c--------------------------------------------------------------------- c--------------------------------------------------------------------- subroutine y_solve c--------------------------------------------------------------------- c--------------------------------------------------------------------- c--------------------------------------------------------------------- c Performs line solves in Y 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' integer i, j, k, m, n, jsize c--------------------------------------------------------------------- c--------------------------------------------------------------------- if (timeron) call timer_start(t_ysolve) c--------------------------------------------------------------------- c--------------------------------------------------------------------- c--------------------------------------------------------------------- c This function computes the left hand side for the three y-factors c--------------------------------------------------------------------- jsize = grid_points(2)-1 c--------------------------------------------------------------------- c Compute the indices for storing the tri-diagonal matrix; c determine a (labeled f) and n jacobians for cell c c--------------------------------------------------------------------- do k = 1, grid_points(3)-2 do i = 1, grid_points(1)-2 do j = 0, jsize tmp1 = rho_i(i,j,k) tmp2 = tmp1 * tmp1 tmp3 = tmp1 * tmp2 fjac(1,1,j) = 0.0d+00 fjac(1,2,j) = 0.0d+00 fjac(1,3,j) = 1.0d+00 fjac(1,4,j) = 0.0d+00 fjac(1,5,j) = 0.0d+00 fjac(2,1,j) = - ( u(2,i,j,k)*u(3,i,j,k) ) > * tmp2 fjac(2,2,j) = u(3,i,j,k) * tmp1 fjac(2,3,j) = u(2,i,j,k) * tmp1 fjac(2,4,j) = 0.0d+00 fjac(2,5,j) = 0.0d+00 fjac(3,1,j) = - ( u(3,i,j,k)*u(3,i,j,k)*tmp2) > + c2 * qs(i,j,k) fjac(3,2,j) = - c2 * u(2,i,j,k) * tmp1 fjac(3,3,j) = ( 2.0d+00 - c2 ) > * u(3,i,j,k) * tmp1 fjac(3,4,j) = - c2 * u(4,i,j,k) * tmp1 fjac(3,5,j) = c2 fjac(4,1,j) = - ( u(3,i,j,k)*u(4,i,j,k) ) > * tmp2 fjac(4,2,j) = 0.0d+00 fjac(4,3,j) = u(4,i,j,k) * tmp1 fjac(4,4,j) = u(3,i,j,k) * tmp1 fjac(4,5,j) = 0.0d+00 fjac(5,1,j) = ( c2 * 2.0d0 * square(i,j,k) > - c1 * u(5,i,j,k) ) > * u(3,i,j,k) * tmp2 fjac(5,2,j) = - c2 * u(2,i,j,k)*u(3,i,j,k) > * tmp2 fjac(5,3,j) = c1 * u(5,i,j,k) * tmp1 > - c2 > * ( qs(i,j,k) > + u(3,i,j,k)*u(3,i,j,k) * tmp2 ) fjac(5,4,j) = - c2 * ( u(3,i,j,k)*u(4,i,j,k) ) > * tmp2 fjac(5,5,j) = c1 * u(3,i,j,k) * tmp1 njac(1,1,j) = 0.0d+00 njac(1,2,j) = 0.0d+00 njac(1,3,j) = 0.0d+00 njac(1,4,j) = 0.0d+00 njac(1,5,j) = 0.0d+00 njac(2,1,j) = - c3c4 * tmp2 * u(2,i,j,k) njac(2,2,j) = c3c4 * tmp1 njac(2,3,j) = 0.0d+00 njac(2,4,j) = 0.0d+00 njac(2,5,j) = 0.0d+00 njac(3,1,j) = - con43 * c3c4 * tmp2 * u(3,i,j,k) njac(3,2,j) = 0.0d+00 njac(3,3,j) = con43 * c3c4 * tmp1 njac(3,4,j) = 0.0d+00 njac(3,5,j) = 0.0d+00 njac(4,1,j) = - c3c4 * tmp2 * u(4,i,j,k) njac(4,2,j) = 0.0d+00 njac(4,3,j) = 0.0d+00 njac(4,4,j) = c3c4 * tmp1 njac(4,5,j) = 0.0d+00 njac(5,1,j) = - ( c3c4 > - c1345 ) * tmp3 * (u(2,i,j,k)**2) > - ( con43 * c3c4 > - c1345 ) * tmp3 * (u(3,i,j,k)**2) > - ( c3c4 - c1345 ) * tmp3 * (u(4,i,j,k)**2) > - c1345 * tmp2 * u(5,i,j,k) njac(5,2,j) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k) njac(5,3,j) = ( con43 * c3c4 > - c1345 ) * tmp2 * u(3,i,j,k) njac(5,4,j) = ( c3c4 - c1345 ) * tmp2 * u(4,i,j,k) njac(5,5,j) = ( c1345 ) * tmp1 enddo c--------------------------------------------------------------------- c now joacobians set, so form left hand side in y direction c--------------------------------------------------------------------- call lhsinit(lhs, jsize) do j = 1, jsize-1 tmp1 = dt * ty1 tmp2 = dt * ty2 lhs(1,1,aa,j) = - tmp2 * fjac(1,1,j-1) > - tmp1 * njac(1,1,j-1) > - tmp1 * dy1 lhs(1,2,aa,j) = - tmp2 * fjac(1,2,j-1) > - tmp1 * njac(1,2,j-1) lhs(1,3,aa,j) = - tmp2 * fjac(1,3,j-1) > - tmp1 * njac(1,3,j-1) lhs(1,4,aa,j) = - tmp2 * fjac(1,4,j-1) > - tmp1 * njac(1,4,j-1) lhs(1,5,aa,j) = - tmp2 * fjac(1,5,j-1) > - tmp1 * njac(1,5,j-1) lhs(2,1,aa,j) = - tmp2 * fjac(2,1,j-1) > - tmp1 * njac(2,1,j-1) lhs(2,2,aa,j) = - tmp2 * fjac(2,2,j-1) > - tmp1 * njac(2,2,j-1) > - tmp1 * dy2 lhs(2,3,aa,j) = - tmp2 * fjac(2,3,j-1) > - tmp1 * njac(2,3,j-1) lhs(2,4,aa,j) = - tmp2 * fjac(2,4,j-1) > - tmp1 * njac(2,4,j-1) lhs(2,5,aa,j) = - tmp2 * fjac(2,5,j-1) > - tmp1 * njac(2,5,j-1) lhs(3,1,aa,j) = - tmp2 * fjac(3,1,j-1) > - tmp1 * njac(3,1,j-1) lhs(3,2,aa,j) = - tmp2 * fjac(3,2,j-1) > - tmp1 * njac(3,2,j-1) lhs(3,3,aa,j) = - tmp2 * fjac(3,3,j-1) > - tmp1 * njac(3,3,j-1) > - tmp1 * dy3 lhs(3,4,aa,j) = - tmp2 * fjac(3,4,j-1) > - tmp1 * njac(3,4,j-1) lhs(3,5,aa,j) = - tmp2 * fjac(3,5,j-1) > - tmp1 * njac(3,5,j-1) lhs(4,1,aa,j) = - tmp2 * fjac(4,1,j-1) > - tmp1 * njac(4,1,j-1) lhs(4,2,aa,j) = - tmp2 * fjac(4,2,j-1) > - tmp1 * njac(4,2,j-1) lhs(4,3,aa,j) = - tmp2 * fjac(4,3,j-1) > - tmp1 * njac(4,3,j-1) lhs(4,4,aa,j) = - tmp2 * fjac(4,4,j-1) > - tmp1 * njac(4,4,j-1) > - tmp1 * dy4 lhs(4,5,aa,j) = - tmp2 * fjac(4,5,j-1) > - tmp1 * njac(4,5,j-1) lhs(5,1,aa,j) = - tmp2 * fjac(5,1,j-1) > - tmp1 * njac(5,1,j-1) lhs(5,2,aa,j) = - tmp2 * fjac(5,2,j-1) > - tmp1 * njac(5,2,j-1) lhs(5,3,aa,j) = - tmp2 * fjac(5,3,j-1) > - tmp1 * njac(5,3,j-1) lhs(5,4,aa,j) = - tmp2 * fjac(5,4,j-1) > - tmp1 * njac(5,4,j-1) lhs(5,5,aa,j) = - tmp2 * fjac(5,5,j-1) > - tmp1 * njac(5,5,j-1) > - tmp1 * dy5 lhs(1,1,bb,j) = 1.0d+00 > + tmp1 * 2.0d+00 * njac(1,1,j) > + tmp1 * 2.0d+00 * dy1 lhs(1,2,bb,j) = tmp1 * 2.0d+00 * njac(1,2,j) lhs(1,3,bb,j) = tmp1 * 2.0d+00 * njac(1,3,j) lhs(1,4,bb,j) = tmp1 * 2.0d+00 * njac(1,4,j) lhs(1,5,bb,j) = tmp1 * 2.0d+00 * njac(1,5,j) lhs(2,1,bb,j) = tmp1 * 2.0d+00 * njac(2,1,j) lhs(2,2,bb,j) = 1.0d+00 > + tmp1 * 2.0d+00 * njac(2,2,j) > + tmp1 * 2.0d+00 * dy2 lhs(2,3,bb,j) = tmp1 * 2.0d+00 * njac(2,3,j) lhs(2,4,bb,j) = tmp1 * 2.0d+00 * njac(2,4,j) lhs(2,5,bb,j) = tmp1 * 2.0d+00 * njac(2,5,j) lhs(3,1,bb,j) = tmp1 * 2.0d+00 * njac(3,1,j) lhs(3,2,bb,j) = tmp1 * 2.0d+00 * njac(3,2,j) lhs(3,3,bb,j) = 1.0d+00 > + tmp1 * 2.0d+00 * njac(3,3,j) > + tmp1 * 2.0d+00 * dy3 lhs(3,4,bb,j) = tmp1 * 2.0d+00 * njac(3,4,j) lhs(3,5,bb,j) = tmp1 * 2.0d+00 * njac(3,5,j) lhs(4,1,bb,j) = tmp1 * 2.0d+00 * njac(4,1,j) lhs(4,2,bb,j) = tmp1 * 2.0d+00 * njac(4,2,j) lhs(4,3,bb,j) = tmp1 * 2.0d+00 * njac(4,3,j) lhs(4,4,bb,j) = 1.0d+00 > + tmp1 * 2.0d+00 * njac(4,4,j) > + tmp1 * 2.0d+00 * dy4 lhs(4,5,bb,j) = tmp1 * 2.0d+00 * njac(4,5,j) lhs(5,1,bb,j) = tmp1 * 2.0d+00 * njac(5,1,j) lhs(5,2,bb,j) = tmp1 * 2.0d+00 * njac(5,2,j) lhs(5,3,bb,j) = tmp1 * 2.0d+00 * njac(5,3,j) lhs(5,4,bb,j) = tmp1 * 2.0d+00 * njac(5,4,j) lhs(5,5,bb,j) = 1.0d+00 > + tmp1 * 2.0d+00 * njac(5,5,j) > + tmp1 * 2.0d+00 * dy5 lhs(1,1,cc,j) = tmp2 * fjac(1,1,j+1) > - tmp1 * njac(1,1,j+1) > - tmp1 * dy1 lhs(1,2,cc,j) = tmp2 * fjac(1,2,j+1) > - tmp1 * njac(1,2,j+1) lhs(1,3,cc,j) = tmp2 * fjac(1,3,j+1) > - tmp1 * njac(1,3,j+1) lhs(1,4,cc,j) = tmp2 * fjac(1,4,j+1) > - tmp1 * njac(1,4,j+1) lhs(1,5,cc,j) = tmp2 * fjac(1,5,j+1) > - tmp1 * njac(1,5,j+1) lhs(2,1,cc,j) = tmp2 * fjac(2,1,j+1) > - tmp1 * njac(2,1,j+1) lhs(2,2,cc,j) = tmp2 * fjac(2,2,j+1) > - tmp1 * njac(2,2,j+1) > - tmp1 * dy2 lhs(2,3,cc,j) = tmp2 * fjac(2,3,j+1) > - tmp1 * njac(2,3,j+1) lhs(2,4,cc,j) = tmp2 * fjac(2,4,j+1) > - tmp1 * njac(2,4,j+1) lhs(2,5,cc,j) = tmp2 * fjac(2,5,j+1) > - tmp1 * njac(2,5,j+1) lhs(3,1,cc,j) = tmp2 * fjac(3,1,j+1) > - tmp1 * njac(3,1,j+1) lhs(3,2,cc,j) = tmp2 * fjac(3,2,j+1) > - tmp1 * njac(3,2,j+1) lhs(3,3,cc,j) = tmp2 * fjac(3,3,j+1) > - tmp1 * njac(3,3,j+1) > - tmp1 * dy3 lhs(3,4,cc,j) = tmp2 * fjac(3,4,j+1) > - tmp1 * njac(3,4,j+1) lhs(3,5,cc,j) = tmp2 * fjac(3,5,j+1) > - tmp1 * njac(3,5,j+1) lhs(4,1,cc,j) = tmp2 * fjac(4,1,j+1) > - tmp1 * njac(4,1,j+1) lhs(4,2,cc,j) = tmp2 * fjac(4,2,j+1) > - tmp1 * njac(4,2,j+1) lhs(4,3,cc,j) = tmp2 * fjac(4,3,j+1) > - tmp1 * njac(4,3,j+1) lhs(4,4,cc,j) = tmp2 * fjac(4,4,j+1) > - tmp1 * njac(4,4,j+1) > - tmp1 * dy4 lhs(4,5,cc,j) = tmp2 * fjac(4,5,j+1) > - tmp1 * njac(4,5,j+1) lhs(5,1,cc,j) = tmp2 * fjac(5,1,j+1) > - tmp1 * njac(5,1,j+1) lhs(5,2,cc,j) = tmp2 * fjac(5,2,j+1) > - tmp1 * njac(5,2,j+1) lhs(5,3,cc,j) = tmp2 * fjac(5,3,j+1) > - tmp1 * njac(5,3,j+1) lhs(5,4,cc,j) = tmp2 * fjac(5,4,j+1) > - tmp1 * njac(5,4,j+1) lhs(5,5,cc,j) = tmp2 * fjac(5,5,j+1) > - tmp1 * njac(5,5,j+1) > - tmp1 * dy5 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'(JMAX) and rhs'(JMAX) will be sent to next cell c--------------------------------------------------------------------- c--------------------------------------------------------------------- c multiply c(i,0,k) 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,0,k) ) c--------------------------------------------------------------------- c begin inner most do loop c do all the elements of the cell unless last c--------------------------------------------------------------------- do j=1,jsize-1 c--------------------------------------------------------------------- c subtract A*lhs_vector(j-1) from lhs_vector(j) c c rhs(j) = rhs(j) - A*rhs(j-1) c--------------------------------------------------------------------- call matvec_sub(lhs(1,1,aa,j), > rhs(1,i,j-1,k),rhs(1,i,j,k)) c--------------------------------------------------------------------- c B(j) = B(j) - C(j-1)*A(j) c--------------------------------------------------------------------- call matmul_sub(lhs(1,1,aa,j), > lhs(1,1,cc,j-1), > lhs(1,1,bb,j)) c--------------------------------------------------------------------- c multiply c(i,j,k) by b_inverse and copy back to c c multiply rhs(i,1,k) by b_inverse(i,1,k) and copy to rhs c--------------------------------------------------------------------- call binvcrhs( lhs(1,1,bb,j), > lhs(1,1,cc,j), > rhs(1,i,j,k) ) enddo c--------------------------------------------------------------------- c rhs(jsize) = rhs(jsize) - A*rhs(jsize-1) c--------------------------------------------------------------------- call matvec_sub(lhs(1,1,aa,jsize), > rhs(1,i,jsize-1,k),rhs(1,i,jsize,k)) c--------------------------------------------------------------------- c B(jsize) = B(jsize) - C(jsize-1)*A(jsize) c call matmul_sub(aa,i,jsize,k,c, c $ cc,i,jsize-1,k,c,bb,i,jsize,k) c--------------------------------------------------------------------- call matmul_sub(lhs(1,1,aa,jsize), > lhs(1,1,cc,jsize-1), > lhs(1,1,bb,jsize)) c--------------------------------------------------------------------- c multiply rhs(jsize) by b_inverse(jsize) and copy to rhs c--------------------------------------------------------------------- call binvrhs( lhs(1,1,bb,jsize), > rhs(1,i,jsize,k) ) c--------------------------------------------------------------------- c back solve: if last cell, then generate U(jsize)=rhs(jsize) c else assume U(jsize) is loaded in un pack backsub_info c so just use it c after call u(jstart) will be sent to next cell c--------------------------------------------------------------------- do j=jsize-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,j)*rhs(n,i,j+1,k) enddo enddo enddo enddo enddo if (timeron) call timer_stop(t_ysolve) return end