| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| subroutine z_solve |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c Performs line solves in Z direction by first factoring |
| c the block-tridiagonal matrix into an upper triangular matrix, |
| c and then performing back substitution to solve for the unknow |
| c vectors of each line. |
| c |
| c Make sure we treat elements zero to cell_size in the direction |
| c of the sweep. |
| c--------------------------------------------------------------------- |
| |
| include 'header.h' |
| include 'work_lhs.h' |
| |
| integer i, j, k, m, n, ksize |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| if (timeron) call timer_start(t_zsolve) |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c This function computes the left hand side for the three z-factors |
| c--------------------------------------------------------------------- |
| |
| ksize = grid_points(3)-1 |
| |
| c--------------------------------------------------------------------- |
| c Compute the indices for storing the block-diagonal matrix; |
| c determine c (labeled f) and s jacobians |
| c--------------------------------------------------------------------- |
| !$omp parallel do default(shared) shared(ksize) |
| !$omp& private(i,j,k,m,n) |
| do j = 1, grid_points(2)-2 |
| do i = 1, grid_points(1)-2 |
| do k = 0, ksize |
| |
| tmp1 = 1.0d+00 / u(1,i,j,k) |
| tmp2 = tmp1 * tmp1 |
| tmp3 = tmp1 * tmp2 |
| |
| fjac(1,1,k) = 0.0d+00 |
| fjac(1,2,k) = 0.0d+00 |
| fjac(1,3,k) = 0.0d+00 |
| fjac(1,4,k) = 1.0d+00 |
| fjac(1,5,k) = 0.0d+00 |
| |
| fjac(2,1,k) = - ( u(2,i,j,k)*u(4,i,j,k) ) |
| > * tmp2 |
| fjac(2,2,k) = u(4,i,j,k) * tmp1 |
| fjac(2,3,k) = 0.0d+00 |
| fjac(2,4,k) = u(2,i,j,k) * tmp1 |
| fjac(2,5,k) = 0.0d+00 |
| |
| fjac(3,1,k) = - ( u(3,i,j,k)*u(4,i,j,k) ) |
| > * tmp2 |
| fjac(3,2,k) = 0.0d+00 |
| fjac(3,3,k) = u(4,i,j,k) * tmp1 |
| fjac(3,4,k) = u(3,i,j,k) * tmp1 |
| fjac(3,5,k) = 0.0d+00 |
| |
| fjac(4,1,k) = - (u(4,i,j,k)*u(4,i,j,k) * tmp2 ) |
| > + c2 * qs(i,j,k) |
| fjac(4,2,k) = - c2 * u(2,i,j,k) * tmp1 |
| fjac(4,3,k) = - c2 * u(3,i,j,k) * tmp1 |
| fjac(4,4,k) = ( 2.0d+00 - c2 ) |
| > * u(4,i,j,k) * tmp1 |
| fjac(4,5,k) = c2 |
| |
| fjac(5,1,k) = ( c2 * 2.0d0 * square(i,j,k) |
| > - c1 * u(5,i,j,k) ) |
| > * u(4,i,j,k) * tmp2 |
| fjac(5,2,k) = - c2 * ( u(2,i,j,k)*u(4,i,j,k) ) |
| > * tmp2 |
| fjac(5,3,k) = - c2 * ( u(3,i,j,k)*u(4,i,j,k) ) |
| > * tmp2 |
| fjac(5,4,k) = c1 * ( u(5,i,j,k) * tmp1 ) |
| > - c2 |
| > * ( qs(i,j,k) |
| > + u(4,i,j,k)*u(4,i,j,k) * tmp2 ) |
| fjac(5,5,k) = c1 * u(4,i,j,k) * tmp1 |
| |
| njac(1,1,k) = 0.0d+00 |
| njac(1,2,k) = 0.0d+00 |
| njac(1,3,k) = 0.0d+00 |
| njac(1,4,k) = 0.0d+00 |
| njac(1,5,k) = 0.0d+00 |
| |
| njac(2,1,k) = - c3c4 * tmp2 * u(2,i,j,k) |
| njac(2,2,k) = c3c4 * tmp1 |
| njac(2,3,k) = 0.0d+00 |
| njac(2,4,k) = 0.0d+00 |
| njac(2,5,k) = 0.0d+00 |
| |
| njac(3,1,k) = - c3c4 * tmp2 * u(3,i,j,k) |
| njac(3,2,k) = 0.0d+00 |
| njac(3,3,k) = c3c4 * tmp1 |
| njac(3,4,k) = 0.0d+00 |
| njac(3,5,k) = 0.0d+00 |
| |
| njac(4,1,k) = - con43 * c3c4 * tmp2 * u(4,i,j,k) |
| njac(4,2,k) = 0.0d+00 |
| njac(4,3,k) = 0.0d+00 |
| njac(4,4,k) = con43 * c3 * c4 * tmp1 |
| njac(4,5,k) = 0.0d+00 |
| |
| njac(5,1,k) = - ( c3c4 |
| > - c1345 ) * tmp3 * (u(2,i,j,k)**2) |
| > - ( c3c4 - c1345 ) * tmp3 * (u(3,i,j,k)**2) |
| > - ( con43 * c3c4 |
| > - c1345 ) * tmp3 * (u(4,i,j,k)**2) |
| > - c1345 * tmp2 * u(5,i,j,k) |
| |
| njac(5,2,k) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k) |
| njac(5,3,k) = ( c3c4 - c1345 ) * tmp2 * u(3,i,j,k) |
| njac(5,4,k) = ( con43 * c3c4 |
| > - c1345 ) * tmp2 * u(4,i,j,k) |
| njac(5,5,k) = ( c1345 )* tmp1 |
| |
| |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c now jacobians set, so form left hand side in z direction |
| c--------------------------------------------------------------------- |
| call lhsinit(lhs, ksize) |
| do k = 1, ksize-1 |
| |
| tmp1 = dt * tz1 |
| tmp2 = dt * tz2 |
| |
| lhs(1,1,aa,k) = - tmp2 * fjac(1,1,k-1) |
| > - tmp1 * njac(1,1,k-1) |
| > - tmp1 * dz1 |
| lhs(1,2,aa,k) = - tmp2 * fjac(1,2,k-1) |
| > - tmp1 * njac(1,2,k-1) |
| lhs(1,3,aa,k) = - tmp2 * fjac(1,3,k-1) |
| > - tmp1 * njac(1,3,k-1) |
| lhs(1,4,aa,k) = - tmp2 * fjac(1,4,k-1) |
| > - tmp1 * njac(1,4,k-1) |
| lhs(1,5,aa,k) = - tmp2 * fjac(1,5,k-1) |
| > - tmp1 * njac(1,5,k-1) |
| |
| lhs(2,1,aa,k) = - tmp2 * fjac(2,1,k-1) |
| > - tmp1 * njac(2,1,k-1) |
| lhs(2,2,aa,k) = - tmp2 * fjac(2,2,k-1) |
| > - tmp1 * njac(2,2,k-1) |
| > - tmp1 * dz2 |
| lhs(2,3,aa,k) = - tmp2 * fjac(2,3,k-1) |
| > - tmp1 * njac(2,3,k-1) |
| lhs(2,4,aa,k) = - tmp2 * fjac(2,4,k-1) |
| > - tmp1 * njac(2,4,k-1) |
| lhs(2,5,aa,k) = - tmp2 * fjac(2,5,k-1) |
| > - tmp1 * njac(2,5,k-1) |
| |
| lhs(3,1,aa,k) = - tmp2 * fjac(3,1,k-1) |
| > - tmp1 * njac(3,1,k-1) |
| lhs(3,2,aa,k) = - tmp2 * fjac(3,2,k-1) |
| > - tmp1 * njac(3,2,k-1) |
| lhs(3,3,aa,k) = - tmp2 * fjac(3,3,k-1) |
| > - tmp1 * njac(3,3,k-1) |
| > - tmp1 * dz3 |
| lhs(3,4,aa,k) = - tmp2 * fjac(3,4,k-1) |
| > - tmp1 * njac(3,4,k-1) |
| lhs(3,5,aa,k) = - tmp2 * fjac(3,5,k-1) |
| > - tmp1 * njac(3,5,k-1) |
| |
| lhs(4,1,aa,k) = - tmp2 * fjac(4,1,k-1) |
| > - tmp1 * njac(4,1,k-1) |
| lhs(4,2,aa,k) = - tmp2 * fjac(4,2,k-1) |
| > - tmp1 * njac(4,2,k-1) |
| lhs(4,3,aa,k) = - tmp2 * fjac(4,3,k-1) |
| > - tmp1 * njac(4,3,k-1) |
| lhs(4,4,aa,k) = - tmp2 * fjac(4,4,k-1) |
| > - tmp1 * njac(4,4,k-1) |
| > - tmp1 * dz4 |
| lhs(4,5,aa,k) = - tmp2 * fjac(4,5,k-1) |
| > - tmp1 * njac(4,5,k-1) |
| |
| lhs(5,1,aa,k) = - tmp2 * fjac(5,1,k-1) |
| > - tmp1 * njac(5,1,k-1) |
| lhs(5,2,aa,k) = - tmp2 * fjac(5,2,k-1) |
| > - tmp1 * njac(5,2,k-1) |
| lhs(5,3,aa,k) = - tmp2 * fjac(5,3,k-1) |
| > - tmp1 * njac(5,3,k-1) |
| lhs(5,4,aa,k) = - tmp2 * fjac(5,4,k-1) |
| > - tmp1 * njac(5,4,k-1) |
| lhs(5,5,aa,k) = - tmp2 * fjac(5,5,k-1) |
| > - tmp1 * njac(5,5,k-1) |
| > - tmp1 * dz5 |
| |
| lhs(1,1,bb,k) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(1,1,k) |
| > + tmp1 * 2.0d+00 * dz1 |
| lhs(1,2,bb,k) = tmp1 * 2.0d+00 * njac(1,2,k) |
| lhs(1,3,bb,k) = tmp1 * 2.0d+00 * njac(1,3,k) |
| lhs(1,4,bb,k) = tmp1 * 2.0d+00 * njac(1,4,k) |
| lhs(1,5,bb,k) = tmp1 * 2.0d+00 * njac(1,5,k) |
| |
| lhs(2,1,bb,k) = tmp1 * 2.0d+00 * njac(2,1,k) |
| lhs(2,2,bb,k) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(2,2,k) |
| > + tmp1 * 2.0d+00 * dz2 |
| lhs(2,3,bb,k) = tmp1 * 2.0d+00 * njac(2,3,k) |
| lhs(2,4,bb,k) = tmp1 * 2.0d+00 * njac(2,4,k) |
| lhs(2,5,bb,k) = tmp1 * 2.0d+00 * njac(2,5,k) |
| |
| lhs(3,1,bb,k) = tmp1 * 2.0d+00 * njac(3,1,k) |
| lhs(3,2,bb,k) = tmp1 * 2.0d+00 * njac(3,2,k) |
| lhs(3,3,bb,k) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(3,3,k) |
| > + tmp1 * 2.0d+00 * dz3 |
| lhs(3,4,bb,k) = tmp1 * 2.0d+00 * njac(3,4,k) |
| lhs(3,5,bb,k) = tmp1 * 2.0d+00 * njac(3,5,k) |
| |
| lhs(4,1,bb,k) = tmp1 * 2.0d+00 * njac(4,1,k) |
| lhs(4,2,bb,k) = tmp1 * 2.0d+00 * njac(4,2,k) |
| lhs(4,3,bb,k) = tmp1 * 2.0d+00 * njac(4,3,k) |
| lhs(4,4,bb,k) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(4,4,k) |
| > + tmp1 * 2.0d+00 * dz4 |
| lhs(4,5,bb,k) = tmp1 * 2.0d+00 * njac(4,5,k) |
| |
| lhs(5,1,bb,k) = tmp1 * 2.0d+00 * njac(5,1,k) |
| lhs(5,2,bb,k) = tmp1 * 2.0d+00 * njac(5,2,k) |
| lhs(5,3,bb,k) = tmp1 * 2.0d+00 * njac(5,3,k) |
| lhs(5,4,bb,k) = tmp1 * 2.0d+00 * njac(5,4,k) |
| lhs(5,5,bb,k) = 1.0d+00 |
| > + tmp1 * 2.0d+00 * njac(5,5,k) |
| > + tmp1 * 2.0d+00 * dz5 |
| |
| lhs(1,1,cc,k) = tmp2 * fjac(1,1,k+1) |
| > - tmp1 * njac(1,1,k+1) |
| > - tmp1 * dz1 |
| lhs(1,2,cc,k) = tmp2 * fjac(1,2,k+1) |
| > - tmp1 * njac(1,2,k+1) |
| lhs(1,3,cc,k) = tmp2 * fjac(1,3,k+1) |
| > - tmp1 * njac(1,3,k+1) |
| lhs(1,4,cc,k) = tmp2 * fjac(1,4,k+1) |
| > - tmp1 * njac(1,4,k+1) |
| lhs(1,5,cc,k) = tmp2 * fjac(1,5,k+1) |
| > - tmp1 * njac(1,5,k+1) |
| |
| lhs(2,1,cc,k) = tmp2 * fjac(2,1,k+1) |
| > - tmp1 * njac(2,1,k+1) |
| lhs(2,2,cc,k) = tmp2 * fjac(2,2,k+1) |
| > - tmp1 * njac(2,2,k+1) |
| > - tmp1 * dz2 |
| lhs(2,3,cc,k) = tmp2 * fjac(2,3,k+1) |
| > - tmp1 * njac(2,3,k+1) |
| lhs(2,4,cc,k) = tmp2 * fjac(2,4,k+1) |
| > - tmp1 * njac(2,4,k+1) |
| lhs(2,5,cc,k) = tmp2 * fjac(2,5,k+1) |
| > - tmp1 * njac(2,5,k+1) |
| |
| lhs(3,1,cc,k) = tmp2 * fjac(3,1,k+1) |
| > - tmp1 * njac(3,1,k+1) |
| lhs(3,2,cc,k) = tmp2 * fjac(3,2,k+1) |
| > - tmp1 * njac(3,2,k+1) |
| lhs(3,3,cc,k) = tmp2 * fjac(3,3,k+1) |
| > - tmp1 * njac(3,3,k+1) |
| > - tmp1 * dz3 |
| lhs(3,4,cc,k) = tmp2 * fjac(3,4,k+1) |
| > - tmp1 * njac(3,4,k+1) |
| lhs(3,5,cc,k) = tmp2 * fjac(3,5,k+1) |
| > - tmp1 * njac(3,5,k+1) |
| |
| lhs(4,1,cc,k) = tmp2 * fjac(4,1,k+1) |
| > - tmp1 * njac(4,1,k+1) |
| lhs(4,2,cc,k) = tmp2 * fjac(4,2,k+1) |
| > - tmp1 * njac(4,2,k+1) |
| lhs(4,3,cc,k) = tmp2 * fjac(4,3,k+1) |
| > - tmp1 * njac(4,3,k+1) |
| lhs(4,4,cc,k) = tmp2 * fjac(4,4,k+1) |
| > - tmp1 * njac(4,4,k+1) |
| > - tmp1 * dz4 |
| lhs(4,5,cc,k) = tmp2 * fjac(4,5,k+1) |
| > - tmp1 * njac(4,5,k+1) |
| |
| lhs(5,1,cc,k) = tmp2 * fjac(5,1,k+1) |
| > - tmp1 * njac(5,1,k+1) |
| lhs(5,2,cc,k) = tmp2 * fjac(5,2,k+1) |
| > - tmp1 * njac(5,2,k+1) |
| lhs(5,3,cc,k) = tmp2 * fjac(5,3,k+1) |
| > - tmp1 * njac(5,3,k+1) |
| lhs(5,4,cc,k) = tmp2 * fjac(5,4,k+1) |
| > - tmp1 * njac(5,4,k+1) |
| lhs(5,5,cc,k) = tmp2 * fjac(5,5,k+1) |
| > - tmp1 * njac(5,5,k+1) |
| > - tmp1 * dz5 |
| |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c performs guaussian elimination on this cell. |
| c |
| c assumes that unpacking routines for non-first cells |
| c preload C' and rhs' from previous cell. |
| c |
| c assumed send happens outside this routine, but that |
| c c'(KMAX) and rhs'(KMAX) will be sent to next cell. |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c outer most do loops - sweeping in i direction |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c multiply c(i,j,0) by b_inverse and copy back to c |
| c multiply rhs(0) by b_inverse(0) and copy to rhs |
| c--------------------------------------------------------------------- |
| call binvcrhs( lhs(1,1,bb,0), |
| > lhs(1,1,cc,0), |
| > rhs(1,i,j,0) ) |
| |
| |
| c--------------------------------------------------------------------- |
| c begin inner most do loop |
| c do all the elements of the cell unless last |
| c--------------------------------------------------------------------- |
| do k=1,ksize-1 |
| |
| c--------------------------------------------------------------------- |
| c subtract A*lhs_vector(k-1) from lhs_vector(k) |
| c |
| c rhs(k) = rhs(k) - A*rhs(k-1) |
| c--------------------------------------------------------------------- |
| call matvec_sub(lhs(1,1,aa,k), |
| > rhs(1,i,j,k-1),rhs(1,i,j,k)) |
| |
| c--------------------------------------------------------------------- |
| c B(k) = B(k) - C(k-1)*A(k) |
| c call matmul_sub(aa,i,j,k,c,cc,i,j,k-1,c,bb,i,j,k) |
| c--------------------------------------------------------------------- |
| call matmul_sub(lhs(1,1,aa,k), |
| > lhs(1,1,cc,k-1), |
| > lhs(1,1,bb,k)) |
| |
| c--------------------------------------------------------------------- |
| c multiply c(i,j,k) by b_inverse and copy back to c |
| c multiply rhs(i,j,1) by b_inverse(i,j,1) and copy to rhs |
| c--------------------------------------------------------------------- |
| call binvcrhs( lhs(1,1,bb,k), |
| > lhs(1,1,cc,k), |
| > rhs(1,i,j,k) ) |
| |
| enddo |
| |
| c--------------------------------------------------------------------- |
| c Now finish up special cases for last cell |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c rhs(ksize) = rhs(ksize) - A*rhs(ksize-1) |
| c--------------------------------------------------------------------- |
| call matvec_sub(lhs(1,1,aa,ksize), |
| > rhs(1,i,j,ksize-1),rhs(1,i,j,ksize)) |
| |
| c--------------------------------------------------------------------- |
| c B(ksize) = B(ksize) - C(ksize-1)*A(ksize) |
| c call matmul_sub(aa,i,j,ksize,c, |
| c $ cc,i,j,ksize-1,c,bb,i,j,ksize) |
| c--------------------------------------------------------------------- |
| call matmul_sub(lhs(1,1,aa,ksize), |
| > lhs(1,1,cc,ksize-1), |
| > lhs(1,1,bb,ksize)) |
| |
| c--------------------------------------------------------------------- |
| c multiply rhs(ksize) by b_inverse(ksize) and copy to rhs |
| c--------------------------------------------------------------------- |
| call binvrhs( lhs(1,1,bb,ksize), |
| > rhs(1,i,j,ksize) ) |
| |
| |
| c--------------------------------------------------------------------- |
| c--------------------------------------------------------------------- |
| |
| c--------------------------------------------------------------------- |
| c back solve: if last cell, then generate U(ksize)=rhs(ksize) |
| c else assume U(ksize) is loaded in un pack backsub_info |
| c so just use it |
| c after call u(kstart) will be sent to next cell |
| c--------------------------------------------------------------------- |
| |
| do k=ksize-1,0,-1 |
| do m=1,BLOCK_SIZE |
| do n=1,BLOCK_SIZE |
| rhs(m,i,j,k) = rhs(m,i,j,k) |
| > - lhs(m,n,cc,k)*rhs(n,i,j,k+1) |
| enddo |
| enddo |
| enddo |
| |
| enddo |
| enddo |
| if (timeron) call timer_stop(t_zsolve) |
| |
| return |
| end |