Date: 2021-03-03T22:27:34+00:00

Actual source code: ex22f.F90
petsc-3.14.5 2021-03-03
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      1: !
      2: !   Laplacian in 3D. Modeled by the partial differential equation
      3: !
      4: !   Laplacian u = 1,0 < x,y,z < 1,
      5: !
      6: !   with boundary conditions
      7: !
      8: !   u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
      9: !
     10: !   This uses multigrid to solve the linear system

     12:       program main

     14: #include <petsc/finclude/petscksp.h>
     15:       use petscdmda
     16:       use petscksp
     17:       implicit none

     19:       PetscErrorCode   ierr
     20:       DM               da
     21:       KSP              ksp
     22:       Vec              x
     23:       external         ComputeRHS,ComputeMatrix
     24:       PetscInt i1,i3
     25:       PetscInt         ctx

     27:       call  PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     28:       if (ierr .ne. 0) then
     29:         print*,'Unable to initialize PETSc'
     30:         stop
     31:       endif

     33:       i3 = 3
     34:       i1 = 1
     35:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
     36:       call DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,                 &
     37:      &                  DMDA_STENCIL_STAR,i3,i3,i3,PETSC_DECIDE,PETSC_DECIDE,                        &
     38:      &                  PETSC_DECIDE,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
     39:       call DMSetFromOptions(da,ierr)
     40:       call DMSetUp(da,ierr)
     41:       call KSPSetDM(ksp,da,ierr)
     42:       call KSPSetComputeRHS(ksp,ComputeRHS,ctx,ierr)
     43:       call KSPSetComputeOperators(ksp,ComputeMatrix,ctx,ierr)

     45:       call KSPSetFromOptions(ksp,ierr)
     46:       call KSPSolve(ksp,PETSC_NULL_VEC,PETSC_NULL_VEC,ierr)
     47:       call KSPGetSolution(ksp,x,ierr)
     48:       call KSPDestroy(ksp,ierr)
     49:       call DMDestroy(da,ierr)
     50:       call PetscFinalize(ierr)

     52:       end

     54:       subroutine ComputeRHS(ksp,b,ctx,ierr)
     55:       use petscksp
     56:       implicit none

     58:       PetscErrorCode  ierr
     59:       PetscInt mx,my,mz
     60:       PetscScalar  h
     61:       Vec          b
     62:       KSP          ksp
     63:       DM           da
     64:       PetscInt     ctx

     66:       call KSPGetDM(ksp,da,ierr)
     67:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,mz,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                 &
     68:      &                 PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                 &
     69:      &                 PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
     70:       h    = 1.0/real((mx-1)*(my-1)*(mz-1))

     72:       call VecSet(b,h,ierr)
     73:       return
     74:       end

     77:       subroutine ComputeMatrix(ksp,JJ,jac,ctx,ierr)
     78:       use petscksp
     79:       implicit none

     81:       Mat          jac,JJ
     82:       PetscErrorCode    ierr
     83:       KSP          ksp
     84:       DM           da
     85:       PetscInt    i,j,k,mx,my,mz,xm
     86:       PetscInt    ym,zm,xs,ys,zs,i1,i7
     87:       PetscScalar  v(7),Hx,Hy,Hz
     88:       PetscScalar  HxHydHz,HyHzdHx
     89:       PetscScalar  HxHzdHy
     90:       MatStencil   row(4),col(4,7)
     91:       PetscInt     ctx
     92:       i1 = 1
     93:       i7 = 7
     94:       call KSPGetDM(ksp,da,ierr)
     95:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,mz,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                &
     96:      &                 PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                &
     97:      &                 PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)

     99:       Hx = 1.0 / real(mx-1)
    100:       Hy = 1.0 / real(my-1)
    101:       Hz = 1.0 / real(mz-1)
    102:       HxHydHz = Hx*Hy/Hz
    103:       HxHzdHy = Hx*Hz/Hy
    104:       HyHzdHx = Hy*Hz/Hx
    105:       call DMDAGetCorners(da,xs,ys,zs,xm,ym,zm,ierr)

    107:       do 10,k=zs,zs+zm-1
    108:         do 20,j=ys,ys+ym-1
    109:           do 30,i=xs,xs+xm-1
    110:           row(MatStencil_i) = i
    111:           row(MatStencil_j) = j
    112:           row(MatStencil_k) = k
    113:           if (i.eq.0 .or. j.eq.0 .or. k.eq.0 .or. i.eq.mx-1 .or. j.eq.my-1 .or. k.eq.mz-1) then
    114:             v(1) = 2.0*(HxHydHz + HxHzdHy + HyHzdHx)
    115:             call MatSetValuesStencil(jac,i1,row,i1,row,v,INSERT_VALUES,ierr)
    116:           else
    117:             v(1) = -HxHydHz
    118:              col(MatStencil_i,1) = i
    119:              col(MatStencil_j,1) = j
    120:              col(MatStencil_k,1) = k-1
    121:             v(2) = -HxHzdHy
    122:              col(MatStencil_i,2) = i
    123:              col(MatStencil_j,2) = j-1
    124:              col(MatStencil_k,2) = k
    125:             v(3) = -HyHzdHx
    126:              col(MatStencil_i,3) = i-1
    127:              col(MatStencil_j,3) = j
    128:              col(MatStencil_k,3) = k
    129:             v(4) = 2.0*(HxHydHz + HxHzdHy + HyHzdHx)
    130:              col(MatStencil_i,4) = i
    131:              col(MatStencil_j,4) = j
    132:              col(MatStencil_k,4) = k
    133:             v(5) = -HyHzdHx
    134:              col(MatStencil_i,5) = i+1
    135:              col(MatStencil_j,5) = j
    136:              col(MatStencil_k,5) = k
    137:             v(6) = -HxHzdHy
    138:              col(MatStencil_i,6) = i
    139:              col(MatStencil_j,6) = j+1
    140:              col(MatStencil_k,6) = k
    141:             v(7) = -HxHydHz
    142:              col(MatStencil_i,7) = i
    143:              col(MatStencil_j,7) = j
    144:              col(MatStencil_k,7) = k+1
    145:       call MatSetValuesStencil(jac,i1,row,i7,col,v,INSERT_VALUES,ierr)
    146:           endif
    147:  30       continue
    148:  20     continue
    149:  10   continue

    151:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    152:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    153:       return
    154:       end

    156: !/*TEST
    157: !
    158: !   test:
    159: !      args: -pc_mg_type full -ksp_monitor_short -mg_levels_ksp_monitor_short -mg_levels_ksp_norm_type preconditioned -pc_type mg -da_refine 2 -ksp_type fgmres
    160: !      requires: !single
    161: !      output_file: output/ex22_1.out
    162: !
    163: !TEST*/