Actual source code: ex7f.F90

petsc-3.15.0 2021-04-05
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2: ! Block Jacobi preconditioner for solving a linear system in parallel with KSP
3: ! The code indicates the procedures for setting the particular block sizes and
4: ! for using different linear solvers on the individual blocks

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

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

12: !/*T
13: !   Concepts: KSP^customizing the block Jacobi preconditioner
14: !   Processors: n
15: !T*/

18: program main
19: #include <petsc/finclude/petscksp.h>
20:       use petscksp

22:       implicit none
23:       Vec             :: x,b,u      ! approx solution, RHS, exact solution
24:       Mat             :: A            ! linear system matrix
25:       KSP             :: ksp         ! KSP context
26:       PC              :: myPc           ! PC context
27:       PC              :: subpc        ! PC context for subdomain
28:       PetscReal       :: norm         ! norm of solution error
29:       PetscReal,parameter :: tol = 1.e-6
30:       PetscErrorCode  :: ierr
31:       PetscInt        :: i,j,Ii,JJ,n
32:       PetscInt, parameter :: m = 4
33:       PetscMPIInt     :: myRank,mySize
34:       PetscInt        :: its,nlocal,first,Istart,Iend
35:       PetscScalar     :: v
36:       PetscScalar, parameter :: &
37:         myNone = -1.0, &
38:         sone   = 1.0
39:       PetscBool       :: isbjacobi,flg
40:       KSP,allocatable,dimension(:)      ::   subksp     ! array of local KSP contexts on this processor
41:       PetscInt,allocatable,dimension(:) :: blks
42:       character(len=PETSC_MAX_PATH_LEN) :: outputString
43:       PetscInt,parameter :: one = 1, five = 5

45:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
46:       if (ierr /= 0) then
47:         write(6,*)'Unable to initialize PETSc'
48:         stop
49:       endif

51:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
52:       CHKERRA(ierr)
53:       call MPI_Comm_rank(PETSC_COMM_WORLD,myRank,ierr)
54:       CHKERRA(ierr)
55:       call MPI_Comm_size(PETSC_COMM_WORLD,mySize,ierr)
56:       CHKERRA(ierr)
57:       n=m+2

59:       !-------------------------------------------------------------------
60:       ! Compute the matrix and right-hand-side vector that define
61:       ! the linear system, Ax = b.
62:       !---------------------------------------------------------------

64:       ! Create and assemble parallel matrix

66:       call  MatCreate(PETSC_COMM_WORLD,A,ierr)
67:       call  MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
68:       call  MatSetFromOptions(A,ierr)
69:       call  MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,five,PETSC_NULL_INTEGER,ierr)
70:       call  MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,ierr)
71:       call  MatGetOwnershipRange(A,Istart,Iend,ierr)

73:       do Ii=Istart,Iend-1
74:           v =-1.0; i = Ii/n; j = Ii - i*n
75:           if (i>0) then
76:             JJ = Ii - n
78:           endif

80:           if (i<m-1) then
81:             JJ = Ii + n
83:           endif

85:           if (j>0) then
86:             JJ = Ii - 1
88:           endif

90:           if (j<n-1) then
91:             JJ = Ii + 1
93:           endif

95:           v=4.0

98:         enddo

100:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
101:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)

103:       ! Create parallel vectors

105:       call  VecCreate(PETSC_COMM_WORLD,u,ierr)
106:       CHKERRA(ierr)
107:       call  VecSetSizes(u,PETSC_DECIDE,m*n,ierr)
108:       CHKERRA(ierr)
109:       call  VecSetFromOptions(u,ierr)
110:       CHKERRA(ierr)
111:       call  VecDuplicate(u,b,ierr)
112:       call  VecDuplicate(b,x,ierr)

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

116:       call Vecset(u,sone,ierr)
117:       CHKERRA(ierr)
118:       call MatMult(A,u,b,ierr)
119:       CHKERRA(ierr)

121:       ! Create linear solver context

123:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
124:       CHKERRA(ierr)

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

129:       call KSPSetOperators(ksp,A,A,ierr)
130:       CHKERRA(ierr)

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

136:       call KSPGetPC(ksp,myPc,ierr)
137:       CHKERRA(ierr)
138:       call PCSetType(myPc,PCBJACOBI,ierr)
139:       CHKERRA(ierr)

141:       ! -----------------------------------------------------------------
142:       !            Define the problem decomposition
143:       !-------------------------------------------------------------------

145:       ! Call PCBJacobiSetTotalBlocks() to set individually the size of
146:       ! each block in the preconditioner.  This could also be done with
147:       ! the runtime option -pc_bjacobi_blocks <blocks>
148:       ! Also, see the command PCBJacobiSetLocalBlocks() to set the
149:       ! local blocks.

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

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

155:       call PCBJacobiSetTotalBlocks(myPc,m,blks,ierr)
156:       CHKERRA(ierr)
157:       deallocate(blks)

159:       !-------------------------------------------------------------------
160:       !       Set the linear solvers for the subblocks
161:       !-------------------------------------------------------------------

163:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164:       ! Basic method, should be sufficient for the needs of most users.
165:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166:       ! By default, the block Jacobi method uses the same solver on each
167:       ! block of the problem.  To set the same solver options on all blocks,
168:       ! use the prefix -sub before the usual PC and KSP options, e.g.,
169:       ! -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4

171:       !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172:       !  Advanced method, setting different solvers for various blocks.
173:       !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

182:       call PetscObjectTypeCompare(myPc,PCBJACOBI,isbjacobi,ierr)

185:       if (isbjacobi) then

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

191:         call KSPSetUp(ksp,ierr)

193:         ! Extract the array of KSP contexts for the local blocks
194:         call PCBJacobiGetSubKSP(myPc,nlocal,first,PETSC_NULL_KSP,ierr)
195:         allocate(subksp(nlocal))
196:         call PCBJacobiGetSubKSP(myPc,nlocal,first,subksp,ierr)

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

201:         do i=0,nlocal-1

203:           call KSPGetPC(subksp(i+1),subpc,ierr)

205:           if (myRank>0) then

207:             if (mod(i,2)==1) then
208:               call PCSetType(subpc,PCILU,ierr); CHKERRA(ierr)

210:             else
211:               call PCSetType(subpc,PCNONE,ierr); CHKERRA(ierr)
212:               call KSPSetType(subksp(i+1),KSPBCGS,ierr); CHKERRA(ierr)
213:               call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
214:               CHKERRA(ierr)
215:             endif

217:           else
218:             call PCSetType(subpc,PCJACOBI,ierr); CHKERRA(ierr)
219:             call KSPSetType(subksp(i+1),KSPGMRES,ierr); CHKERRA(ierr)
220:             call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
221:             CHKERRA(ierr)
222:           endif

224:         end do

226:       endif

228:       !----------------------------------------------------------------
229:       !                Solve the linear system
230:       !-----------------------------------------------------------------

232:       ! Set runtime options

234:       call KSPSetFromOptions(ksp,ierr); CHKERRA(ierr)

236:       ! Solve the linear system

238:       call KSPSolve(ksp,b,x,ierr); CHKERRA(ierr)

240:       !  -----------------------------------------------------------------
241:       !               Check solution and clean up
242:       !-------------------------------------------------------------------

245:       !  -----------------------------------------------------------------
246:       ! Check the error
247:       !  -----------------------------------------------------------------

249:       !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)

251:       call VecAXPY(x,myNone,u,ierr)

253:       !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)

256:       call VecNorm(x,NORM_2,norm,ierr); CHKERRA(ierr)
257:       call KSPGetIterationNumber(ksp,its,ierr); CHKERRA(ierr)
258:       write(outputString,*)'Norm of error',real(norm),'Iterations',its,'\n'         ! PETScScalar might be of complex type
259:       call PetscPrintf(PETSC_COMM_WORLD,outputString,ierr); CHKERRA(ierr)

261:       ! Free work space.  All PETSc objects should be destroyed when they
262:       ! are no longer needed.
263:       deallocate(subksp)
264:       call KSPDestroy(ksp,ierr);CHKERRA(ierr)
265:       call VecDestroy(u,ierr); CHKERRA(ierr)
266:       call VecDestroy(b,ierr); CHKERRA(ierr)
267:       call MatDestroy(A,ierr); CHKERRA(ierr)
268:       call VecDestroy(x,ierr); CHKERRA(ierr)
269:       call PetscFinalize(ierr); CHKERRA(ierr)

271: end program main

273: !/*TEST
274: !
275: !   test:
276: !      nsize: 2
277: !      args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
278: !
279: !   test:
280: !      suffix: 2
281: !      nsize: 2
282: !      args: -ksp_view ::ascii_info_detail
283: !
284: !TEST*/
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