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,allocatable,dimension(:)      ::   subksp     ! array of local KSP contexts on this processor
 34:       PetscInt,allocatable,dimension(:) :: blks
 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

 45:       !-------------------------------------------------------------------
 46:       ! Compute the matrix and right-hand-side vector that define
 47:       ! the linear system, Ax = b.
 48:       !---------------------------------------------------------------

 50:       ! Create and assemble parallel matrix

 52:       PetscCallA( MatCreate(PETSC_COMM_WORLD,A,ierr))
 53:       PetscCallA( MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
 54:       PetscCallA( MatSetFromOptions(A,ierr))
 55:       PetscCallA( MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,five,PETSC_NULL_INTEGER,ierr))
 56:       PetscCallA( MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,ierr))
 57:       PetscCallA( MatGetOwnershipRange(A,Istart,Iend,ierr))

 59:       do Ii=Istart,Iend-1
 60:           v =-1.0; i = Ii/n; j = Ii - i*n
 61:           if (i>0) then
 62:             JJ = Ii - n
 63:             PetscCallA(MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr))
 64:           endif

 66:           if (i<m-1) then
 67:             JJ = Ii + n
 68:             PetscCallA(MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr))
 69:           endif

 71:           if (j>0) then
 72:             JJ = Ii - 1
 73:             PetscCallA(MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr))
 74:           endif

 76:           if (j<n-1) then
 77:             JJ = Ii + 1
 78:             PetscCallA(MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr))
 79:           endif

 81:           v=4.0
 82:           PetscCallA(MatSetValues(A,one,Ii,one,Ii,v,ADD_VALUES,ierr))

 84:         enddo

 86:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
 87:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

 89:       ! Create parallel vectors

 91:       PetscCallA( VecCreate(PETSC_COMM_WORLD,u,ierr))
 92:       PetscCallA( VecSetSizes(u,PETSC_DECIDE,m*n,ierr))
 93:       PetscCallA( VecSetFromOptions(u,ierr))
 94:       PetscCallA( VecDuplicate(u,b,ierr))
 95:       PetscCallA( VecDuplicate(b,x,ierr))

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

 99:       PetscCallA(Vecset(u,sone,ierr))
100:       PetscCallA(MatMult(A,u,b,ierr))

102:       ! Create linear solver context

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

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

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

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

115:       PetscCallA(KSPGetPC(ksp,myPc,ierr))
116:       PetscCallA(PCSetType(myPc,PCBJACOBI,ierr))

118:       ! -----------------------------------------------------------------
119:       !            Define the problem decomposition
120:       !-------------------------------------------------------------------

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

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

130:       allocate(blks(m),source = n)

132:       PetscCallA(PCBJacobiSetTotalBlocks(myPc,m,blks,ierr))
133:       deallocate(blks)

135:       !-------------------------------------------------------------------
136:       !       Set the linear solvers for the subblocks
137:       !-------------------------------------------------------------------

139:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:       ! Basic method, should be sufficient for the needs of most users.
141:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:       ! By default, the block Jacobi method uses the same solver on each
143:       ! block of the problem.  To set the same solver options on all blocks,
144:       ! use the prefix -sub before the usual PC and KSP options, e.g.,
145:       ! -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4

147:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:       !  Advanced method, setting different solvers for various blocks.
149:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

160:       if (isbjacobi) then

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

166:         PetscCallA(KSPSetUp(ksp,ierr))

168:         ! Extract the array of KSP contexts for the local blocks
169:         PetscCallA(PCBJacobiGetSubKSP(myPc,nlocal,first,PETSC_NULL_KSP,ierr))
170:         allocate(subksp(nlocal))
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_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_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_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_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:       deallocate(subksp)
234:       PetscCallA(KSPDestroy(ksp,ierr))
235:       PetscCallA(VecDestroy(u,ierr))
236:       PetscCallA(VecDestroy(b,ierr))
237:       PetscCallA(MatDestroy(A,ierr))
238:       PetscCallA(VecDestroy(x,ierr))
239:       PetscCallA(PetscFinalize(ierr))

241: end program main

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