Date: 2025-03-28T21:10:54+00:00

Actual source code: ex6f.F90

      1: !
      2: !  Description: This example demonstrates repeated linear solves as
      3: !  well as the use of different preconditioner and linear system
      4: !  matrices.  This example also illustrates how to save PETSc objects
      5: !  in common blocks.
      6: !
      7: !

      9:       program main
     10: #include <petsc/finclude/petscksp.h>
     11:       use petscksp
     12:       implicit none

     14: !  Variables:
     15: !
     16: !  A       - matrix that defines linear system
     17: !  ksp    - KSP context
     18: !  ksp     - KSP context
     19: !  x, b, u - approx solution, RHS, exact solution vectors
     20: !
     21:       Vec     x,u,b
     22:       Mat     A,A2
     23:       KSP    ksp
     24:       PetscInt i,j,II,JJ,m,n
     25:       PetscInt Istart,Iend
     26:       PetscInt nsteps,one
     27:       PetscErrorCode ierr
     28:       PetscBool  flg
     29:       PetscScalar  v

     31:       PetscCallA(PetscInitialize(ierr))
     32:       m      = 3
     33:       n      = 3
     34:       nsteps = 2
     35:       one    = 1
     36:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
     37:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
     38:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-nsteps',nsteps,flg,ierr))

     40: !  Create parallel matrix, specifying only its global dimensions.
     41: !  When using MatCreate(), the matrix format can be specified at
     42: !  runtime. Also, the parallel partitioning of the matrix is
     43: !  determined by PETSc at runtime.

     45:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
     46:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
     47:       PetscCallA(MatSetFromOptions(A,ierr))
     48:       PetscCallA(MatSetUp(A,ierr))

     50: !  The matrix is partitioned by contiguous chunks of rows across the
     51: !  processors.  Determine which rows of the matrix are locally owned.

     53:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))

     55: !  Set matrix elements.
     56: !   - Each processor needs to insert only elements that it owns
     57: !     locally (but any non-local elements will be sent to the
     58: !     appropriate processor during matrix assembly).
     59: !   - Always specify global rows and columns of matrix entries.

     61:       do 10, II=Istart,Iend-1
     62:         v = -1.0
     63:         i = II/n
     64:         j = II - i*n
     65:         if (i.gt.0) then
     66:           JJ = II - n
     67:           PetscCallA(MatSetValues(A,one,[II],one,[JJ],[v],ADD_VALUES,ierr))
     68:         endif
     69:         if (i.lt.m-1) then
     70:           JJ = II + n
     71:           PetscCallA(MatSetValues(A,one,[II],one,[JJ],[v],ADD_VALUES,ierr))
     72:         endif
     73:         if (j.gt.0) then
     74:           JJ = II - 1
     75:           PetscCallA(MatSetValues(A,one,[II],one,[JJ],[v],ADD_VALUES,ierr))
     76:         endif
     77:         if (j.lt.n-1) then
     78:           JJ = II + 1
     79:           PetscCallA(MatSetValues(A,one,[II],one,[JJ],[v],ADD_VALUES,ierr))
     80:         endif
     81:         v = 4.0
     82:         PetscCallA( MatSetValues(A,one,[II],one,[II],[v],ADD_VALUES,ierr))
     83:  10   continue

     85: !  Assemble matrix, using the 2-step process:
     86: !       MatAssemblyBegin(), MatAssemblyEnd()
     87: !  Computations can be done while messages are in transition
     88: !  by placing code between these two statements.

     90:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
     91:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

     93: !  Create parallel vectors.
     94: !   - When using VecCreate(), the parallel partitioning of the vector
     95: !     is determined by PETSc at runtime.
     96: !   - Note: We form 1 vector from scratch and then duplicate as needed.

     98:       PetscCallA(VecCreate(PETSC_COMM_WORLD,u,ierr))
     99:       PetscCallA(VecSetSizes(u,PETSC_DECIDE,m*n,ierr))
    100:       PetscCallA(VecSetFromOptions(u,ierr))
    101:       PetscCallA(VecDuplicate(u,b,ierr))
    102:       PetscCallA(VecDuplicate(b,x,ierr))

    104: !  Create linear solver context

    106:       PetscCallA(KSPCreate(PETSC_COMM_WORLD,ksp,ierr))

    108: !  Set runtime options (e.g., -ksp_type <type> -pc_type <type>)

    110:       PetscCallA(KSPSetFromOptions(ksp,ierr))

    112: !  Solve several linear systems in succession

    114:       do 100 i=1,nsteps
    115:          PetscCallA(solve1(ksp,A,x,b,u,i,nsteps,A2,ierr))
    116:  100  continue

    118: !  Free work space.  All PETSc objects should be destroyed when they
    119: !  are no longer needed.

    121:       PetscCallA(VecDestroy(u,ierr))
    122:       PetscCallA(VecDestroy(x,ierr))
    123:       PetscCallA(VecDestroy(b,ierr))
    124:       PetscCallA(MatDestroy(A,ierr))
    125:       PetscCallA(KSPDestroy(ksp,ierr))

    127:       PetscCallA(PetscFinalize(ierr))
    128:       end

    130: ! -----------------------------------------------------------------------
    131: !
    132:       subroutine solve1(ksp,A,x,b,u,count,nsteps,A2,ierr)
    133:       use petscksp
    134:       implicit none

    136: !
    137: !   solve1 - This routine is used for repeated linear system solves.
    138: !   We update the linear system matrix each time, but retain the same
    139: !   preconditioning matrix for all linear solves.
    140: !
    141: !      A - linear system matrix
    142: !      A2 - preconditioning matrix
    143: !
    144:       PetscScalar  v,val
    145:       PetscInt II,Istart,Iend
    146:       PetscInt count,nsteps,one
    147:       PetscErrorCode ierr
    148:       Mat     A
    149:       KSP     ksp
    150:       Vec     x,b,u

    152: ! Use common block to retain matrix between successive subroutine calls
    153:       Mat              A2
    154:       PetscMPIInt      rank
    155:       PetscBool        pflag
    156:       common /my_data/ pflag,rank

    158:       one = 1
    159: ! First time thorough: Create new matrix to define the linear system
    160:       if (count .eq. 1) then
    161:         PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
    162:         pflag = .false.
    163:         PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mat_view',pflag,ierr))
    164:         if (pflag) then
    165:           if (rank .eq. 0) write(6,100)
    166:           call PetscFlush(6)
    167:         endif
    168:         PetscCallA(MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,A2,ierr))
    169: ! All other times: Set previous solution as initial guess for next solve.
    170:       else
    171:         PetscCallA(KSPSetInitialGuessNonzero(ksp,PETSC_TRUE,ierr))
    172:       endif

    174: ! Alter the matrix A a bit
    175:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))
    176:       do 20, II=Istart,Iend-1
    177:         v = 2.0
    178:         PetscCallA(MatSetValues(A,one,[II],one,[II],[v],ADD_VALUES,ierr))
    179:  20   continue
    180:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
    181:       if (pflag) then
    182:         if (rank .eq. 0) write(6,110)
    183:         call PetscFlush(6)
    184:       endif
    185:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

    187: ! Set the exact solution; compute the right-hand-side vector
    188:       val = 1.0*real(count)
    189:       PetscCallA(VecSet(u,val,ierr))
    190:       PetscCallA(MatMult(A,u,b,ierr))

    192: ! Set operators, keeping the identical preconditioner matrix for
    193: ! all linear solves.  This approach is often effective when the
    194: ! linear systems do not change very much between successive steps.
    195:       PetscCallA(KSPSetReusePreconditioner(ksp,PETSC_TRUE,ierr))
    196:       PetscCallA(KSPSetOperators(ksp,A,A2,ierr))

    198: ! Solve linear system
    199:       PetscCallA(KSPSolve(ksp,b,x,ierr))

    201: ! Destroy the preconditioner matrix on the last time through
    202:       if (count .eq. nsteps) PetscCallA(MatDestroy(A2,ierr))

    204:  100  format('previous matrix: preconditioning')
    205:  110  format('next matrix: defines linear system')

    207:       end

    209: !/*TEST
    210: !
    211: !   test:
    212: !      args: -pc_type jacobi -mat_view -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    213: !
    214: !TEST*/