Actual source code: ex7f.F90
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*/
17: program main
18: #include <petsc/finclude/petscksp.h>
19: use petscksp
21: implicit none
22: Vec :: x,b,u ! approx solution, RHS, exact solution
23: Mat :: A ! linear system matrix
24: KSP :: ksp ! KSP context
25: PC :: myPc ! PC context
26: PC :: subpc ! PC context for subdomain
27: PetscReal :: norm ! norm of solution error
28: PetscReal,parameter :: tol = 1.e-6
29: PetscErrorCode :: ierr
30: PetscInt :: i,j,Ii,JJ,n
31: PetscInt :: m
32: PetscMPIInt :: myRank,mySize
33: PetscInt :: its,nlocal,first,Istart,Iend
34: PetscScalar :: v
35: PetscScalar, parameter :: &
36: myNone = -1.0, &
37: sone = 1.0
38: PetscBool :: isbjacobi,flg
39: KSP,allocatable,dimension(:) :: subksp ! array of local KSP contexts on this processor
40: PetscInt,allocatable,dimension(:) :: blks
41: character(len=PETSC_MAX_PATH_LEN) :: outputString
42: PetscInt,parameter :: one = 1, five = 5
44: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
45: if (ierr /= 0) then
46: write(6,*)'Unable to initialize PETSc'
47: stop
48: endif
50: m = 4
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
77: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
78: endif
80: if (i<m-1) then
81: JJ = Ii + n
82: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
83: endif
85: if (j>0) then
86: JJ = Ii - 1
87: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
88: endif
90: if (j<n-1) then
91: JJ = Ii + 1
92: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
93: endif
95: v=4.0
96: call MatSetValues(A,one,Ii,one,Ii,v,ADD_VALUES,ierr);CHKERRA(ierr)
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)
184: if (isbjacobi) then
186: ! Call KSPSetUp() to set the block Jacobi data structures (including
187: ! creation of an internal KSP context for each block).
188: ! Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP()
190: call KSPSetUp(ksp,ierr)
192: ! Extract the array of KSP contexts for the local blocks
193: call PCBJacobiGetSubKSP(myPc,nlocal,first,PETSC_NULL_KSP,ierr)
194: allocate(subksp(nlocal))
195: call PCBJacobiGetSubKSP(myPc,nlocal,first,subksp,ierr)
197: ! Loop over the local blocks, setting various KSP options for each block
199: do i=0,nlocal-1
201: call KSPGetPC(subksp(i+1),subpc,ierr)
203: if (myRank>0) then
205: if (mod(i,2)==1) then
206: call PCSetType(subpc,PCILU,ierr); CHKERRA(ierr)
208: else
209: call PCSetType(subpc,PCNONE,ierr); CHKERRA(ierr)
210: call KSPSetType(subksp(i+1),KSPBCGS,ierr); CHKERRA(ierr)
211: call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
212: CHKERRA(ierr)
213: endif
215: else
216: call PCSetType(subpc,PCJACOBI,ierr); CHKERRA(ierr)
217: call KSPSetType(subksp(i+1),KSPGMRES,ierr); CHKERRA(ierr)
218: call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
219: CHKERRA(ierr)
220: endif
222: end do
224: endif
226: !----------------------------------------------------------------
227: ! Solve the linear system
228: !-----------------------------------------------------------------
230: ! Set runtime options
232: call KSPSetFromOptions(ksp,ierr); CHKERRA(ierr)
234: ! Solve the linear system
236: call KSPSolve(ksp,b,x,ierr); CHKERRA(ierr)
238: ! -----------------------------------------------------------------
239: ! Check solution and clean up
240: !-------------------------------------------------------------------
242: ! -----------------------------------------------------------------
243: ! Check the error
244: ! -----------------------------------------------------------------
246: !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
248: call VecAXPY(x,myNone,u,ierr)
250: !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
252: call VecNorm(x,NORM_2,norm,ierr); CHKERRA(ierr)
253: call KSPGetIterationNumber(ksp,its,ierr); CHKERRA(ierr)
254: write(outputString,*)'Norm of error',real(norm),'Iterations',its,'\n' ! PETScScalar might be of complex type
255: call PetscPrintf(PETSC_COMM_WORLD,outputString,ierr); CHKERRA(ierr)
257: ! Free work space. All PETSc objects should be destroyed when they
258: ! are no longer needed.
259: deallocate(subksp)
260: call KSPDestroy(ksp,ierr);CHKERRA(ierr)
261: call VecDestroy(u,ierr); CHKERRA(ierr)
262: call VecDestroy(b,ierr); CHKERRA(ierr)
263: call MatDestroy(A,ierr); CHKERRA(ierr)
264: call VecDestroy(x,ierr); CHKERRA(ierr)
265: call PetscFinalize(ierr); CHKERRA(ierr)
267: end program main
269: !/*TEST
270: !
271: ! test:
272: ! nsize: 2
273: ! args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
274: !
275: ! test:
276: ! suffix: 2
277: ! nsize: 2
278: ! args: -ksp_view ::ascii_info_detail
279: !
280: !TEST*/