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MODULE GeneralRoutines
IMPLICIT NONE
CONTAINS
!--------------------------------------------------------------------------------------------------
REAL FUNCTION d3_determinant(m)
! Function to calculate the determinant of a 3x3 matrix.
REAL, INTENT(IN) :: m(3,3)
d3_determinant = ABS( &
m(1,1)*( m(2,2)*m(3,3) - m(2,3)*m(3,2) ) + &
m(1,2)*( m(2,3)*m(3,1) - m(2,1)*m(3,3) ) + &
m(1,3)*( m(2,1)*m(3,2) - m(2,2)*m(3,1) ) &
)
END FUNCTION d3_determinant
!--------------------------------------------------------------------------------------------------
REAL FUNCTION d4_determinant(m)
! Function to calculate the determinant of a 4x4 matrix.
REAL, INTENT(IN) :: m(4,4)
d4_determinant = ABS( &
m(1,1)*m(2,2)*m(3,3)*m(4,4) - m(1,1)*m(2,2)*m(3,4)*m(4,3) + m(1,1)*m(2,3)*m(3,4)*m(4,2) &
- m(1,1)*m(2,3)*m(3,2)*m(4,4) + m(1,1)*m(2,4)*m(3,2)*m(4,3) - m(1,1)*m(2,4)*m(3,3)*m(4,2) &
- m(1,2)*m(2,3)*m(3,4)*m(4,1) + m(1,2)*m(2,3)*m(3,1)*m(4,4) - m(1,2)*m(2,4)*m(3,1)*m(4,3) &
+ m(1,2)*m(2,4)*m(3,3)*m(4,1) - m(1,2)*m(2,1)*m(3,3)*m(4,4) + m(1,2)*m(2,1)*m(3,4)*m(4,3) &
+ m(1,3)*m(2,4)*m(3,1)*m(4,2) - m(1,3)*m(2,4)*m(3,2)*m(4,1) + m(1,3)*m(2,1)*m(3,2)*m(4,4) &
- m(1,3)*m(2,1)*m(3,4)*m(4,2) + m(1,3)*m(2,2)*m(3,4)*m(4,1) - m(1,3)*m(2,2)*m(3,1)*m(4,4) &
- m(1,4)*m(2,1)*m(3,2)*m(4,3) + m(1,4)*m(2,1)*m(3,3)*m(4,2) - m(1,4)*m(2,2)*m(3,3)*m(4,1) &
+ m(1,4)*m(2,2)*m(3,1)*m(4,3) - m(1,4)*m(2,3)*m(3,1)*m(4,2) + m(1,4)*m(2,3)*m(3,2)*m(4,1) &
)
END FUNCTION d4_determinant
!--------------------------------------------------------------------------------------------------
SUBROUTINE reorder_nodes(node_coords,reordered_coords,vol_tracer,reordered_vol,int_tracer,reordered_int)
! Subroutine to reorder the nodes so that the "highest" node, in terms of its tracer value, will be
! included in the volume, instead of excluded.
! Loop variables.
INTEGER :: j
! Original arrays.
REAL, DIMENSION(4,3),INTENT(IN) :: node_coords
REAL, DIMENSION(4),INTENT(IN) :: vol_tracer, int_tracer
! Reordered arrays.
REAL, DIMENSION(4,3),INTENT(INOUT) :: reordered_coords
REAL, DIMENSION(4),INTENT(INOUT) :: reordered_vol, reordered_int
! Re-order the nodes so that the only one "above" T_0 is first in the array.
! If you don't do this, the edge_vectors are wrong for the small_tet routines, since they are taken
! from the node in position one of the array.
reordered_coords(1,1:3) = node_coords(4,1:3)
reordered_coords(2,1:3) = node_coords(3,1:3)
reordered_coords(3,1:3) = node_coords(2,1:3)
reordered_coords(4,1:3) = node_coords(1,1:3)
! Also re-order the vol_tracer values.
reordered_vol(1) = vol_tracer(4)
reordered_vol(2) = vol_tracer(3)
reordered_vol(3) = vol_tracer(2)
reordered_vol(4) = vol_tracer(1)
! Also re-order the int_tracer values.
reordered_int(1) = int_tracer(4)
reordered_int(2) = int_tracer(3)
reordered_int(3) = int_tracer(2)
reordered_int(4) = int_tracer(1)
END SUBROUTINE reorder_nodes
!--------------------------------------------------------------------------------------------------
REAL FUNCTION integrate(int_basis,tracer_values)
! Function to actually calculate the value of the tracer over the selected section of the
! current element.
REAL, DIMENSION(4) :: int_basis, tracer_values
integrate = int_basis(1)*tracer_values(1) + int_basis(2)*tracer_values(2) &
+ int_basis(3)*tracer_values(3) + int_basis(4)*tracer_values(4)
END FUNCTION integrate
!--------------------------------------------------------------------------------------------------
SUBROUTINE calc_edge_vectors(edge_vectors,node_coords,n)
! Subroutine to return the edge vectors for the calculation of a 3D tetrahedron's volume.
IMPLICIT NONE
! Loop variables.
INTEGER :: j,k
! Passed variables.
INTEGER :: n
REAL, INTENT(IN) :: node_coords(n+1,n)
! Result variable.
REAL, DIMENSION(n,n), INTENT(INOUT) :: edge_vectors
DO j = 1,n ! Loop over nodes.
DO k = 1,n ! Loop over coordinates.
edge_vectors(j,k) = node_coords(j+1,k) &
- node_coords(1,k)
END DO
END DO
RETURN
END SUBROUTINE calc_edge_vectors
!--------------------------------------------------------------------------------------------------
SUBROUTINE calc_subnode_coords(node_coords,subnode_coords,edge_fraction)
! This subroutine calculates the subnode coordinates when only one vertex of the tetrahedron has been
! clipped. It returns (x,y,z) for three subnodes placed along the edges of the main tetrahedron.
! Loop variables.
INTEGER :: j, k
! Passed variables.
REAL, INTENT(IN) :: edge_fraction(4), node_coords(4,3)
REAL, INTENT(INOUT) :: subnode_coords(4,3)
! Internal variables.
REAL :: edge_vectors(3,3)
! Construct edge_vectors for the entire element.
CALL calc_edge_vectors(edge_vectors,node_coords,3)
! Scale the edge_vectors by the relevant entry of edge_fraction.
DO j = 1,3
DO k = 1,3
edge_vectors(j,k) = edge_fraction(j+1)*edge_vectors(j,k)
END DO
END DO
! Construct the array containing the positions of one of the element's nodes and three subnodes
! that are distance "fraction" between this node and the other three.
subnode_coords(1,:) = node_coords(1,:)
DO j = 1,3 ! Loop over nodes.
subnode_coords(j+1,:) = node_coords(1,:) + edge_vectors(j,:)
END DO
END SUBROUTINE calc_subnode_coords
!--------------------------------------------------------------------------------------------------
SUBROUTINE calc_half_subnode_coords(node_coords,subnode_coords,edge_fraction)
! This subroutine calculates the (x,y,z) coordinates of the four subnodes formed when two vertices
! of the element are clipped.
! Loop variables
INTEGER :: j
! Passed variables.
REAL, INTENT(IN) :: node_coords(4,3), edge_fraction(4)
REAL, INTENT(INOUT) :: subnode_coords(4,3)
! Internal variables.
REAL :: evecs_1(2,3), evecs_2(2,3)
DO j = 1,2
! Compute the edge_vectors leading from nodes 3 & 4 to node 1, to locate subnodes A & B.
evecs_1(j,1:3) = node_coords(1,1:3) - node_coords(j+2,1:3)
! Compute the edge_vectors leading from nodes 3 & 4 to node 2, to locate subnodes C & D.
evecs_2(j,1:3) = node_coords(2,1:3) - node_coords(j+2,1:3)
END DO
! We now have the vectors from node 1 to 3, 1 to 4 as well as from node 2 to 3, and 2 to 4.
! Points a,b,c,d lie somewhere along these lines depending on the temperature fraction, i.e.
! where T_0 cuts the lines between nodes. We need to multiply these vectors by the correct
! temperature fraction and add the result to the coordinates of the correct node.
DO j = 1,2
! Compute the coordinates of subnodes A & B.
subnode_coords(j,1:3) = node_coords(j+2,1:3) + edge_fraction(j)*evecs_1(j,1:3)
! Compute the coordinates of subnodes C & D.
subnode_coords(j+2,1:3) = node_coords(j+2,1:3) + edge_fraction(j+2)*evecs_2(j,1:3)
END DO
END SUBROUTINE calc_half_subnode_coords
!--------------------------------------------------------------------------------------------------
END MODULE GeneralRoutines
!--------------------------------------------------------------------------------------------------
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