c--------------------------------------------------------------------- c--------------------------------------------------------------------- subroutine y_solve(rho_i, vs, speed, rhs, nx, nxmax, ny, nz) c--------------------------------------------------------------------- c--------------------------------------------------------------------- c--------------------------------------------------------------------- c this function performs the solution of the approximate factorization c step in the y-direction for all five matrix components c simultaneously. The Thomas algorithm is employed to solve the c systems for the y-lines. Boundary conditions are non-periodic c--------------------------------------------------------------------- include 'header.h' integer nx, nxmax, ny, nz double precision rho_i( 0:nxmax-1,0:ny-1,0:nz-1), $ vs ( 0:nxmax-1,0:ny-1,0:nz-1), $ speed( 0:nxmax-1,0:ny-1,0:nz-1), $ rhs (5,0:nxmax-1,0:ny-1,0:nz-1) integer i, j, k, j1, j2, m double precision ru1, fac1, fac2 c--------------------------------------------------------------------- c--------------------------------------------------------------------- if (timeron) call timer_start(t_ysolve) !$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(fac2,m,fac1,j2,j1,ru1,j,i,k) !$OMP& SHARED(comz6,comz1,comz4,comz5,c2dtty1,dtty1,dtty2,dy1,dymax, !$OMP& c1c5,dy5,con43,dy3,c3c4,ny,nx,nz) do k = 1, nz-2 c--------------------------------------------------------------------- c Computes the left hand side for the three y-factors c--------------------------------------------------------------------- c--------------------------------------------------------------------- c zap the whole left hand side for starters c--------------------------------------------------------------------- do i = 1, nx-2 do m = 1, 5 lhs (m,i,0) = 0.0d0 lhsp(m,i,0) = 0.0d0 lhsm(m,i,0) = 0.0d0 lhs (m,i,ny-1) = 0.0d0 lhsp(m,i,ny-1) = 0.0d0 lhsm(m,i,ny-1) = 0.0d0 end do c--------------------------------------------------------------------- c next, set all diagonal values to 1. This is overkill, but c convenient c--------------------------------------------------------------------- lhs (3,i,0) = 1.0d0 lhsp(3,i,0) = 1.0d0 lhsm(3,i,0) = 1.0d0 lhs (3,i,ny-1) = 1.0d0 lhsp(3,i,ny-1) = 1.0d0 lhsm(3,i,ny-1) = 1.0d0 end do c--------------------------------------------------------------------- c first fill the lhs for the u-eigenvalue c--------------------------------------------------------------------- do i = 1, nx-2 do j = 0, ny-1 ru1 = c3c4*rho_i(i,j,k) cv(j) = vs(i,j,k) rhoq(j) = dmax1( dy3 + con43 * ru1, > dy5 + c1c5*ru1, > dymax + ru1, > dy1) end do do j = 1, ny-2 lhs(1,i,j) = 0.0d0 lhs(2,i,j) = -dtty2 * cv(j-1) - dtty1 * rhoq(j-1) lhs(3,i,j) = 1.0 + c2dtty1 * rhoq(j) lhs(4,i,j) = dtty2 * cv(j+1) - dtty1 * rhoq(j+1) lhs(5,i,j) = 0.0d0 end do end do c--------------------------------------------------------------------- c add fourth order dissipation c--------------------------------------------------------------------- do i = 1, nx-2 j = 1 lhs(3,i,j) = lhs(3,i,j) + comz5 lhs(4,i,j) = lhs(4,i,j) - comz4 lhs(5,i,j) = lhs(5,i,j) + comz1 j = 2 lhs(2,i,j) = lhs(2,i,j) - comz4 lhs(3,i,j) = lhs(3,i,j) + comz6 lhs(4,i,j) = lhs(4,i,j) - comz4 lhs(5,i,j) = lhs(5,i,j) + comz1 end do do j=3, ny-4 do i = 1, nx-2 lhs(1,i,j) = lhs(1,i,j) + comz1 lhs(2,i,j) = lhs(2,i,j) - comz4 lhs(3,i,j) = lhs(3,i,j) + comz6 lhs(4,i,j) = lhs(4,i,j) - comz4 lhs(5,i,j) = lhs(5,i,j) + comz1 end do end do do i = 1, nx-2 j = ny-3 lhs(1,i,j) = lhs(1,i,j) + comz1 lhs(2,i,j) = lhs(2,i,j) - comz4 lhs(3,i,j) = lhs(3,i,j) + comz6 lhs(4,i,j) = lhs(4,i,j) - comz4 j = ny-2 lhs(1,i,j) = lhs(1,i,j) + comz1 lhs(2,i,j) = lhs(2,i,j) - comz4 lhs(3,i,j) = lhs(3,i,j) + comz5 end do c--------------------------------------------------------------------- c subsequently, do the other two factors c--------------------------------------------------------------------- do j = 1, ny-2 do i = 1, nx-2 lhsp(1,i,j) = lhs(1,i,j) lhsp(2,i,j) = lhs(2,i,j) - > dtty2 * speed(i,j-1,k) lhsp(3,i,j) = lhs(3,i,j) lhsp(4,i,j) = lhs(4,i,j) + > dtty2 * speed(i,j+1,k) lhsp(5,i,j) = lhs(5,i,j) lhsm(1,i,j) = lhs(1,i,j) lhsm(2,i,j) = lhs(2,i,j) + > dtty2 * speed(i,j-1,k) lhsm(3,i,j) = lhs(3,i,j) lhsm(4,i,j) = lhs(4,i,j) - > dtty2 * speed(i,j+1,k) lhsm(5,i,j) = lhs(5,i,j) end do end do c--------------------------------------------------------------------- c FORWARD ELIMINATION c--------------------------------------------------------------------- do j = 0, ny-3 j1 = j + 1 j2 = j + 2 do i = 1, nx-2 fac1 = 1.d0/lhs(3,i,j) lhs(4,i,j) = fac1*lhs(4,i,j) lhs(5,i,j) = fac1*lhs(5,i,j) do m = 1, 3 rhs(m,i,j,k) = fac1*rhs(m,i,j,k) end do lhs(3,i,j1) = lhs(3,i,j1) - > lhs(2,i,j1)*lhs(4,i,j) lhs(4,i,j1) = lhs(4,i,j1) - > lhs(2,i,j1)*lhs(5,i,j) do m = 1, 3 rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhs(2,i,j1)*rhs(m,i,j,k) end do lhs(2,i,j2) = lhs(2,i,j2) - > lhs(1,i,j2)*lhs(4,i,j) lhs(3,i,j2) = lhs(3,i,j2) - > lhs(1,i,j2)*lhs(5,i,j) do m = 1, 3 rhs(m,i,j2,k) = rhs(m,i,j2,k) - > lhs(1,i,j2)*rhs(m,i,j,k) end do end do end do c--------------------------------------------------------------------- c The last two rows in this zone are a bit different, c since they do not have two more rows available for the c elimination of off-diagonal entries c--------------------------------------------------------------------- j = ny-2 j1 = ny-1 do i = 1, nx-2 fac1 = 1.d0/lhs(3,i,j) lhs(4,i,j) = fac1*lhs(4,i,j) lhs(5,i,j) = fac1*lhs(5,i,j) do m = 1, 3 rhs(m,i,j,k) = fac1*rhs(m,i,j,k) end do lhs(3,i,j1) = lhs(3,i,j1) - > lhs(2,i,j1)*lhs(4,i,j) lhs(4,i,j1) = lhs(4,i,j1) - > lhs(2,i,j1)*lhs(5,i,j) do m = 1, 3 rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhs(2,i,j1)*rhs(m,i,j,k) end do c--------------------------------------------------------------------- c scale the last row immediately c--------------------------------------------------------------------- fac2 = 1.d0/lhs(3,i,j1) do m = 1, 3 rhs(m,i,j1,k) = fac2*rhs(m,i,j1,k) end do end do c--------------------------------------------------------------------- c do the u+c and the u-c factors c--------------------------------------------------------------------- do j = 0, ny-3 j1 = j + 1 j2 = j + 2 do i = 1, nx-2 m = 4 fac1 = 1.d0/lhsp(3,i,j) lhsp(4,i,j) = fac1*lhsp(4,i,j) lhsp(5,i,j) = fac1*lhsp(5,i,j) rhs(m,i,j,k) = fac1*rhs(m,i,j,k) lhsp(3,i,j1) = lhsp(3,i,j1) - > lhsp(2,i,j1)*lhsp(4,i,j) lhsp(4,i,j1) = lhsp(4,i,j1) - > lhsp(2,i,j1)*lhsp(5,i,j) rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhsp(2,i,j1)*rhs(m,i,j,k) lhsp(2,i,j2) = lhsp(2,i,j2) - > lhsp(1,i,j2)*lhsp(4,i,j) lhsp(3,i,j2) = lhsp(3,i,j2) - > lhsp(1,i,j2)*lhsp(5,i,j) rhs(m,i,j2,k) = rhs(m,i,j2,k) - > lhsp(1,i,j2)*rhs(m,i,j,k) m = 5 fac1 = 1.d0/lhsm(3,i,j) lhsm(4,i,j) = fac1*lhsm(4,i,j) lhsm(5,i,j) = fac1*lhsm(5,i,j) rhs(m,i,j,k) = fac1*rhs(m,i,j,k) lhsm(3,i,j1) = lhsm(3,i,j1) - > lhsm(2,i,j1)*lhsm(4,i,j) lhsm(4,i,j1) = lhsm(4,i,j1) - > lhsm(2,i,j1)*lhsm(5,i,j) rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhsm(2,i,j1)*rhs(m,i,j,k) lhsm(2,i,j2) = lhsm(2,i,j2) - > lhsm(1,i,j2)*lhsm(4,i,j) lhsm(3,i,j2) = lhsm(3,i,j2) - > lhsm(1,i,j2)*lhsm(5,i,j) rhs(m,i,j2,k) = rhs(m,i,j2,k) - > lhsm(1,i,j2)*rhs(m,i,j,k) end do end do c--------------------------------------------------------------------- c And again the last two rows separately c--------------------------------------------------------------------- j = ny-2 j1 = ny-1 do i = 1, nx-2 m = 4 fac1 = 1.d0/lhsp(3,i,j) lhsp(4,i,j) = fac1*lhsp(4,i,j) lhsp(5,i,j) = fac1*lhsp(5,i,j) rhs(m,i,j,k) = fac1*rhs(m,i,j,k) lhsp(3,i,j1) = lhsp(3,i,j1) - > lhsp(2,i,j1)*lhsp(4,i,j) lhsp(4,i,j1) = lhsp(4,i,j1) - > lhsp(2,i,j1)*lhsp(5,i,j) rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhsp(2,i,j1)*rhs(m,i,j,k) m = 5 fac1 = 1.d0/lhsm(3,i,j) lhsm(4,i,j) = fac1*lhsm(4,i,j) lhsm(5,i,j) = fac1*lhsm(5,i,j) rhs(m,i,j,k) = fac1*rhs(m,i,j,k) lhsm(3,i,j1) = lhsm(3,i,j1) - > lhsm(2,i,j1)*lhsm(4,i,j) lhsm(4,i,j1) = lhsm(4,i,j1) - > lhsm(2,i,j1)*lhsm(5,i,j) rhs(m,i,j1,k) = rhs(m,i,j1,k) - > lhsm(2,i,j1)*rhs(m,i,j,k) c--------------------------------------------------------------------- c Scale the last row immediately c--------------------------------------------------------------------- rhs(4,i,j1,k) = rhs(4,i,j1,k)/lhsp(3,i,j1) rhs(5,i,j1,k) = rhs(5,i,j1,k)/lhsm(3,i,j1) end do c--------------------------------------------------------------------- c BACKSUBSTITUTION c--------------------------------------------------------------------- j = ny-2 j1 = ny-1 do i = 1, nx-2 do m = 1, 3 rhs(m,i,j,k) = rhs(m,i,j,k) - > lhs(4,i,j)*rhs(m,i,j1,k) end do rhs(4,i,j,k) = rhs(4,i,j,k) - > lhsp(4,i,j)*rhs(4,i,j1,k) rhs(5,i,j,k) = rhs(5,i,j,k) - > lhsm(4,i,j)*rhs(5,i,j1,k) end do c--------------------------------------------------------------------- c The first three factors c--------------------------------------------------------------------- do j = ny-3, 0, -1 j1 = j + 1 j2 = j + 2 do i = 1, nx-2 do m = 1, 3 rhs(m,i,j,k) = rhs(m,i,j,k) - > lhs(4,i,j)*rhs(m,i,j1,k) - > lhs(5,i,j)*rhs(m,i,j2,k) end do c--------------------------------------------------------------------- c And the remaining two c--------------------------------------------------------------------- rhs(4,i,j,k) = rhs(4,i,j,k) - > lhsp(4,i,j)*rhs(4,i,j1,k) - > lhsp(5,i,j)*rhs(4,i,j2,k) rhs(5,i,j,k) = rhs(5,i,j,k) - > lhsm(4,i,j)*rhs(5,i,j1,k) - > lhsm(5,i,j)*rhs(5,i,j2,k) end do end do end do !$OMP END PARALLEL DO if (timeron) call timer_stop(t_ysolve) if (timeron) call timer_start(t_pinvr) call pinvr(rhs, nx, nxmax, ny, nz) if (timeron) call timer_stop(t_pinvr) return end