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- Committer: Bazaar Package Importer
- Author(s): Johannes Ring
- Date: 2010-07-01 19:54:32 UTC
- mfrom: (1.1.5 upstream)
- Revision ID: james.westby@ubuntu.com-20100701195432-xz3gw5nprdj79jcb
Tags: 0.9.3-1
* New upstream release.
* debian/control:
- Minor fix in Vcs fields.
- Bump Standards-Version to 3.9.0 (no changes needed).
- Update version for python-ufc, python-fiat, and python-ufl in
Depends field.
* Switch to dpkg-source 3.0 (quilt) format.
* Update debian/copyright and debian/copyright_hints.
* debian/control:
- Minor fix in Vcs fields.
- Bump Standards-Version to 3.9.0 (no changes needed).
- Update version for python-ufc, python-fiat, and python-ufl in
Depends field.
* Switch to dpkg-source 3.0 (quilt) format.
* Update debian/copyright and debian/copyright_hints.
- files added:
- bench/MassH1_2D_1.ufl
- bench/results
- debian/source
- files removed:
- bench/NavierStokes.form
- files modified:
- ChangeLog
added
removed
test/regression/references/FacetIntegrals.h
1
// This code conforms with the UFC specification version 1.4
2
// and was automatically generated by FFC version 0.9.2.
1
// This code conforms with the UFC specification version 1.4.1
2
// and was automatically generated by FFC version 0.9.3.
3
3
//
4
4
// This code was generated with the following parameters:
5
5
//
96
96
// Reset values.
97
97
*values = 0.00000000;
98
98
99
// Map degree of freedom to element degree of freedom
100
const unsigned int dof = i;
101
102
99
// Array of basisvalues.
103
100
double basisvalues[1] = {0.00000000};
104
101
108
105
basisvalues[0] = 1.00000000;
109
106
110
107
// Table(s) of coefficients.
111
static const double coefficients0[1][1] = \
112
{{1.00000000}};
108
static const double coefficients0[1] = \
109
{1.00000000};
113
110
114
111
// Compute value(s).
115
112
for (unsigned int r = 0; r < 1; r++)
116
113
{
117
*values += coefficients0[dof][r]*basisvalues[r];
114
*values += coefficients0[r]*basisvalues[r];
118
115
}// end loop over 'r'
119
116
}
120
117
220
217
values[r] = 0.00000000;
221
218
}// end loop over 'r'
222
219
223
// Map degree of freedom to element degree of freedom
224
const unsigned int dof = i;
225
220
226
221
// Array of basisvalues.
227
222
double basisvalues[1] = {0.00000000};
232
227
basisvalues[0] = 1.00000000;
233
228
234
229
// Table(s) of coefficients.
235
static const double coefficients0[1][1] = \
236
{{1.00000000}};
230
static const double coefficients0[1] = \
231
{1.00000000};
237
232
238
233
// Tables of derivatives of the polynomial base (transpose).
239
234
static const double dmats0[1][1] = \
322
317
{
323
318
for (unsigned int t = 0; t < 1; t++)
324
319
{
325
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
320
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
326
321
}// end loop over 't'
327
322
}// end loop over 's'
328
323
}// end loop over 'r'
508
503
// Reset values.
509
504
values[0] = 0.00000000;
510
505
values[1] = 0.00000000;
511
if (0 <= i && i <= 0)
512
{
513
// Map degree of freedom to element degree of freedom
514
const unsigned int dof = i;
515
516
// Array of basisvalues.
517
double basisvalues[1] = {0.00000000};
518
519
// Declare helper variables.
520
521
// Compute basisvalues.
522
basisvalues[0] = 1.00000000;
523
524
// Table(s) of coefficients.
525
static const double coefficients0[1][1] = \
526
{{1.00000000}};
527
528
// Compute value(s).
529
for (unsigned int r = 0; r < 1; r++)
530
{
531
values[0] += coefficients0[dof][r]*basisvalues[r];
532
}// end loop over 'r'
533
}
534
535
if (1 <= i && i <= 1)
536
{
537
// Map degree of freedom to element degree of freedom
538
const unsigned int dof = i - 1;
539
540
// Array of basisvalues.
541
double basisvalues[1] = {0.00000000};
542
543
// Declare helper variables.
544
545
// Compute basisvalues.
546
basisvalues[0] = 1.00000000;
547
548
// Table(s) of coefficients.
549
static const double coefficients0[1][1] = \
550
{{1.00000000}};
551
552
// Compute value(s).
553
for (unsigned int r = 0; r < 1; r++)
554
{
555
values[1] += coefficients0[dof][r]*basisvalues[r];
556
}// end loop over 'r'
506
switch (i)
507
{
508
case 0:
509
{
510
511
// Array of basisvalues.
512
double basisvalues[1] = {0.00000000};
513
514
// Declare helper variables.
515
516
// Compute basisvalues.
517
basisvalues[0] = 1.00000000;
518
519
// Table(s) of coefficients.
520
static const double coefficients0[1] = \
521
{1.00000000};
522
523
// Compute value(s).
524
for (unsigned int r = 0; r < 1; r++)
525
{
526
values[0] += coefficients0[r]*basisvalues[r];
527
}// end loop over 'r'
528
break;
529
}
530
case 1:
531
{
532
533
// Array of basisvalues.
534
double basisvalues[1] = {0.00000000};
535
536
// Declare helper variables.
537
538
// Compute basisvalues.
539
basisvalues[0] = 1.00000000;
540
541
// Table(s) of coefficients.
542
static const double coefficients0[1] = \
543
{1.00000000};
544
545
// Compute value(s).
546
for (unsigned int r = 0; r < 1; r++)
547
{
548
values[1] += coefficients0[r]*basisvalues[r];
549
}// end loop over 'r'
550
break;
551
}
557
552
}
558
553
559
554
}
670
665
values[r] = 0.00000000;
671
666
}// end loop over 'r'
672
667
673
if (0 <= i && i <= 0)
668
switch (i)
674
669
{
675
// Map degree of freedom to element degree of freedom
676
const unsigned int dof = i;
677
670
case 0:
671
{
672
678
673
// Array of basisvalues.
679
674
double basisvalues[1] = {0.00000000};
680
675
684
679
basisvalues[0] = 1.00000000;
685
680
686
681
// Table(s) of coefficients.
687
static const double coefficients0[1][1] = \
688
{{1.00000000}};
682
static const double coefficients0[1] = \
683
{1.00000000};
689
684
690
685
// Tables of derivatives of the polynomial base (transpose).
691
686
static const double dmats0[1][1] = \
774
769
{
775
770
for (unsigned int t = 0; t < 1; t++)
776
771
{
777
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
772
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
778
773
}// end loop over 't'
779
774
}// end loop over 's'
780
775
}// end loop over 'r'
802
797
delete [] transform[r];
803
798
}// end loop over 'r'
804
799
delete [] transform;
805
}
806
807
if (1 <= i && i <= 1)
808
{
809
// Map degree of freedom to element degree of freedom
810
const unsigned int dof = i - 1;
811
800
break;
801
}
802
case 1:
803
{
804
812
805
// Array of basisvalues.
813
806
double basisvalues[1] = {0.00000000};
814
807
818
811
basisvalues[0] = 1.00000000;
819
812
820
813
// Table(s) of coefficients.
821
static const double coefficients0[1][1] = \
822
{{1.00000000}};
814
static const double coefficients0[1] = \
815
{1.00000000};
823
816
824
817
// Tables of derivatives of the polynomial base (transpose).
825
818
static const double dmats0[1][1] = \
908
901
{
909
902
for (unsigned int t = 0; t < 1; t++)
910
903
{
911
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
904
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
912
905
}// end loop over 't'
913
906
}// end loop over 's'
914
907
}// end loop over 'r'
936
929
delete [] transform[r];
937
930
}// end loop over 'r'
938
931
delete [] transform;
932
break;
933
}
939
934
}
940
935
941
936
}
1150
1145
1151
1146
// Reset values.
1152
1147
*values = 0.00000000;
1153
1154
// Map degree of freedom to element degree of freedom
1155
const unsigned int dof = i;
1156
1157
// Array of basisvalues.
1158
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1159
1160
// Declare helper variables.
1161
unsigned int rr = 0;
1162
unsigned int ss = 0;
1163
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1164
1165
// Compute basisvalues.
1166
basisvalues[0] = 1.00000000;
1167
basisvalues[1] = tmp0;
1168
for (unsigned int r = 0; r < 1; r++)
1169
{
1170
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1171
ss = r*(r + 1)/2;
1172
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1173
}// end loop over 'r'
1174
for (unsigned int r = 0; r < 2; r++)
1175
{
1176
for (unsigned int s = 0; s < 2 - r; s++)
1177
{
1178
rr = (r + s)*(r + s + 1)/2 + s;
1179
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1180
}// end loop over 's'
1181
}// end loop over 'r'
1182
1183
// Table(s) of coefficients.
1184
static const double coefficients0[3][3] = \
1185
{{0.47140452, -0.28867513, -0.16666667},
1186
{0.47140452, 0.28867513, -0.16666667},
1187
{0.47140452, 0.00000000, 0.33333333}};
1188
1189
// Compute value(s).
1190
for (unsigned int r = 0; r < 3; r++)
1191
{
1192
*values += coefficients0[dof][r]*basisvalues[r];
1193
}// end loop over 'r'
1148
switch (i)
1149
{
1150
case 0:
1151
{
1152
1153
// Array of basisvalues.
1154
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1155
1156
// Declare helper variables.
1157
unsigned int rr = 0;
1158
unsigned int ss = 0;
1159
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1160
1161
// Compute basisvalues.
1162
basisvalues[0] = 1.00000000;
1163
basisvalues[1] = tmp0;
1164
for (unsigned int r = 0; r < 1; r++)
1165
{
1166
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1167
ss = r*(r + 1)/2;
1168
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1169
}// end loop over 'r'
1170
for (unsigned int r = 0; r < 2; r++)
1171
{
1172
for (unsigned int s = 0; s < 2 - r; s++)
1173
{
1174
rr = (r + s)*(r + s + 1)/2 + s;
1175
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1176
}// end loop over 's'
1177
}// end loop over 'r'
1178
1179
// Table(s) of coefficients.
1180
static const double coefficients0[3] = \
1181
{0.47140452, -0.28867513, -0.16666667};
1182
1183
// Compute value(s).
1184
for (unsigned int r = 0; r < 3; r++)
1185
{
1186
*values += coefficients0[r]*basisvalues[r];
1187
}// end loop over 'r'
1188
break;
1189
}
1190
case 1:
1191
{
1192
1193
// Array of basisvalues.
1194
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1195
1196
// Declare helper variables.
1197
unsigned int rr = 0;
1198
unsigned int ss = 0;
1199
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1200
1201
// Compute basisvalues.
1202
basisvalues[0] = 1.00000000;
1203
basisvalues[1] = tmp0;
1204
for (unsigned int r = 0; r < 1; r++)
1205
{
1206
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1207
ss = r*(r + 1)/2;
1208
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1209
}// end loop over 'r'
1210
for (unsigned int r = 0; r < 2; r++)
1211
{
1212
for (unsigned int s = 0; s < 2 - r; s++)
1213
{
1214
rr = (r + s)*(r + s + 1)/2 + s;
1215
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1216
}// end loop over 's'
1217
}// end loop over 'r'
1218
1219
// Table(s) of coefficients.
1220
static const double coefficients0[3] = \
1221
{0.47140452, 0.28867513, -0.16666667};
1222
1223
// Compute value(s).
1224
for (unsigned int r = 0; r < 3; r++)
1225
{
1226
*values += coefficients0[r]*basisvalues[r];
1227
}// end loop over 'r'
1228
break;
1229
}
1230
case 2:
1231
{
1232
1233
// Array of basisvalues.
1234
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1235
1236
// Declare helper variables.
1237
unsigned int rr = 0;
1238
unsigned int ss = 0;
1239
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1240
1241
// Compute basisvalues.
1242
basisvalues[0] = 1.00000000;
1243
basisvalues[1] = tmp0;
1244
for (unsigned int r = 0; r < 1; r++)
1245
{
1246
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1247
ss = r*(r + 1)/2;
1248
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1249
}// end loop over 'r'
1250
for (unsigned int r = 0; r < 2; r++)
1251
{
1252
for (unsigned int s = 0; s < 2 - r; s++)
1253
{
1254
rr = (r + s)*(r + s + 1)/2 + s;
1255
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1256
}// end loop over 's'
1257
}// end loop over 'r'
1258
1259
// Table(s) of coefficients.
1260
static const double coefficients0[3] = \
1261
{0.47140452, 0.00000000, 0.33333333};
1262
1263
// Compute value(s).
1264
for (unsigned int r = 0; r < 3; r++)
1265
{
1266
*values += coefficients0[r]*basisvalues[r];
1267
}// end loop over 'r'
1268
break;
1269
}
1270
}
1271
1194
1272
}
1195
1273
1196
1274
/// Evaluate all basis functions at given point in cell
1306
1384
values[r] = 0.00000000;
1307
1385
}// end loop over 'r'
1308
1386
1309
// Map degree of freedom to element degree of freedom
1310
const unsigned int dof = i;
1311
1312
// Array of basisvalues.
1313
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1314
1315
// Declare helper variables.
1316
unsigned int rr = 0;
1317
unsigned int ss = 0;
1318
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1319
1320
// Compute basisvalues.
1321
basisvalues[0] = 1.00000000;
1322
basisvalues[1] = tmp0;
1323
for (unsigned int r = 0; r < 1; r++)
1324
{
1325
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1326
ss = r*(r + 1)/2;
1327
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1328
}// end loop over 'r'
1329
for (unsigned int r = 0; r < 2; r++)
1330
{
1331
for (unsigned int s = 0; s < 2 - r; s++)
1332
{
1333
rr = (r + s)*(r + s + 1)/2 + s;
1334
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1335
}// end loop over 's'
1336
}// end loop over 'r'
1337
1338
// Table(s) of coefficients.
1339
static const double coefficients0[3][3] = \
1340
{{0.47140452, -0.28867513, -0.16666667},
1341
{0.47140452, 0.28867513, -0.16666667},
1342
{0.47140452, 0.00000000, 0.33333333}};
1343
1344
// Tables of derivatives of the polynomial base (transpose).
1345
static const double dmats0[3][3] = \
1346
{{0.00000000, 0.00000000, 0.00000000},
1347
{4.89897949, 0.00000000, 0.00000000},
1348
{0.00000000, 0.00000000, 0.00000000}};
1349
1350
static const double dmats1[3][3] = \
1351
{{0.00000000, 0.00000000, 0.00000000},
1352
{2.44948974, 0.00000000, 0.00000000},
1353
{4.24264069, 0.00000000, 0.00000000}};
1354
1355
// Compute reference derivatives.
1356
// Declare pointer to array of derivatives on FIAT element.
1357
double *derivatives = new double[num_derivatives];
1358
for (unsigned int r = 0; r < num_derivatives; r++)
1359
{
1360
derivatives[r] = 0.00000000;
1361
}// end loop over 'r'
1362
1363
// Declare derivative matrix (of polynomial basis).
1364
double dmats[3][3] = \
1365
{{1.00000000, 0.00000000, 0.00000000},
1366
{0.00000000, 1.00000000, 0.00000000},
1367
{0.00000000, 0.00000000, 1.00000000}};
1368
1369
// Declare (auxiliary) derivative matrix (of polynomial basis).
1370
double dmats_old[3][3] = \
1371
{{1.00000000, 0.00000000, 0.00000000},
1372
{0.00000000, 1.00000000, 0.00000000},
1373
{0.00000000, 0.00000000, 1.00000000}};
1374
1375
// Loop possible derivatives.
1376
for (unsigned int r = 0; r < num_derivatives; r++)
1377
{
1378
// Resetting dmats values to compute next derivative.
1379
for (unsigned int t = 0; t < 3; t++)
1380
{
1381
for (unsigned int u = 0; u < 3; u++)
1382
{
1383
dmats[t][u] = 0.00000000;
1384
if (t == u)
1385
{
1386
dmats[t][u] = 1.00000000;
1387
}
1388
1389
}// end loop over 'u'
1390
}// end loop over 't'
1391
1392
// Looping derivative order to generate dmats.
1393
for (unsigned int s = 0; s < n; s++)
1394
{
1395
// Updating dmats_old with new values and resetting dmats.
1396
for (unsigned int t = 0; t < 3; t++)
1397
{
1398
for (unsigned int u = 0; u < 3; u++)
1399
{
1400
dmats_old[t][u] = dmats[t][u];
1401
dmats[t][u] = 0.00000000;
1402
}// end loop over 'u'
1403
}// end loop over 't'
1404
1405
// Update dmats using an inner product.
1406
if (combinations[r][s] == 0)
1407
{
1408
for (unsigned int t = 0; t < 3; t++)
1409
{
1410
for (unsigned int u = 0; u < 3; u++)
1411
{
1412
for (unsigned int tu = 0; tu < 3; tu++)
1413
{
1414
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1415
}// end loop over 'tu'
1416
}// end loop over 'u'
1417
}// end loop over 't'
1418
}
1419
1420
if (combinations[r][s] == 1)
1421
{
1422
for (unsigned int t = 0; t < 3; t++)
1423
{
1424
for (unsigned int u = 0; u < 3; u++)
1425
{
1426
for (unsigned int tu = 0; tu < 3; tu++)
1427
{
1428
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1429
}// end loop over 'tu'
1430
}// end loop over 'u'
1431
}// end loop over 't'
1432
}
1433
1434
}// end loop over 's'
1435
for (unsigned int s = 0; s < 3; s++)
1436
{
1437
for (unsigned int t = 0; t < 3; t++)
1438
{
1439
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
1440
}// end loop over 't'
1441
}// end loop over 's'
1442
}// end loop over 'r'
1443
1444
// Transform derivatives back to physical element
1445
for (unsigned int r = 0; r < num_derivatives; r++)
1446
{
1447
for (unsigned int s = 0; s < num_derivatives; s++)
1448
{
1449
values[r] += transform[r][s]*derivatives[s];
1450
}// end loop over 's'
1451
}// end loop over 'r'
1452
1453
// Delete pointer to array of derivatives on FIAT element
1454
delete [] derivatives;
1455
1456
// Delete pointer to array of combinations of derivatives and transform
1457
for (unsigned int r = 0; r < num_derivatives; r++)
1458
{
1459
delete [] combinations[r];
1460
}// end loop over 'r'
1461
delete [] combinations;
1462
for (unsigned int r = 0; r < num_derivatives; r++)
1463
{
1464
delete [] transform[r];
1465
}// end loop over 'r'
1466
delete [] transform;
1387
switch (i)
1388
{
1389
case 0:
1390
{
1391
1392
// Array of basisvalues.
1393
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1394
1395
// Declare helper variables.
1396
unsigned int rr = 0;
1397
unsigned int ss = 0;
1398
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1399
1400
// Compute basisvalues.
1401
basisvalues[0] = 1.00000000;
1402
basisvalues[1] = tmp0;
1403
for (unsigned int r = 0; r < 1; r++)
1404
{
1405
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1406
ss = r*(r + 1)/2;
1407
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1408
}// end loop over 'r'
1409
for (unsigned int r = 0; r < 2; r++)
1410
{
1411
for (unsigned int s = 0; s < 2 - r; s++)
1412
{
1413
rr = (r + s)*(r + s + 1)/2 + s;
1414
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1415
}// end loop over 's'
1416
}// end loop over 'r'
1417
1418
// Table(s) of coefficients.
1419
static const double coefficients0[3] = \
1420
{0.47140452, -0.28867513, -0.16666667};
1421
1422
// Tables of derivatives of the polynomial base (transpose).
1423
static const double dmats0[3][3] = \
1424
{{0.00000000, 0.00000000, 0.00000000},
1425
{4.89897949, 0.00000000, 0.00000000},
1426
{0.00000000, 0.00000000, 0.00000000}};
1427
1428
static const double dmats1[3][3] = \
1429
{{0.00000000, 0.00000000, 0.00000000},
1430
{2.44948974, 0.00000000, 0.00000000},
1431
{4.24264069, 0.00000000, 0.00000000}};
1432
1433
// Compute reference derivatives.
1434
// Declare pointer to array of derivatives on FIAT element.
1435
double *derivatives = new double[num_derivatives];
1436
for (unsigned int r = 0; r < num_derivatives; r++)
1437
{
1438
derivatives[r] = 0.00000000;
1439
}// end loop over 'r'
1440
1441
// Declare derivative matrix (of polynomial basis).
1442
double dmats[3][3] = \
1443
{{1.00000000, 0.00000000, 0.00000000},
1444
{0.00000000, 1.00000000, 0.00000000},
1445
{0.00000000, 0.00000000, 1.00000000}};
1446
1447
// Declare (auxiliary) derivative matrix (of polynomial basis).
1448
double dmats_old[3][3] = \
1449
{{1.00000000, 0.00000000, 0.00000000},
1450
{0.00000000, 1.00000000, 0.00000000},
1451
{0.00000000, 0.00000000, 1.00000000}};
1452
1453
// Loop possible derivatives.
1454
for (unsigned int r = 0; r < num_derivatives; r++)
1455
{
1456
// Resetting dmats values to compute next derivative.
1457
for (unsigned int t = 0; t < 3; t++)
1458
{
1459
for (unsigned int u = 0; u < 3; u++)
1460
{
1461
dmats[t][u] = 0.00000000;
1462
if (t == u)
1463
{
1464
dmats[t][u] = 1.00000000;
1465
}
1466
1467
}// end loop over 'u'
1468
}// end loop over 't'
1469
1470
// Looping derivative order to generate dmats.
1471
for (unsigned int s = 0; s < n; s++)
1472
{
1473
// Updating dmats_old with new values and resetting dmats.
1474
for (unsigned int t = 0; t < 3; t++)
1475
{
1476
for (unsigned int u = 0; u < 3; u++)
1477
{
1478
dmats_old[t][u] = dmats[t][u];
1479
dmats[t][u] = 0.00000000;
1480
}// end loop over 'u'
1481
}// end loop over 't'
1482
1483
// Update dmats using an inner product.
1484
if (combinations[r][s] == 0)
1485
{
1486
for (unsigned int t = 0; t < 3; t++)
1487
{
1488
for (unsigned int u = 0; u < 3; u++)
1489
{
1490
for (unsigned int tu = 0; tu < 3; tu++)
1491
{
1492
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1493
}// end loop over 'tu'
1494
}// end loop over 'u'
1495
}// end loop over 't'
1496
}
1497
1498
if (combinations[r][s] == 1)
1499
{
1500
for (unsigned int t = 0; t < 3; t++)
1501
{
1502
for (unsigned int u = 0; u < 3; u++)
1503
{
1504
for (unsigned int tu = 0; tu < 3; tu++)
1505
{
1506
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1507
}// end loop over 'tu'
1508
}// end loop over 'u'
1509
}// end loop over 't'
1510
}
1511
1512
}// end loop over 's'
1513
for (unsigned int s = 0; s < 3; s++)
1514
{
1515
for (unsigned int t = 0; t < 3; t++)
1516
{
1517
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1518
}// end loop over 't'
1519
}// end loop over 's'
1520
}// end loop over 'r'
1521
1522
// Transform derivatives back to physical element
1523
for (unsigned int r = 0; r < num_derivatives; r++)
1524
{
1525
for (unsigned int s = 0; s < num_derivatives; s++)
1526
{
1527
values[r] += transform[r][s]*derivatives[s];
1528
}// end loop over 's'
1529
}// end loop over 'r'
1530
1531
// Delete pointer to array of derivatives on FIAT element
1532
delete [] derivatives;
1533
1534
// Delete pointer to array of combinations of derivatives and transform
1535
for (unsigned int r = 0; r < num_derivatives; r++)
1536
{
1537
delete [] combinations[r];
1538
}// end loop over 'r'
1539
delete [] combinations;
1540
for (unsigned int r = 0; r < num_derivatives; r++)
1541
{
1542
delete [] transform[r];
1543
}// end loop over 'r'
1544
delete [] transform;
1545
break;
1546
}
1547
case 1:
1548
{
1549
1550
// Array of basisvalues.
1551
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1552
1553
// Declare helper variables.
1554
unsigned int rr = 0;
1555
unsigned int ss = 0;
1556
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1557
1558
// Compute basisvalues.
1559
basisvalues[0] = 1.00000000;
1560
basisvalues[1] = tmp0;
1561
for (unsigned int r = 0; r < 1; r++)
1562
{
1563
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1564
ss = r*(r + 1)/2;
1565
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1566
}// end loop over 'r'
1567
for (unsigned int r = 0; r < 2; r++)
1568
{
1569
for (unsigned int s = 0; s < 2 - r; s++)
1570
{
1571
rr = (r + s)*(r + s + 1)/2 + s;
1572
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1573
}// end loop over 's'
1574
}// end loop over 'r'
1575
1576
// Table(s) of coefficients.
1577
static const double coefficients0[3] = \
1578
{0.47140452, 0.28867513, -0.16666667};
1579
1580
// Tables of derivatives of the polynomial base (transpose).
1581
static const double dmats0[3][3] = \
1582
{{0.00000000, 0.00000000, 0.00000000},
1583
{4.89897949, 0.00000000, 0.00000000},
1584
{0.00000000, 0.00000000, 0.00000000}};
1585
1586
static const double dmats1[3][3] = \
1587
{{0.00000000, 0.00000000, 0.00000000},
1588
{2.44948974, 0.00000000, 0.00000000},
1589
{4.24264069, 0.00000000, 0.00000000}};
1590
1591
// Compute reference derivatives.
1592
// Declare pointer to array of derivatives on FIAT element.
1593
double *derivatives = new double[num_derivatives];
1594
for (unsigned int r = 0; r < num_derivatives; r++)
1595
{
1596
derivatives[r] = 0.00000000;
1597
}// end loop over 'r'
1598
1599
// Declare derivative matrix (of polynomial basis).
1600
double dmats[3][3] = \
1601
{{1.00000000, 0.00000000, 0.00000000},
1602
{0.00000000, 1.00000000, 0.00000000},
1603
{0.00000000, 0.00000000, 1.00000000}};
1604
1605
// Declare (auxiliary) derivative matrix (of polynomial basis).
1606
double dmats_old[3][3] = \
1607
{{1.00000000, 0.00000000, 0.00000000},
1608
{0.00000000, 1.00000000, 0.00000000},
1609
{0.00000000, 0.00000000, 1.00000000}};
1610
1611
// Loop possible derivatives.
1612
for (unsigned int r = 0; r < num_derivatives; r++)
1613
{
1614
// Resetting dmats values to compute next derivative.
1615
for (unsigned int t = 0; t < 3; t++)
1616
{
1617
for (unsigned int u = 0; u < 3; u++)
1618
{
1619
dmats[t][u] = 0.00000000;
1620
if (t == u)
1621
{
1622
dmats[t][u] = 1.00000000;
1623
}
1624
1625
}// end loop over 'u'
1626
}// end loop over 't'
1627
1628
// Looping derivative order to generate dmats.
1629
for (unsigned int s = 0; s < n; s++)
1630
{
1631
// Updating dmats_old with new values and resetting dmats.
1632
for (unsigned int t = 0; t < 3; t++)
1633
{
1634
for (unsigned int u = 0; u < 3; u++)
1635
{
1636
dmats_old[t][u] = dmats[t][u];
1637
dmats[t][u] = 0.00000000;
1638
}// end loop over 'u'
1639
}// end loop over 't'
1640
1641
// Update dmats using an inner product.
1642
if (combinations[r][s] == 0)
1643
{
1644
for (unsigned int t = 0; t < 3; t++)
1645
{
1646
for (unsigned int u = 0; u < 3; u++)
1647
{
1648
for (unsigned int tu = 0; tu < 3; tu++)
1649
{
1650
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1651
}// end loop over 'tu'
1652
}// end loop over 'u'
1653
}// end loop over 't'
1654
}
1655
1656
if (combinations[r][s] == 1)
1657
{
1658
for (unsigned int t = 0; t < 3; t++)
1659
{
1660
for (unsigned int u = 0; u < 3; u++)
1661
{
1662
for (unsigned int tu = 0; tu < 3; tu++)
1663
{
1664
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1665
}// end loop over 'tu'
1666
}// end loop over 'u'
1667
}// end loop over 't'
1668
}
1669
1670
}// end loop over 's'
1671
for (unsigned int s = 0; s < 3; s++)
1672
{
1673
for (unsigned int t = 0; t < 3; t++)
1674
{
1675
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1676
}// end loop over 't'
1677
}// end loop over 's'
1678
}// end loop over 'r'
1679
1680
// Transform derivatives back to physical element
1681
for (unsigned int r = 0; r < num_derivatives; r++)
1682
{
1683
for (unsigned int s = 0; s < num_derivatives; s++)
1684
{
1685
values[r] += transform[r][s]*derivatives[s];
1686
}// end loop over 's'
1687
}// end loop over 'r'
1688
1689
// Delete pointer to array of derivatives on FIAT element
1690
delete [] derivatives;
1691
1692
// Delete pointer to array of combinations of derivatives and transform
1693
for (unsigned int r = 0; r < num_derivatives; r++)
1694
{
1695
delete [] combinations[r];
1696
}// end loop over 'r'
1697
delete [] combinations;
1698
for (unsigned int r = 0; r < num_derivatives; r++)
1699
{
1700
delete [] transform[r];
1701
}// end loop over 'r'
1702
delete [] transform;
1703
break;
1704
}
1705
case 2:
1706
{
1707
1708
// Array of basisvalues.
1709
double basisvalues[3] = {0.00000000, 0.00000000, 0.00000000};
1710
1711
// Declare helper variables.
1712
unsigned int rr = 0;
1713
unsigned int ss = 0;
1714
double tmp0 = (1.00000000 + Y + 2.00000000*X)/2.00000000;
1715
1716
// Compute basisvalues.
1717
basisvalues[0] = 1.00000000;
1718
basisvalues[1] = tmp0;
1719
for (unsigned int r = 0; r < 1; r++)
1720
{
1721
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1722
ss = r*(r + 1)/2;
1723
basisvalues[rr] = basisvalues[ss]*(0.50000000 + r + Y*(1.50000000 + r));
1724
}// end loop over 'r'
1725
for (unsigned int r = 0; r < 2; r++)
1726
{
1727
for (unsigned int s = 0; s < 2 - r; s++)
1728
{
1729
rr = (r + s)*(r + s + 1)/2 + s;
1730
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s));
1731
}// end loop over 's'
1732
}// end loop over 'r'
1733
1734
// Table(s) of coefficients.
1735
static const double coefficients0[3] = \
1736
{0.47140452, 0.00000000, 0.33333333};
1737
1738
// Tables of derivatives of the polynomial base (transpose).
1739
static const double dmats0[3][3] = \
1740
{{0.00000000, 0.00000000, 0.00000000},
1741
{4.89897949, 0.00000000, 0.00000000},
1742
{0.00000000, 0.00000000, 0.00000000}};
1743
1744
static const double dmats1[3][3] = \
1745
{{0.00000000, 0.00000000, 0.00000000},
1746
{2.44948974, 0.00000000, 0.00000000},
1747
{4.24264069, 0.00000000, 0.00000000}};
1748
1749
// Compute reference derivatives.
1750
// Declare pointer to array of derivatives on FIAT element.
1751
double *derivatives = new double[num_derivatives];
1752
for (unsigned int r = 0; r < num_derivatives; r++)
1753
{
1754
derivatives[r] = 0.00000000;
1755
}// end loop over 'r'
1756
1757
// Declare derivative matrix (of polynomial basis).
1758
double dmats[3][3] = \
1759
{{1.00000000, 0.00000000, 0.00000000},
1760
{0.00000000, 1.00000000, 0.00000000},
1761
{0.00000000, 0.00000000, 1.00000000}};
1762
1763
// Declare (auxiliary) derivative matrix (of polynomial basis).
1764
double dmats_old[3][3] = \
1765
{{1.00000000, 0.00000000, 0.00000000},
1766
{0.00000000, 1.00000000, 0.00000000},
1767
{0.00000000, 0.00000000, 1.00000000}};
1768
1769
// Loop possible derivatives.
1770
for (unsigned int r = 0; r < num_derivatives; r++)
1771
{
1772
// Resetting dmats values to compute next derivative.
1773
for (unsigned int t = 0; t < 3; t++)
1774
{
1775
for (unsigned int u = 0; u < 3; u++)
1776
{
1777
dmats[t][u] = 0.00000000;
1778
if (t == u)
1779
{
1780
dmats[t][u] = 1.00000000;
1781
}
1782
1783
}// end loop over 'u'
1784
}// end loop over 't'
1785
1786
// Looping derivative order to generate dmats.
1787
for (unsigned int s = 0; s < n; s++)
1788
{
1789
// Updating dmats_old with new values and resetting dmats.
1790
for (unsigned int t = 0; t < 3; t++)
1791
{
1792
for (unsigned int u = 0; u < 3; u++)
1793
{
1794
dmats_old[t][u] = dmats[t][u];
1795
dmats[t][u] = 0.00000000;
1796
}// end loop over 'u'
1797
}// end loop over 't'
1798
1799
// Update dmats using an inner product.
1800
if (combinations[r][s] == 0)
1801
{
1802
for (unsigned int t = 0; t < 3; t++)
1803
{
1804
for (unsigned int u = 0; u < 3; u++)
1805
{
1806
for (unsigned int tu = 0; tu < 3; tu++)
1807
{
1808
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1809
}// end loop over 'tu'
1810
}// end loop over 'u'
1811
}// end loop over 't'
1812
}
1813
1814
if (combinations[r][s] == 1)
1815
{
1816
for (unsigned int t = 0; t < 3; t++)
1817
{
1818
for (unsigned int u = 0; u < 3; u++)
1819
{
1820
for (unsigned int tu = 0; tu < 3; tu++)
1821
{
1822
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1823
}// end loop over 'tu'
1824
}// end loop over 'u'
1825
}// end loop over 't'
1826
}
1827
1828
}// end loop over 's'
1829
for (unsigned int s = 0; s < 3; s++)
1830
{
1831
for (unsigned int t = 0; t < 3; t++)
1832
{
1833
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1834
}// end loop over 't'
1835
}// end loop over 's'
1836
}// end loop over 'r'
1837
1838
// Transform derivatives back to physical element
1839
for (unsigned int r = 0; r < num_derivatives; r++)
1840
{
1841
for (unsigned int s = 0; s < num_derivatives; s++)
1842
{
1843
values[r] += transform[r][s]*derivatives[s];
1844
}// end loop over 's'
1845
}// end loop over 'r'
1846
1847
// Delete pointer to array of derivatives on FIAT element
1848
delete [] derivatives;
1849
1850
// Delete pointer to array of combinations of derivatives and transform
1851
for (unsigned int r = 0; r < num_derivatives; r++)
1852
{
1853
delete [] combinations[r];
1854
}// end loop over 'r'
1855
delete [] combinations;
1856
for (unsigned int r = 0; r < num_derivatives; r++)
1857
{
1858
delete [] transform[r];
1859
}// end loop over 'r'
1860
delete [] transform;
1861
break;
1862
}
1863
}
1864
1467
1865
}
1468
1866
1469
1867
/// Evaluate order n derivatives of all basis functions at given point in cell
Loggerhead is a web-based interface for Breezy
Version: 2.0.1