15819
}
15588
15820
15589
15821
/// Tabulate the local-to-global mapping of dofs on a cell
15590
virtual void tabulate_dofs(unsigned int* dofs,
15591
const ufc::mesh& m,
15822
virtual void tabulate_dofs(std::size_t* dofs,
15823
const std::vector<std::size_t>& num_global_entities,
15592
15824
const ufc::cell& c) const
15593
15825
{
15594
15826
unsigned int offset = 0;
15595
15827
dofs[0] = offset + c.entity_indices[2][0];
15596
offset += m.num_entities[2];
15828
offset += num_global_entities[2];
15597
15829
dofs[1] = offset + c.entity_indices[2][0];
15598
offset += m.num_entities[2];
15830
offset += num_global_entities[2];
15599
15831
}
15600
15832
15601
15833
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
15602
virtual void tabulate_facet_dofs(unsigned int* dofs,
15603
unsigned int facet) const
15834
virtual void tabulate_facet_dofs(std::size_t* dofs,
15835
std::size_t facet) const
15604
15836
{
15605
15837
switch (facet)
15606
15838
{
15624
15856
}
15625
15857
15626
15858
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
15627
virtual void tabulate_entity_dofs(unsigned int* dofs,
15628
unsigned int d, unsigned int i) const
15859
virtual void tabulate_entity_dofs(std::size_t* dofs,
15860
std::size_t d, std::size_t i) const
15629
15861
{
15630
15862
if (d > 2)
15631
15863
{
15660
15892
}
15661
15893
15662
15894
/// Tabulate the coordinates of all dofs on a cell
15663
virtual void tabulate_coordinates(double** coordinates,
15664
const ufc::cell& c) const
15895
virtual void tabulate_coordinates(double** dof_coordinates,
15896
const double* vertex_coordinates) const
15665
15897
{
15666
const double * const * x = c.coordinates;
15667
15668
coordinates[0][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
15669
coordinates[0][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15670
coordinates[1][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
15671
coordinates[1][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
15898
dof_coordinates[0][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15899
dof_coordinates[0][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
15900
dof_coordinates[1][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
15901
dof_coordinates[1][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
15672
15902
}
15673
15903
15674
15904
/// Return the number of sub dofmaps (for a mixed element)
15675
virtual unsigned int num_sub_dofmaps() const
15905
virtual std::size_t num_sub_dofmaps() const
15676
15906
{
15677
15907
return 2;
15678
15908
}
15679
15909
15680
15910
/// Create a new dofmap for sub dofmap i (for a mixed element)
15681
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
15911
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
15682
15912
{
15683
15913
switch (i)
15684
15914
{
15710
15940
15711
15941
class mixedmixedelement_dofmap_2: public ufc::dofmap
15712
15942
{
15713
private:
15714
15715
unsigned int _global_dimension;
15716
15943
public:
15717
15944
15718
15945
/// Constructor
15719
15946
mixedmixedelement_dofmap_2() : ufc::dofmap()
15720
15947
{
15721
_global_dimension = 0;
15948
// Do nothing
15722
15949
}
15723
15950
15724
15951
/// Destructor
15730
15957
/// Return a string identifying the dofmap
15731
15958
virtual const char* signature() const
15732
15959
{
15733
return "FFC dofmap for FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)";
15960
return "FFC dofmap for FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)";
15734
15961
}
15735
15962
15736
15963
/// Return true iff mesh entities of topological dimension d are needed
15737
virtual bool needs_mesh_entities(unsigned int d) const
15964
virtual bool needs_mesh_entities(std::size_t d) const
15738
15965
{
15739
15966
switch (d)
15740
15967
{
15758
15985
return false;
15759
15986
}
15760
15987
15761
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
15762
virtual bool init_mesh(const ufc::mesh& m)
15763
{
15764
_global_dimension = m.num_entities[0] + m.num_entities[1];
15765
return false;
15766
}
15767
15768
/// Initialize dofmap for given cell
15769
virtual void init_cell(const ufc::mesh& m,
15770
const ufc::cell& c)
15771
{
15772
// Do nothing
15773
}
15774
15775
/// Finish initialization of dofmap for cells
15776
virtual void init_cell_finalize()
15777
{
15778
// Do nothing
15779
}
15780
15781
15988
/// Return the topological dimension of the associated cell shape
15782
virtual unsigned int topological_dimension() const
15989
virtual std::size_t topological_dimension() const
15783
15990
{
15784
15991
return 2;
15785
15992
}
15786
15993
15787
15994
/// Return the geometric dimension of the associated cell shape
15788
virtual unsigned int geometric_dimension() const
15995
virtual std::size_t geometric_dimension() const
15789
15996
{
15790
15997
return 2;
15791
15998
}
15792
15999
15793
16000
/// Return the dimension of the global finite element function space
15794
virtual unsigned int global_dimension() const
16001
virtual std::size_t global_dimension(const std::vector<std::size_t>&
16002
num_global_entities) const
15795
16003
{
15796
return _global_dimension;
16004
return num_global_entities[0] + num_global_entities[1];
15797
16005
}
15798
16006
15799
16007
/// Return the dimension of the local finite element function space for a cell
15800
virtual unsigned int local_dimension(const ufc::cell& c) const
16008
virtual std::size_t local_dimension(const ufc::cell& c) const
15801
16009
{
15802
16010
return 6;
15803
16011
}
15804
16012
15805
16013
/// Return the maximum dimension of the local finite element function space
15806
virtual unsigned int max_local_dimension() const
16014
virtual std::size_t max_local_dimension() const
15807
16015
{
15808
16016
return 6;
15809
16017
}
15810
16018
15811
16019
/// Return the number of dofs on each cell facet
15812
virtual unsigned int num_facet_dofs() const
16020
virtual std::size_t num_facet_dofs() const
15813
16021
{
15814
16022
return 3;
15815
16023
}
15816
16024
15817
16025
/// Return the number of dofs associated with each cell entity of dimension d
15818
virtual unsigned int num_entity_dofs(unsigned int d) const
16026
virtual std::size_t num_entity_dofs(std::size_t d) const
15819
16027
{
15820
16028
switch (d)
15821
16029
{
15840
16048
}
15841
16049
15842
16050
/// Tabulate the local-to-global mapping of dofs on a cell
15843
virtual void tabulate_dofs(unsigned int* dofs,
15844
const ufc::mesh& m,
16051
virtual void tabulate_dofs(std::size_t* dofs,
16052
const std::vector<std::size_t>& num_global_entities,
15845
16053
const ufc::cell& c) const
15846
16054
{
15847
16055
unsigned int offset = 0;
15848
16056
dofs[0] = offset + c.entity_indices[0][0];
15849
16057
dofs[1] = offset + c.entity_indices[0][1];
15850
16058
dofs[2] = offset + c.entity_indices[0][2];
15851
offset += m.num_entities[0];
16059
offset += num_global_entities[0];
15852
16060
dofs[3] = offset + c.entity_indices[1][0];
15853
16061
dofs[4] = offset + c.entity_indices[1][1];
15854
16062
dofs[5] = offset + c.entity_indices[1][2];
15855
offset += m.num_entities[1];
16063
offset += num_global_entities[1];
15856
16064
}
15857
16065
15858
16066
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
15859
virtual void tabulate_facet_dofs(unsigned int* dofs,
15860
unsigned int facet) const
16067
virtual void tabulate_facet_dofs(std::size_t* dofs,
16068
std::size_t facet) const
15861
16069
{
15862
16070
switch (facet)
15863
16071
{
15887
16095
}
15888
16096
15889
16097
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
15890
virtual void tabulate_entity_dofs(unsigned int* dofs,
15891
unsigned int d, unsigned int i) const
16098
virtual void tabulate_entity_dofs(std::size_t* dofs,
16099
std::size_t d, std::size_t i) const
15892
16100
{
15893
16101
if (d > 2)
15894
16102
{
15963
16171
}
15964
16172
15965
16173
/// Tabulate the coordinates of all dofs on a cell
15966
virtual void tabulate_coordinates(double** coordinates,
15967
const ufc::cell& c) const
16174
virtual void tabulate_coordinates(double** dof_coordinates,
16175
const double* vertex_coordinates) const
15968
16176
{
15969
const double * const * x = c.coordinates;
15970
15971
coordinates[0][0] = x[0][0];
15972
coordinates[0][1] = x[0][1];
15973
coordinates[1][0] = x[1][0];
15974
coordinates[1][1] = x[1][1];
15975
coordinates[2][0] = x[2][0];
15976
coordinates[2][1] = x[2][1];
15977
coordinates[3][0] = 0.5*x[1][0] + 0.5*x[2][0];
15978
coordinates[3][1] = 0.5*x[1][1] + 0.5*x[2][1];
15979
coordinates[4][0] = 0.5*x[0][0] + 0.5*x[2][0];
15980
coordinates[4][1] = 0.5*x[0][1] + 0.5*x[2][1];
15981
coordinates[5][0] = 0.5*x[0][0] + 0.5*x[1][0];
15982
coordinates[5][1] = 0.5*x[0][1] + 0.5*x[1][1];
16177
dof_coordinates[0][0] = vertex_coordinates[0];
16178
dof_coordinates[0][1] = vertex_coordinates[1];
16179
dof_coordinates[1][0] = vertex_coordinates[2];
16180
dof_coordinates[1][1] = vertex_coordinates[3];
16181
dof_coordinates[2][0] = vertex_coordinates[4];
16182
dof_coordinates[2][1] = vertex_coordinates[5];
16183
dof_coordinates[3][0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
16184
dof_coordinates[3][1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
16185
dof_coordinates[4][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
16186
dof_coordinates[4][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
16187
dof_coordinates[5][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
16188
dof_coordinates[5][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
15983
16189
}
15984
16190
15985
16191
/// Return the number of sub dofmaps (for a mixed element)
15986
virtual unsigned int num_sub_dofmaps() const
16192
virtual std::size_t num_sub_dofmaps() const
15987
16193
{
15988
16194
return 0;
15989
16195
}
15990
16196
15991
16197
/// Create a new dofmap for sub dofmap i (for a mixed element)
15992
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
16198
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
15993
16199
{
15994
16200
return 0;
15995
16201
}
16007
16213
16008
16214
class mixedmixedelement_dofmap_3: public ufc::dofmap
16009
16215
{
16010
private:
16011
16012
unsigned int _global_dimension;
16013
16216
public:
16014
16217
16015
16218
/// Constructor
16016
16219
mixedmixedelement_dofmap_3() : ufc::dofmap()
16017
16220
{
16018
_global_dimension = 0;
16221
// Do nothing
16019
16222
}
16020
16223
16021
16224
/// Destructor
16027
16230
/// Return a string identifying the dofmap
16028
16231
virtual const char* signature() const
16029
16232
{
16030
return "FFC dofmap for MixedElement(*[VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None), FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)], **{'value_shape': (3,) })";
16233
return "FFC dofmap for MixedElement(*[VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None), FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)], **{'value_shape': (3,) })";
16031
16234
}
16032
16235
16033
16236
/// Return true iff mesh entities of topological dimension d are needed
16034
virtual bool needs_mesh_entities(unsigned int d) const
16237
virtual bool needs_mesh_entities(std::size_t d) const
16035
16238
{
16036
16239
switch (d)
16037
16240
{
16055
16258
return false;
16056
16259
}
16057
16260
16058
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
16059
virtual bool init_mesh(const ufc::mesh& m)
16060
{
16061
_global_dimension = m.num_entities[0] + m.num_entities[1] + 2*m.num_entities[2];
16062
return false;
16063
}
16064
16065
/// Initialize dofmap for given cell
16066
virtual void init_cell(const ufc::mesh& m,
16067
const ufc::cell& c)
16068
{
16069
// Do nothing
16070
}
16071
16072
/// Finish initialization of dofmap for cells
16073
virtual void init_cell_finalize()
16074
{
16075
// Do nothing
16076
}
16077
16078
16261
/// Return the topological dimension of the associated cell shape
16079
virtual unsigned int topological_dimension() const
16262
virtual std::size_t topological_dimension() const
16080
16263
{
16081
16264
return 2;
16082
16265
}
16083
16266
16084
16267
/// Return the geometric dimension of the associated cell shape
16085
virtual unsigned int geometric_dimension() const
16268
virtual std::size_t geometric_dimension() const
16086
16269
{
16087
16270
return 2;
16088
16271
}
16089
16272
16090
16273
/// Return the dimension of the global finite element function space
16091
virtual unsigned int global_dimension() const
16274
virtual std::size_t global_dimension(const std::vector<std::size_t>&
16275
num_global_entities) const
16092
16276
{
16093
return _global_dimension;
16277
return num_global_entities[0] + num_global_entities[1] + 2*num_global_entities[2];
16094
16278
}
16095
16279
16096
16280
/// Return the dimension of the local finite element function space for a cell
16097
virtual unsigned int local_dimension(const ufc::cell& c) const
16281
virtual std::size_t local_dimension(const ufc::cell& c) const
16098
16282
{
16099
16283
return 8;
16100
16284
}
16101
16285
16102
16286
/// Return the maximum dimension of the local finite element function space
16103
virtual unsigned int max_local_dimension() const
16287
virtual std::size_t max_local_dimension() const
16104
16288
{
16105
16289
return 8;
16106
16290
}
16107
16291
16108
16292
/// Return the number of dofs on each cell facet
16109
virtual unsigned int num_facet_dofs() const
16293
virtual std::size_t num_facet_dofs() const
16110
16294
{
16111
16295
return 3;
16112
16296
}
16113
16297
16114
16298
/// Return the number of dofs associated with each cell entity of dimension d
16115
virtual unsigned int num_entity_dofs(unsigned int d) const
16299
virtual std::size_t num_entity_dofs(std::size_t d) const
16116
16300
{
16117
16301
switch (d)
16118
16302
{
16137
16321
}
16138
16322
16139
16323
/// Tabulate the local-to-global mapping of dofs on a cell
16140
virtual void tabulate_dofs(unsigned int* dofs,
16141
const ufc::mesh& m,
16324
virtual void tabulate_dofs(std::size_t* dofs,
16325
const std::vector<std::size_t>& num_global_entities,
16142
16326
const ufc::cell& c) const
16143
16327
{
16144
16328
unsigned int offset = 0;
16145
16329
dofs[0] = offset + c.entity_indices[2][0];
16146
offset += m.num_entities[2];
16330
offset += num_global_entities[2];
16147
16331
dofs[1] = offset + c.entity_indices[2][0];
16148
offset += m.num_entities[2];
16332
offset += num_global_entities[2];
16149
16333
dofs[2] = offset + c.entity_indices[0][0];
16150
16334
dofs[3] = offset + c.entity_indices[0][1];
16151
16335
dofs[4] = offset + c.entity_indices[0][2];
16152
offset += m.num_entities[0];
16336
offset += num_global_entities[0];
16153
16337
dofs[5] = offset + c.entity_indices[1][0];
16154
16338
dofs[6] = offset + c.entity_indices[1][1];
16155
16339
dofs[7] = offset + c.entity_indices[1][2];
16156
offset += m.num_entities[1];
16340
offset += num_global_entities[1];
16157
16341
}
16158
16342
16159
16343
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
16160
virtual void tabulate_facet_dofs(unsigned int* dofs,
16161
unsigned int facet) const
16344
virtual void tabulate_facet_dofs(std::size_t* dofs,
16345
std::size_t facet) const
16162
16346
{
16163
16347
switch (facet)
16164
16348
{
16188
16372
}
16189
16373
16190
16374
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
16191
virtual void tabulate_entity_dofs(unsigned int* dofs,
16192
unsigned int d, unsigned int i) const
16375
virtual void tabulate_entity_dofs(std::size_t* dofs,
16376
std::size_t d, std::size_t i) const
16193
16377
{
16194
16378
if (d > 2)
16195
16379
{
16270
16454
}
16271
16455
16272
16456
/// Tabulate the coordinates of all dofs on a cell
16273
virtual void tabulate_coordinates(double** coordinates,
16274
const ufc::cell& c) const
16457
virtual void tabulate_coordinates(double** dof_coordinates,
16458
const double* vertex_coordinates) const
16275
16459
{
16276
const double * const * x = c.coordinates;
16277
16278
coordinates[0][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
16279
coordinates[0][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
16280
coordinates[1][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
16281
coordinates[1][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
16282
coordinates[2][0] = x[0][0];
16283
coordinates[2][1] = x[0][1];
16284
coordinates[3][0] = x[1][0];
16285
coordinates[3][1] = x[1][1];
16286
coordinates[4][0] = x[2][0];
16287
coordinates[4][1] = x[2][1];
16288
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[2][0];
16289
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[2][1];
16290
coordinates[6][0] = 0.5*x[0][0] + 0.5*x[2][0];
16291
coordinates[6][1] = 0.5*x[0][1] + 0.5*x[2][1];
16292
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[1][0];
16293
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[1][1];
16460
dof_coordinates[0][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
16461
dof_coordinates[0][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
16462
dof_coordinates[1][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
16463
dof_coordinates[1][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
16464
dof_coordinates[2][0] = vertex_coordinates[0];
16465
dof_coordinates[2][1] = vertex_coordinates[1];
16466
dof_coordinates[3][0] = vertex_coordinates[2];
16467
dof_coordinates[3][1] = vertex_coordinates[3];
16468
dof_coordinates[4][0] = vertex_coordinates[4];
16469
dof_coordinates[4][1] = vertex_coordinates[5];
16470
dof_coordinates[5][0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
16471
dof_coordinates[5][1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
16472
dof_coordinates[6][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
16473
dof_coordinates[6][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
16474
dof_coordinates[7][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
16475
dof_coordinates[7][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
16294
16476
}
16295
16477
16296
16478
/// Return the number of sub dofmaps (for a mixed element)
16297
virtual unsigned int num_sub_dofmaps() const
16479
virtual std::size_t num_sub_dofmaps() const
16298
16480
{
16299
16481
return 2;
16300
16482
}
16301
16483
16302
16484
/// Create a new dofmap for sub dofmap i (for a mixed element)
16303
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
16485
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
16304
16486
{
16305
16487
switch (i)
16306
16488
{
16332
16514
16333
16515
class mixedmixedelement_dofmap_4: public ufc::dofmap
16334
16516
{
16335
private:
16336
16337
unsigned int _global_dimension;
16338
16517
public:
16339
16518
16340
16519
/// Constructor
16341
16520
mixedmixedelement_dofmap_4() : ufc::dofmap()
16342
16521
{
16343
_global_dimension = 0;
16522
// Do nothing
16344
16523
}
16345
16524
16346
16525
/// Destructor
16352
16531
/// Return a string identifying the dofmap
16353
16532
virtual const char* signature() const
16354
16533
{
16355
return "FFC dofmap for FiniteElement('Raviart-Thomas', Cell('triangle', Space(2)), 3, None)";
16534
return "FFC dofmap for FiniteElement('Raviart-Thomas', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 3, None)";
16356
16535
}
16357
16536
16358
16537
/// Return true iff mesh entities of topological dimension d are needed
16359
virtual bool needs_mesh_entities(unsigned int d) const
16538
virtual bool needs_mesh_entities(std::size_t d) const
16360
16539
{
16361
16540
switch (d)
16362
16541
{
16380
16559
return false;
16381
16560
}
16382
16561
16383
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
16384
virtual bool init_mesh(const ufc::mesh& m)
16385
{
16386
_global_dimension = 3*m.num_entities[1] + 6*m.num_entities[2];
16387
return false;
16388
}
16389
16390
/// Initialize dofmap for given cell
16391
virtual void init_cell(const ufc::mesh& m,
16392
const ufc::cell& c)
16393
{
16394
// Do nothing
16395
}
16396
16397
/// Finish initialization of dofmap for cells
16398
virtual void init_cell_finalize()
16399
{
16400
// Do nothing
16401
}
16402
16403
16562
/// Return the topological dimension of the associated cell shape
16404
virtual unsigned int topological_dimension() const
16563
virtual std::size_t topological_dimension() const
16405
16564
{
16406
16565
return 2;
16407
16566
}
16408
16567
16409
16568
/// Return the geometric dimension of the associated cell shape
16410
virtual unsigned int geometric_dimension() const
16569
virtual std::size_t geometric_dimension() const
16411
16570
{
16412
16571
return 2;
16413
16572
}
16414
16573
16415
16574
/// Return the dimension of the global finite element function space
16416
virtual unsigned int global_dimension() const
16575
virtual std::size_t global_dimension(const std::vector<std::size_t>&
16576
num_global_entities) const
16417
16577
{
16418
return _global_dimension;
16578
return 3*num_global_entities[1] + 6*num_global_entities[2];
16419
16579
}
16420
16580
16421
16581
/// Return the dimension of the local finite element function space for a cell
16422
virtual unsigned int local_dimension(const ufc::cell& c) const
16582
virtual std::size_t local_dimension(const ufc::cell& c) const
16423
16583
{
16424
16584
return 15;
16425
16585
}
16426
16586
16427
16587
/// Return the maximum dimension of the local finite element function space
16428
virtual unsigned int max_local_dimension() const
16588
virtual std::size_t max_local_dimension() const
16429
16589
{
16430
16590
return 15;
16431
16591
}
16432
16592
16433
16593
/// Return the number of dofs on each cell facet
16434
virtual unsigned int num_facet_dofs() const
16594
virtual std::size_t num_facet_dofs() const
16435
16595
{
16436
16596
return 3;
16437
16597
}
16438
16598
16439
16599
/// Return the number of dofs associated with each cell entity of dimension d
16440
virtual unsigned int num_entity_dofs(unsigned int d) const
16600
virtual std::size_t num_entity_dofs(std::size_t d) const
16441
16601
{
16442
16602
switch (d)
16443
16603
{
16462
16622
}
16463
16623
16464
16624
/// Tabulate the local-to-global mapping of dofs on a cell
16465
virtual void tabulate_dofs(unsigned int* dofs,
16466
const ufc::mesh& m,
16625
virtual void tabulate_dofs(std::size_t* dofs,
16626
const std::vector<std::size_t>& num_global_entities,
16467
16627
const ufc::cell& c) const
16468
16628
{
16469
16629
unsigned int offset = 0;
16476
16636
dofs[6] = offset + 3*c.entity_indices[1][2];
16477
16637
dofs[7] = offset + 3*c.entity_indices[1][2] + 1;
16478
16638
dofs[8] = offset + 3*c.entity_indices[1][2] + 2;
16479
offset += 3*m.num_entities[1];
16639
offset += 3*num_global_entities[1];
16480
16640
dofs[9] = offset + 6*c.entity_indices[2][0];
16481
16641
dofs[10] = offset + 6*c.entity_indices[2][0] + 1;
16482
16642
dofs[11] = offset + 6*c.entity_indices[2][0] + 2;
16483
16643
dofs[12] = offset + 6*c.entity_indices[2][0] + 3;
16484
16644
dofs[13] = offset + 6*c.entity_indices[2][0] + 4;
16485
16645
dofs[14] = offset + 6*c.entity_indices[2][0] + 5;
16486
offset += 6*m.num_entities[2];
16646
offset += 6*num_global_entities[2];
16487
16647
}
16488
16648
16489
16649
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
16490
virtual void tabulate_facet_dofs(unsigned int* dofs,
16491
unsigned int facet) const
16650
virtual void tabulate_facet_dofs(std::size_t* dofs,
16651
std::size_t facet) const
16492
16652
{
16493
16653
switch (facet)
16494
16654
{
16518
16678
}
16519
16679
16520
16680
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
16521
virtual void tabulate_entity_dofs(unsigned int* dofs,
16522
unsigned int d, unsigned int i) const
16681
virtual void tabulate_entity_dofs(std::size_t* dofs,
16682
std::size_t d, std::size_t i) const
16523
16683
{
16524
16684
if (d > 2)
16525
16685
{
16587
16747
}
16588
16748
16589
16749
/// Tabulate the coordinates of all dofs on a cell
16590
virtual void tabulate_coordinates(double** coordinates,
16591
const ufc::cell& c) const
16750
virtual void tabulate_coordinates(double** dof_coordinates,
16751
const double* vertex_coordinates) const
16592
16752
{
16593
const double * const * x = c.coordinates;
16594
16595
coordinates[0][0] = 0.75*x[1][0] + 0.25*x[2][0];
16596
coordinates[0][1] = 0.75*x[1][1] + 0.25*x[2][1];
16597
coordinates[1][0] = 0.5*x[1][0] + 0.5*x[2][0];
16598
coordinates[1][1] = 0.5*x[1][1] + 0.5*x[2][1];
16599
coordinates[2][0] = 0.25*x[1][0] + 0.75*x[2][0];
16600
coordinates[2][1] = 0.25*x[1][1] + 0.75*x[2][1];
16601
coordinates[3][0] = 0.75*x[0][0] + 0.25*x[2][0];
16602
coordinates[3][1] = 0.75*x[0][1] + 0.25*x[2][1];
16603
coordinates[4][0] = 0.5*x[0][0] + 0.5*x[2][0];
16604
coordinates[4][1] = 0.5*x[0][1] + 0.5*x[2][1];
16605
coordinates[5][0] = 0.25*x[0][0] + 0.75*x[2][0];
16606
coordinates[5][1] = 0.25*x[0][1] + 0.75*x[2][1];
16607
coordinates[6][0] = 0.75*x[0][0] + 0.25*x[1][0];
16608
coordinates[6][1] = 0.75*x[0][1] + 0.25*x[1][1];
16609
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[1][0];
16610
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[1][1];
16611
coordinates[8][0] = 0.25*x[0][0] + 0.75*x[1][0];
16612
coordinates[8][1] = 0.25*x[0][1] + 0.75*x[1][1];
16613
coordinates[9][0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
16614
coordinates[9][1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
16615
coordinates[10][0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
16616
coordinates[10][1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
16617
coordinates[11][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
16618
coordinates[11][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
16619
coordinates[12][0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
16620
coordinates[12][1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
16621
coordinates[13][0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
16622
coordinates[13][1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
16623
coordinates[14][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
16624
coordinates[14][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
16753
dof_coordinates[0][0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
16754
dof_coordinates[0][1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
16755
dof_coordinates[1][0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
16756
dof_coordinates[1][1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
16757
dof_coordinates[2][0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
16758
dof_coordinates[2][1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
16759
dof_coordinates[3][0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
16760
dof_coordinates[3][1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
16761
dof_coordinates[4][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
16762
dof_coordinates[4][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
16763
dof_coordinates[5][0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
16764
dof_coordinates[5][1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
16765
dof_coordinates[6][0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
16766
dof_coordinates[6][1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
16767
dof_coordinates[7][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
16768
dof_coordinates[7][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
16769
dof_coordinates[8][0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
16770
dof_coordinates[8][1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
16771
dof_coordinates[9][0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
16772
dof_coordinates[9][1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
16773
dof_coordinates[10][0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
16774
dof_coordinates[10][1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
16775
dof_coordinates[11][0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
16776
dof_coordinates[11][1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
16777
dof_coordinates[12][0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
16778
dof_coordinates[12][1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
16779
dof_coordinates[13][0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
16780
dof_coordinates[13][1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
16781
dof_coordinates[14][0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
16782
dof_coordinates[14][1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
16625
16783
}
16626
16784
16627
16785
/// Return the number of sub dofmaps (for a mixed element)
16628
virtual unsigned int num_sub_dofmaps() const
16786
virtual std::size_t num_sub_dofmaps() const
16629
16787
{
16630
16788
return 0;
16631
16789
}
16632
16790
16633
16791
/// Create a new dofmap for sub dofmap i (for a mixed element)
16634
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
16792
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
16635
16793
{
16636
16794
return 0;
16637
16795
}
16649
16807
16650
16808
class mixedmixedelement_dofmap_5: public ufc::dofmap
16651
16809
{
16652
private:
16653
16654
unsigned int _global_dimension;
16655
16810
public:
16656
16811
16657
16812
/// Constructor
16658
16813
mixedmixedelement_dofmap_5() : ufc::dofmap()
16659
16814
{
16660
_global_dimension = 0;
16815
// Do nothing
16661
16816
}
16662
16817
16663
16818
/// Destructor
16669
16824
/// Return a string identifying the dofmap
16670
16825
virtual const char* signature() const
16671
16826
{
16672
return "FFC dofmap for MixedElement(*[MixedElement(*[VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None), FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)], **{'value_shape': (3,) }), FiniteElement('Raviart-Thomas', Cell('triangle', Space(2)), 3, None)], **{'value_shape': (5,) })";
16827
return "FFC dofmap for MixedElement(*[MixedElement(*[VectorElement('Discontinuous Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 0, 2, None), FiniteElement('Lagrange', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 2, None)], **{'value_shape': (3,) }), FiniteElement('Raviart-Thomas', Domain(Cell('triangle', 2), 'triangle_multiverse', 2, 2), 3, None)], **{'value_shape': (5,) })";
16673
16828
}
16674
16829
16675
16830
/// Return true iff mesh entities of topological dimension d are needed
16676
virtual bool needs_mesh_entities(unsigned int d) const
16831
virtual bool needs_mesh_entities(std::size_t d) const
16677
16832
{
16678
16833
switch (d)
16679
16834
{
16697
16852
return false;
16698
16853
}
16699
16854
16700
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
16701
virtual bool init_mesh(const ufc::mesh& m)
16702
{
16703
_global_dimension = m.num_entities[0] + 4*m.num_entities[1] + 8*m.num_entities[2];
16704
return false;
16705
}
16706
16707
/// Initialize dofmap for given cell
16708
virtual void init_cell(const ufc::mesh& m,
16709
const ufc::cell& c)
16710
{
16711
// Do nothing
16712
}
16713
16714
/// Finish initialization of dofmap for cells
16715
virtual void init_cell_finalize()
16716
{
16717
// Do nothing
16718
}
16719
16720
16855
/// Return the topological dimension of the associated cell shape
16721
virtual unsigned int topological_dimension() const
16856
virtual std::size_t topological_dimension() const
16722
16857
{
16723
16858
return 2;
16724
16859
}
16725
16860
16726
16861
/// Return the geometric dimension of the associated cell shape
16727
virtual unsigned int geometric_dimension() const
16862
virtual std::size_t geometric_dimension() const
16728
16863
{
16729
16864
return 2;
16730
16865
}
16731
16866
16732
16867
/// Return the dimension of the global finite element function space
16733
virtual unsigned int global_dimension() const
16868
virtual std::size_t global_dimension(const std::vector<std::size_t>&
16869
num_global_entities) const
16734
16870
{
16735
return _global_dimension;
16871
return num_global_entities[0] + 4*num_global_entities[1] + 8*num_global_entities[2];
16736
16872
}
16737
16873
16738
16874
/// Return the dimension of the local finite element function space for a cell
16739
virtual unsigned int local_dimension(const ufc::cell& c) const
16875
virtual std::size_t local_dimension(const ufc::cell& c) const
16740
16876
{
16741
16877
return 23;
16742
16878
}
16743
16879
16744
16880
/// Return the maximum dimension of the local finite element function space
16745
virtual unsigned int max_local_dimension() const
16881
virtual std::size_t max_local_dimension() const
16746
16882
{
16747
16883
return 23;
16748
16884
}
16749
16885
16750
16886
/// Return the number of dofs on each cell facet
16751
virtual unsigned int num_facet_dofs() const
16887
virtual std::size_t num_facet_dofs() const
16752
16888
{
16753
16889
return 6;
16754
16890
}
16755
16891
16756
16892
/// Return the number of dofs associated with each cell entity of dimension d
16757
virtual unsigned int num_entity_dofs(unsigned int d) const
16893
virtual std::size_t num_entity_dofs(std::size_t d) const
16758
16894
{
16759
16895
switch (d)
16760
16896
{
16779
16915
}
16780
16916
16781
16917
/// Tabulate the local-to-global mapping of dofs on a cell
16782
virtual void tabulate_dofs(unsigned int* dofs,
16783
const ufc::mesh& m,
16918
virtual void tabulate_dofs(std::size_t* dofs,
16919
const std::vector<std::size_t>& num_global_entities,
16784
16920
const ufc::cell& c) const
16785
16921
{
16786
16922
unsigned int offset = 0;
16787
16923
dofs[0] = offset + c.entity_indices[2][0];
16788
offset += m.num_entities[2];
16924
offset += num_global_entities[2];
16789
16925
dofs[1] = offset + c.entity_indices[2][0];
16790
offset += m.num_entities[2];
16926
offset += num_global_entities[2];
16791
16927
dofs[2] = offset + c.entity_indices[0][0];
16792
16928
dofs[3] = offset + c.entity_indices[0][1];
16793
16929
dofs[4] = offset + c.entity_indices[0][2];
16794
offset += m.num_entities[0];
16930
offset += num_global_entities[0];
16795
16931
dofs[5] = offset + c.entity_indices[1][0];
16796
16932
dofs[6] = offset + c.entity_indices[1][1];
16797
16933
dofs[7] = offset + c.entity_indices[1][2];
16798
offset += m.num_entities[1];
16934
offset += num_global_entities[1];
16799
16935
dofs[8] = offset + 3*c.entity_indices[1][0];
16800
16936
dofs[9] = offset + 3*c.entity_indices[1][0] + 1;
16801
16937
dofs[10] = offset + 3*c.entity_indices[1][0] + 2;
16805
16941
dofs[14] = offset + 3*c.entity_indices[1][2];
16806
16942
dofs[15] = offset + 3*c.entity_indices[1][2] + 1;
16807
16943
dofs[16] = offset + 3*c.entity_indices[1][2] + 2;
16808
offset += 3*m.num_entities[1];
16944
offset += 3*num_global_entities[1];
16809
16945
dofs[17] = offset + 6*c.entity_indices[2][0];
16810
16946
dofs[18] = offset + 6*c.entity_indices[2][0] + 1;
16811
16947
dofs[19] = offset + 6*c.entity_indices[2][0] + 2;
16812
16948
dofs[20] = offset + 6*c.entity_indices[2][0] + 3;
16813
16949
dofs[21] = offset + 6*c.entity_indices[2][0] + 4;
16814
16950
dofs[22] = offset + 6*c.entity_indices[2][0] + 5;
16815
offset += 6*m.num_entities[2];
16951
offset += 6*num_global_entities[2];
16816
16952
}
16817
16953
16818
16954
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
16819
virtual void tabulate_facet_dofs(unsigned int* dofs,
16820
unsigned int facet) const
16955
virtual void tabulate_facet_dofs(std::size_t* dofs,
16956
std::size_t facet) const
16821
16957
{
16822
16958
switch (facet)
16823
16959
{
16856
16992
}
16857
16993
16858
16994
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
16859
virtual void tabulate_entity_dofs(unsigned int* dofs,
16860
unsigned int d, unsigned int i) const
16995
virtual void tabulate_entity_dofs(std::size_t* dofs,
16996
std::size_t d, std::size_t i) const
16861
16997
{
16862
16998
if (d > 2)
16863
16999
{
16953
17089
}
16954
17090
16955
17091
/// Tabulate the coordinates of all dofs on a cell
16956
virtual void tabulate_coordinates(double** coordinates,
16957
const ufc::cell& c) const
17092
virtual void tabulate_coordinates(double** dof_coordinates,
17093
const double* vertex_coordinates) const
16958
17094
{
16959
const double * const * x = c.coordinates;
16960
16961
coordinates[0][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
16962
coordinates[0][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
16963
coordinates[1][0] = 0.33333333*x[0][0] + 0.33333333*x[1][0] + 0.33333333*x[2][0];
16964
coordinates[1][1] = 0.33333333*x[0][1] + 0.33333333*x[1][1] + 0.33333333*x[2][1];
16965
coordinates[2][0] = x[0][0];
16966
coordinates[2][1] = x[0][1];
16967
coordinates[3][0] = x[1][0];
16968
coordinates[3][1] = x[1][1];
16969
coordinates[4][0] = x[2][0];
16970
coordinates[4][1] = x[2][1];
16971
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[2][0];
16972
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[2][1];
16973
coordinates[6][0] = 0.5*x[0][0] + 0.5*x[2][0];
16974
coordinates[6][1] = 0.5*x[0][1] + 0.5*x[2][1];
16975
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[1][0];
16976
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[1][1];
16977
coordinates[8][0] = 0.75*x[1][0] + 0.25*x[2][0];
16978
coordinates[8][1] = 0.75*x[1][1] + 0.25*x[2][1];
16979
coordinates[9][0] = 0.5*x[1][0] + 0.5*x[2][0];
16980
coordinates[9][1] = 0.5*x[1][1] + 0.5*x[2][1];
16981
coordinates[10][0] = 0.25*x[1][0] + 0.75*x[2][0];
16982
coordinates[10][1] = 0.25*x[1][1] + 0.75*x[2][1];
16983
coordinates[11][0] = 0.75*x[0][0] + 0.25*x[2][0];
16984
coordinates[11][1] = 0.75*x[0][1] + 0.25*x[2][1];
16985
coordinates[12][0] = 0.5*x[0][0] + 0.5*x[2][0];
16986
coordinates[12][1] = 0.5*x[0][1] + 0.5*x[2][1];
16987
coordinates[13][0] = 0.25*x[0][0] + 0.75*x[2][0];
16988
coordinates[13][1] = 0.25*x[0][1] + 0.75*x[2][1];
16989
coordinates[14][0] = 0.75*x[0][0] + 0.25*x[1][0];
16990
coordinates[14][1] = 0.75*x[0][1] + 0.25*x[1][1];
16991
coordinates[15][0] = 0.5*x[0][0] + 0.5*x[1][0];
16992
coordinates[15][1] = 0.5*x[0][1] + 0.5*x[1][1];
16993
coordinates[16][0] = 0.25*x[0][0] + 0.75*x[1][0];
16994
coordinates[16][1] = 0.25*x[0][1] + 0.75*x[1][1];
16995
coordinates[17][0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
16996
coordinates[17][1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
16997
coordinates[18][0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
16998
coordinates[18][1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
16999
coordinates[19][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
17000
coordinates[19][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
17001
coordinates[20][0] = 0.5*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0];
17002
coordinates[20][1] = 0.5*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1];
17003
coordinates[21][0] = 0.25*x[0][0] + 0.5*x[1][0] + 0.25*x[2][0];
17004
coordinates[21][1] = 0.25*x[0][1] + 0.5*x[1][1] + 0.25*x[2][1];
17005
coordinates[22][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.5*x[2][0];
17006
coordinates[22][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.5*x[2][1];
17095
dof_coordinates[0][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
17096
dof_coordinates[0][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
17097
dof_coordinates[1][0] = 0.33333333*vertex_coordinates[0] + 0.33333333*vertex_coordinates[2] + 0.33333333*vertex_coordinates[4];
17098
dof_coordinates[1][1] = 0.33333333*vertex_coordinates[1] + 0.33333333*vertex_coordinates[3] + 0.33333333*vertex_coordinates[5];
17099
dof_coordinates[2][0] = vertex_coordinates[0];
17100
dof_coordinates[2][1] = vertex_coordinates[1];
17101
dof_coordinates[3][0] = vertex_coordinates[2];
17102
dof_coordinates[3][1] = vertex_coordinates[3];
17103
dof_coordinates[4][0] = vertex_coordinates[4];
17104
dof_coordinates[4][1] = vertex_coordinates[5];
17105
dof_coordinates[5][0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
17106
dof_coordinates[5][1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
17107
dof_coordinates[6][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
17108
dof_coordinates[6][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
17109
dof_coordinates[7][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
17110
dof_coordinates[7][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
17111
dof_coordinates[8][0] = 0.75*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
17112
dof_coordinates[8][1] = 0.75*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
17113
dof_coordinates[9][0] = 0.5*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
17114
dof_coordinates[9][1] = 0.5*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
17115
dof_coordinates[10][0] = 0.25*vertex_coordinates[2] + 0.75*vertex_coordinates[4];
17116
dof_coordinates[10][1] = 0.25*vertex_coordinates[3] + 0.75*vertex_coordinates[5];
17117
dof_coordinates[11][0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[4];
17118
dof_coordinates[11][1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[5];
17119
dof_coordinates[12][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[4];
17120
dof_coordinates[12][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[5];
17121
dof_coordinates[13][0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[4];
17122
dof_coordinates[13][1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[5];
17123
dof_coordinates[14][0] = 0.75*vertex_coordinates[0] + 0.25*vertex_coordinates[2];
17124
dof_coordinates[14][1] = 0.75*vertex_coordinates[1] + 0.25*vertex_coordinates[3];
17125
dof_coordinates[15][0] = 0.5*vertex_coordinates[0] + 0.5*vertex_coordinates[2];
17126
dof_coordinates[15][1] = 0.5*vertex_coordinates[1] + 0.5*vertex_coordinates[3];
17127
dof_coordinates[16][0] = 0.25*vertex_coordinates[0] + 0.75*vertex_coordinates[2];
17128
dof_coordinates[16][1] = 0.25*vertex_coordinates[1] + 0.75*vertex_coordinates[3];
17129
dof_coordinates[17][0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
17130
dof_coordinates[17][1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
17131
dof_coordinates[18][0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
17132
dof_coordinates[18][1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
17133
dof_coordinates[19][0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
17134
dof_coordinates[19][1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
17135
dof_coordinates[20][0] = 0.5*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
17136
dof_coordinates[20][1] = 0.5*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
17137
dof_coordinates[21][0] = 0.25*vertex_coordinates[0] + 0.5*vertex_coordinates[2] + 0.25*vertex_coordinates[4];
17138
dof_coordinates[21][1] = 0.25*vertex_coordinates[1] + 0.5*vertex_coordinates[3] + 0.25*vertex_coordinates[5];
17139
dof_coordinates[22][0] = 0.25*vertex_coordinates[0] + 0.25*vertex_coordinates[2] + 0.5*vertex_coordinates[4];
17140
dof_coordinates[22][1] = 0.25*vertex_coordinates[1] + 0.25*vertex_coordinates[3] + 0.5*vertex_coordinates[5];
17007
17141
}
17008
17142
17009
17143
/// Return the number of sub dofmaps (for a mixed element)
17010
virtual unsigned int num_sub_dofmaps() const
17144
virtual std::size_t num_sub_dofmaps() const
17011
17145
{
17012
17146
return 2;
17013
17147
}
17014
17148
17015
17149
/// Create a new dofmap for sub dofmap i (for a mixed element)
17016
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
17150
virtual ufc::dofmap* create_sub_dofmap(std::size_t i) const
17017
17151
{
17018
17152
switch (i)
17019
17153
{
17044
17178
/// tensor corresponding to the local contribution to a form from
17045
17179
/// the integral over a cell.
17046
17180
17047
class mixedmixedelement_cell_integral_0_0: public ufc::cell_integral
17181
class mixedmixedelement_cell_integral_0_otherwise: public ufc::cell_integral
17048
17182
{
17049
17183
public:
17050
17184
17051
17185
/// Constructor
17052
mixedmixedelement_cell_integral_0_0() : ufc::cell_integral()
17186
mixedmixedelement_cell_integral_0_otherwise() : ufc::cell_integral()
17053
17187
{
17054
17188
// Do nothing
17055
17189
}
17056
17190
17057
17191
/// Destructor
17058
virtual ~mixedmixedelement_cell_integral_0_0()
17192
virtual ~mixedmixedelement_cell_integral_0_otherwise()
17059
17193
{
17060
17194
// Do nothing
17061
17195
}
17063
17197
/// Tabulate the tensor for the contribution from a local cell
17064
17198
virtual void tabulate_tensor(double* A,
17065
17199
const double * const * w,
17066
const ufc::cell& c) const
17200
const double* vertex_coordinates,
17201
int cell_orientation) const
17067
17202
{
17068
// Number of operations (multiply-add pairs) for Jacobian data: 9
17203
// Number of operations (multiply-add pairs) for Jacobian data: 3
17069
17204
// Number of operations (multiply-add pairs) for geometry tensor: 0
17070
17205
// Number of operations (multiply-add pairs) for tensor contraction: 0
17071
// Total number of operations (multiply-add pairs): 9
17072
17073
// Extract vertex coordinates
17074
const double * const * x = c.coordinates;
17075
17076
// Compute Jacobian of affine map from reference cell
17077
const double J_00 = x[1][0] - x[0][0];
17078
const double J_01 = x[2][0] - x[0][0];
17079
const double J_10 = x[1][1] - x[0][1];
17080
const double J_11 = x[2][1] - x[0][1];
17081
17082
// Compute determinant of Jacobian
17083
double detJ = J_00*J_11 - J_01*J_10;
17084
17085
// Compute inverse of Jacobian
17206
// Total number of operations (multiply-add pairs): 3
17207
17208
// Compute Jacobian
17209
double J[4];
17210
compute_jacobian_triangle_2d(J, vertex_coordinates);
17211
17212
// Compute Jacobian inverse and determinant
17213
double K[4];
17214
double detJ;
17215
compute_jacobian_inverse_triangle_2d(K, detJ, J);
17086
17216
17087
17217
// Set scale factor
17088
17218
const double det = std::abs(detJ);
17116
17246
A[22] = 0.0;
17117
17247
}
17118
17248
17119
/// Tabulate the tensor for the contribution from a local cell
17120
/// using the specified reference cell quadrature points/weights
17121
virtual void tabulate_tensor(double* A,
17122
const double * const * w,
17123
const ufc::cell& c,
17124
unsigned int num_quadrature_points,
17125
const double * const * quadrature_points,
17126
const double* quadrature_weights) const
17127
{
17128
std::cerr << "*** FFC warning: " << "Quadrature version of tabulate_tensor not available when using the FFC tensor representation." << std::endl;
17129
}
17130
17131
17249
};
17132
17250
17133
17251
/// This class defines the interface for the assembly of the global
17164
17282
/// Return a string identifying the form
17165
17283
virtual const char* signature() const
17166
17284
{
17167
return "Form([Integral(Indexed(Argument(MixedElement(*[MixedElement(*[VectorElement('Discontinuous Lagrange', Cell('triangle', Space(2)), 0, 2, None), FiniteElement('Lagrange', Cell('triangle', Space(2)), 2, None)], **{'value_shape': (3,) }), FiniteElement('Raviart-Thomas', Cell('triangle', Space(2)), 3, None)], **{'value_shape': (5,) }), 0), MultiIndex((FixedIndex(0),), {})), Measure('cell', 0, None))])";
17285
return "4dbd6ffce91104cca6203350dd5899d91933e7a0ff03b5e3d1e43c46be855704ea0938c37d2dc1542a93ea929629248d53f538a8c8fd87383de2bb660568b10b";
17168
17286
}
17169
17287
17170
17288
/// Return the rank of the global tensor (r)
17171
virtual unsigned int rank() const
17289
virtual std::size_t rank() const
17172
17290
{
17173
17291
return 1;
17174
17292
}
17175
17293
17176
17294
/// Return the number of coefficients (n)
17177
virtual unsigned int num_coefficients() const
17295
virtual std::size_t num_coefficients() const
17178
17296
{
17179
17297
return 0;
17180
17298
}
17181
17299
17182
17300
/// Return the number of cell domains
17183
virtual unsigned int num_cell_domains() const
17301
virtual std::size_t num_cell_domains() const
17184
17302
{
17185
return 1;
17303
return 0;
17186
17304
}
17187
17305
17188
17306
/// Return the number of exterior facet domains
17189
virtual unsigned int num_exterior_facet_domains() const
17307
virtual std::size_t num_exterior_facet_domains() const
17190
17308
{
17191
17309
return 0;
17192
17310
}
17193
17311
17194
17312
/// Return the number of interior facet domains
17195
virtual unsigned int num_interior_facet_domains() const
17196
{
17197
return 0;
17313
virtual std::size_t num_interior_facet_domains() const
17314
{
17315
return 0;
17316
}
17317
17318
/// Return the number of point domains
17319
virtual std::size_t num_point_domains() const
17320
{
17321
return 0;
17322
}
17323
17324
/// Return whether the form has any cell integrals
17325
virtual bool has_cell_integrals() const
17326
{
17327
return true;
17328
}
17329
17330
/// Return whether the form has any exterior facet integrals
17331
virtual bool has_exterior_facet_integrals() const
17332
{
17333
return false;
17334
}
17335
17336
/// Return whether the form has any interior facet integrals
17337
virtual bool has_interior_facet_integrals() const
17338
{
17339
return false;
17340
}
17341
17342
/// Return whether the form has any point integrals
17343
virtual bool has_point_integrals() const
17344
{
17345
return false;
17198
17346
}
17199
17347
17200
17348
/// Create a new finite element for argument function i
17201
virtual ufc::finite_element* create_finite_element(unsigned int i) const
17349
virtual ufc::finite_element* create_finite_element(std::size_t i) const
17202
17350
{
17203
17351
switch (i)
17204
17352
{
17213
17361
}
17214
17362
17215
17363
/// Create a new dofmap for argument function i
17216
virtual ufc::dofmap* create_dofmap(unsigned int i) const
17364
virtual ufc::dofmap* create_dofmap(std::size_t i) const
17217
17365
{
17218
17366
switch (i)
17219
17367
{
17228
17376
}
17229
17377
17230
17378
/// Create a new cell integral on sub domain i
17231
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
17379
virtual ufc::cell_integral* create_cell_integral(std::size_t i) const
17232
17380
{
17233
switch (i)
17234
{
17235
case 0:
17236
{
17237
return new mixedmixedelement_cell_integral_0_0();
17238
break;
17239
}
17240
}
17241
17242
17381
return 0;
17243
17382
}
17244
17383
17245
17384
/// Create a new exterior facet integral on sub domain i
17246
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
17385
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(std::size_t i) const
17247
17386
{
17248
17387
return 0;
17249
17388
}
17250
17389
17251
17390
/// Create a new interior facet integral on sub domain i
17252
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
17391
virtual ufc::interior_facet_integral* create_interior_facet_integral(std::size_t i) const
17392
{
17393
return 0;
17394
}
17395
17396
/// Create a new point integral on sub domain i
17397
virtual ufc::point_integral* create_point_integral(std::size_t i) const
17398
{
17399
return 0;
17400
}
17401
17402
/// Create a new cell integral on everywhere else
17403
virtual ufc::cell_integral* create_default_cell_integral() const
17404
{
17405
return new mixedmixedelement_cell_integral_0_otherwise();
17406
}
17407
17408
/// Create a new exterior facet integral on everywhere else
17409
virtual ufc::exterior_facet_integral* create_default_exterior_facet_integral() const
17410
{
17411
return 0;
17412
}
17413
17414
/// Create a new interior facet integral on everywhere else
17415
virtual ufc::interior_facet_integral* create_default_interior_facet_integral() const
17416
{
17417
return 0;
17418
}
17419
17420
/// Create a new point integral on everywhere else
17421
virtual ufc::point_integral* create_default_point_integral() const
17253
17422
{
17254
17423
return 0;
17255
17424
}
Loggerhead is a web-based interface for Breezy
Version: 2.0.1