Date: 2025-03-29T05:58:28+00:00

Actual source code: ex7f.F90

      1: ! Block Jacobi preconditioner for solving a linear system in parallel with KSP
      2: ! The code indicates the procedures for setting the particular block sizes and
      3: ! for using different linear solvers on the individual blocks

      5: ! This example focuses on ways to customize the block Jacobi preconditioner.
      6: ! See ex1.c and ex2.c for more detailed comments on the basic usage of KSP
      7: ! (including working with matrices and vectors)

      9: ! Recall: The block Jacobi method is equivalent to the ASM preconditioner with zero overlap.

     11: program main
     12: #include <petsc/finclude/petscksp.h>
     13:       use petscksp

     15:       implicit none
     16:       Vec             :: x,b,u      ! approx solution, RHS, exact solution
     17:       Mat             :: A            ! linear system matrix
     18:       KSP             :: ksp         ! KSP context
     19:       PC              :: myPc           ! PC context
     20:       PC              :: subpc        ! PC context for subdomain
     21:       PetscReal       :: norm         ! norm of solution error
     22:       PetscReal,parameter :: tol = 1.e-6
     23:       PetscErrorCode  :: ierr
     24:       PetscInt        :: i,j,Ii,JJ,n
     25:       PetscInt        :: m
     26:       PetscMPIInt     :: rank,size
     27:       PetscInt        :: its,nlocal,first,Istart,Iend
     28:       PetscScalar     :: v
     29:       PetscScalar, parameter :: &
     30:         myNone = -1.0, &
     31:         sone   = 1.0
     32:       PetscBool       :: isbjacobi,flg
     33:       KSP,pointer      ::   subksp(:) => null()
     34:       PetscInt :: blks(4)
     35:       character(len=PETSC_MAX_PATH_LEN) :: outputString
     36:       PetscInt,parameter :: one = 1, five = 5

     38:       PetscCallA(PetscInitialize(ierr))
     39:       m = 4
     40:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
     41:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
     42:       PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr))
     43:       n=m+2
     44:       blks(1) = n
     45:       blks(2) = n
     46:       blks(3) = n
     47:       blks(4) = n

     49:       !-------------------------------------------------------------------
     50:       ! Compute the matrix and right-hand-side vector that define
     51:       ! the linear system, Ax = b.
     52:       !---------------------------------------------------------------

     54:       ! Create and assemble parallel matrix

     56:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
     57:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
     58:       PetscCallA(MatSetFromOptions(A,ierr))
     59:       PetscCallA(MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,five,PETSC_NULL_INTEGER_ARRAY,ierr))
     60:       PetscCallA(MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,ierr))
     61:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))

     63:       do Ii=Istart,Iend-1
     64:           v =-1.0; i = Ii/n; j = Ii - i*n
     65:           if (i>0) then
     66:             JJ = Ii - n
     67:             PetscCallA(MatSetValues(A,one,[Ii],one,[JJ],[v],ADD_VALUES,ierr))
     68:           endif

     70:           if (i<m-1) then
     71:             JJ = Ii + n
     72:             PetscCallA(MatSetValues(A,one,[Ii],one,[JJ],[v],ADD_VALUES,ierr))
     73:           endif

     75:           if (j>0) then
     76:             JJ = Ii - 1
     77:             PetscCallA(MatSetValues(A,one,[Ii],one,[JJ],[v],ADD_VALUES,ierr))
     78:           endif

     80:           if (j<n-1) then
     81:             JJ = Ii + 1
     82:             PetscCallA(MatSetValues(A,one,[Ii],one,[JJ],[v],ADD_VALUES,ierr))
     83:           endif

     85:           v=4.0
     86:           PetscCallA(MatSetValues(A,one,[Ii],one,[Ii],[v],ADD_VALUES,ierr))

     88:         enddo

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

     93:       ! Create parallel vectors

     95:       PetscCallA(VecCreate(PETSC_COMM_WORLD,u,ierr))
     96:       PetscCallA(VecSetSizes(u,PETSC_DECIDE,m*n,ierr))
     97:       PetscCallA(VecSetFromOptions(u,ierr))
     98:       PetscCallA(VecDuplicate(u,b,ierr))
     99:       PetscCallA(VecDuplicate(b,x,ierr))

    101:       ! Set exact solution; then compute right-hand-side vector.

    103:       PetscCallA(Vecset(u,sone,ierr))
    104:       PetscCallA(MatMult(A,u,b,ierr))

    106:       ! Create linear solver context

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

    110:       ! Set operators. Here the matrix that defines the linear system
    111:       ! also serves as the preconditioning matrix.

    113:       PetscCallA(KSPSetOperators(ksp,A,A,ierr))

    115:       ! Set default preconditioner for this program to be block Jacobi.
    116:       ! This choice can be overridden at runtime with the option
    117:       ! -pc_type <type>

    119:       PetscCallA(KSPGetPC(ksp,myPc,ierr))
    120:       PetscCallA(PCSetType(myPc,PCBJACOBI,ierr))

    122:       ! -----------------------------------------------------------------
    123:       !            Define the problem decomposition
    124:       !-------------------------------------------------------------------

    126:       ! Call PCBJacobiSetTotalBlocks() to set individually the size of
    127:       ! each block in the preconditioner.  This could also be done with
    128:       ! the runtime option -pc_bjacobi_blocks <blocks>
    129:       ! Also, see the command PCBJacobiSetLocalBlocks() to set the
    130:       ! local blocks.

    132:       ! Note: The default decomposition is 1 block per processor.

    134:       PetscCallA(PCBJacobiSetTotalBlocks(myPc,m,blks,ierr))

    136:       !-------------------------------------------------------------------
    137:       !       Set the linear solvers for the subblocks
    138:       !-------------------------------------------------------------------

    140:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:       ! Basic method, should be sufficient for the needs of most users.
    142:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:       ! By default, the block Jacobi method uses the same solver on each
    144:       ! block of the problem.  To set the same solver options on all blocks,
    145:       ! use the prefix -sub before the usual PC and KSP options, e.g.,
    146:       ! -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4

    148:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:       !  Advanced method, setting different solvers for various blocks.
    150:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    152:       ! Note that each block's KSP context is completely independent of
    153:       ! the others, and the full range of uniprocessor KSP options is
    154:       ! available for each block. The following section of code is intended
    155:       ! to be a simple illustration of setting different linear solvers for
    156:       ! the individual blocks.  These choices are obviously not recommended
    157:       ! for solving this particular problem.

    159:       PetscCallA(PetscObjectTypeCompare(myPc,PCBJACOBI,isbjacobi,ierr))

    161:       if (isbjacobi) then

    163:         ! Call KSPSetUp() to set the block Jacobi data structures (including
    164:         ! creation of an internal KSP context for each block).
    165:         ! Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP()

    167:         PetscCallA(KSPSetUp(ksp,ierr))

    169:         ! Extract the array of KSP contexts for the local blocks
    170:         PetscCallA(PCBJacobiGetSubKSP(myPc,nlocal,first,PETSC_NULL_KSP_POINTER,ierr))
    171:         PetscCallA(PCBJacobiGetSubKSP(myPc,nlocal,first,subksp,ierr))

    173:         ! Loop over the local blocks, setting various KSP options for each block

    175:         do i=0,nlocal-1

    177:           PetscCallA(KSPGetPC(subksp(i+1),subpc,ierr))

    179:           if (rank>0) then

    181:             if (mod(i,2)==1) then
    182:               PetscCallA(PCSetType(subpc,PCILU,ierr))

    184:             else
    185:               PetscCallA(PCSetType(subpc,PCNONE,ierr))
    186:               PetscCallA(KSPSetType(subksp(i+1),KSPBCGS,ierr))
    187:               PetscCallA(KSPSetTolerances(subksp(i+1),tol,PETSC_CURRENT_REAL,PETSC_CURRENT_REAL,PETSC_CURRENT_INTEGER,ierr))
    188:             endif

    190:           else
    191:             PetscCallA(PCSetType(subpc,PCJACOBI,ierr))
    192:             PetscCallA(KSPSetType(subksp(i+1),KSPGMRES,ierr))
    193:             PetscCallA(KSPSetTolerances(subksp(i+1),tol,PETSC_CURRENT_REAL,PETSC_CURRENT_REAL,PETSC_CURRENT_INTEGER,ierr))
    194:           endif

    196:         end do

    198:       endif

    200:       !----------------------------------------------------------------
    201:       !                Solve the linear system
    202:       !-----------------------------------------------------------------

    204:       ! Set runtime options

    206:       PetscCallA(KSPSetFromOptions(ksp,ierr))

    208:       ! Solve the linear system

    210:       PetscCallA(KSPSolve(ksp,b,x,ierr))

    212:       !  -----------------------------------------------------------------
    213:       !               Check solution and clean up
    214:       !-------------------------------------------------------------------

    216:       !  -----------------------------------------------------------------
    217:       ! Check the error
    218:       !  -----------------------------------------------------------------

    220:       !PetscCallA(VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr))

    222:       PetscCallA(VecAXPY(x,myNone,u,ierr))

    224:       !PetscCallA(VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr))

    226:       PetscCallA(VecNorm(x,NORM_2,norm,ierr))
    227:       PetscCallA(KSPGetIterationNumber(ksp,its,ierr))
    228:       write(outputString,*)'Norm of error',real(norm),'Iterations',its,'\n'         ! PETScScalar might be of complex type
    229:       PetscCallA(PetscPrintf(PETSC_COMM_WORLD,outputString,ierr))

    231:       ! Free work space.  All PETSc objects should be destroyed when they
    232:       ! are no longer needed.
    233:       PetscCallA(KSPDestroy(ksp,ierr))
    234:       PetscCallA(VecDestroy(u,ierr))
    235:       PetscCallA(VecDestroy(b,ierr))
    236:       PetscCallA(MatDestroy(A,ierr))
    237:       PetscCallA(VecDestroy(x,ierr))
    238:       PetscCallA(PetscFinalize(ierr))

    240: end program main

    242: !/*TEST
    243: !
    244: !   test:
    245: !      nsize: 2
    246: !      args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    247: !
    248: !   test:
    249: !      suffix: 2
    250: !      nsize: 2
    251: !      args: -ksp_view ::ascii_info_detail
    252: !
    253: !TEST*/