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, parameter :: m = 4
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: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
51: CHKERRA(ierr)
52: call MPI_Comm_rank(PETSC_COMM_WORLD,myRank,ierr)
53: CHKERRA(ierr)
54: call MPI_Comm_size(PETSC_COMM_WORLD,mySize,ierr)
55: CHKERRA(ierr)
56: n=m+2
58: !-------------------------------------------------------------------
59: ! Compute the matrix and right-hand-side vector that define
60: ! the linear system, Ax = b.
61: !---------------------------------------------------------------
63: ! Create and assemble parallel matrix
65: call MatCreate(PETSC_COMM_WORLD,A,ierr)
66: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
67: call MatSetFromOptions(A,ierr)
68: call MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,five,PETSC_NULL_INTEGER,ierr)
69: call MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,ierr)
70: call MatGetOwnershipRange(A,Istart,Iend,ierr)
72: do Ii=Istart,Iend-1
73: v =-1.0; i = Ii/n; j = Ii - i*n
74: if (i>0) then
75: JJ = Ii - n
76: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
77: endif
79: if (i<m-1) then
80: JJ = Ii + n
81: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
82: endif
84: if (j>0) then
85: JJ = Ii - 1
86: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
87: endif
89: if (j<n-1) then
90: JJ = Ii + 1
91: call MatSetValues(A,one,Ii,one,JJ,v,ADD_VALUES,ierr);CHKERRA(ierr)
92: endif
94: v=4.0
95: call MatSetValues(A,one,Ii,one,Ii,v,ADD_VALUES,ierr);CHKERRA(ierr)
97: enddo
99: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
100: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
102: ! Create parallel vectors
104: call VecCreate(PETSC_COMM_WORLD,u,ierr)
105: CHKERRA(ierr)
106: call VecSetSizes(u,PETSC_DECIDE,m*n,ierr)
107: CHKERRA(ierr)
108: call VecSetFromOptions(u,ierr)
109: CHKERRA(ierr)
110: call VecDuplicate(u,b,ierr)
111: call VecDuplicate(b,x,ierr)
113: ! Set exact solution; then compute right-hand-side vector.
115: call Vecset(u,sone,ierr)
116: CHKERRA(ierr)
117: call MatMult(A,u,b,ierr)
118: CHKERRA(ierr)
120: ! Create linear solver context
122: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
123: CHKERRA(ierr)
125: ! Set operators. Here the matrix that defines the linear system
126: ! also serves as the preconditioning matrix.
128: call KSPSetOperators(ksp,A,A,ierr)
129: CHKERRA(ierr)
131: ! Set default preconditioner for this program to be block Jacobi.
132: ! This choice can be overridden at runtime with the option
133: ! -pc_type <type>
135: call KSPGetPC(ksp,myPc,ierr)
136: CHKERRA(ierr)
137: call PCSetType(myPc,PCBJACOBI,ierr)
138: CHKERRA(ierr)
140: ! -----------------------------------------------------------------
141: ! Define the problem decomposition
142: !-------------------------------------------------------------------
144: ! Call PCBJacobiSetTotalBlocks() to set individually the size of
145: ! each block in the preconditioner. This could also be done with
146: ! the runtime option -pc_bjacobi_blocks <blocks>
147: ! Also, see the command PCBJacobiSetLocalBlocks() to set the
148: ! local blocks.
150: ! Note: The default decomposition is 1 block per processor.
152: allocate(blks(m),source = n)
154: call PCBJacobiSetTotalBlocks(myPc,m,blks,ierr)
155: CHKERRA(ierr)
156: deallocate(blks)
158: !-------------------------------------------------------------------
159: ! Set the linear solvers for the subblocks
160: !-------------------------------------------------------------------
162: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: ! Basic method, should be sufficient for the needs of most users.
164: !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: ! By default, the block Jacobi method uses the same solver on each
166: ! block of the problem. To set the same solver options on all blocks,
167: ! use the prefix -sub before the usual PC and KSP options, e.g.,
168: ! -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
170: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: ! Advanced method, setting different solvers for various blocks.
172: !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174: ! Note that each block's KSP context is completely independent of
175: ! the others, and the full range of uniprocessor KSP options is
176: ! available for each block. The following section of code is intended
177: ! to be a simple illustration of setting different linear solvers for
178: ! the individual blocks. These choices are obviously not recommended
179: ! for solving this particular problem.
181: call PetscObjectTypeCompare(myPc,PCBJACOBI,isbjacobi,ierr)
183: if (isbjacobi) then
185: ! Call KSPSetUp() to set the block Jacobi data structures (including
186: ! creation of an internal KSP context for each block).
187: ! Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP()
189: call KSPSetUp(ksp,ierr)
191: ! Extract the array of KSP contexts for the local blocks
192: call PCBJacobiGetSubKSP(myPc,nlocal,first,PETSC_NULL_KSP,ierr)
193: allocate(subksp(nlocal))
194: call PCBJacobiGetSubKSP(myPc,nlocal,first,subksp,ierr)
196: ! Loop over the local blocks, setting various KSP options for each block
198: do i=0,nlocal-1
200: call KSPGetPC(subksp(i+1),subpc,ierr)
202: if (myRank>0) then
204: if (mod(i,2)==1) then
205: call PCSetType(subpc,PCILU,ierr); CHKERRA(ierr)
207: else
208: call PCSetType(subpc,PCNONE,ierr); CHKERRA(ierr)
209: call KSPSetType(subksp(i+1),KSPBCGS,ierr); CHKERRA(ierr)
210: call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
211: CHKERRA(ierr)
212: endif
214: else
215: call PCSetType(subpc,PCJACOBI,ierr); CHKERRA(ierr)
216: call KSPSetType(subksp(i+1),KSPGMRES,ierr); CHKERRA(ierr)
217: call KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
218: CHKERRA(ierr)
219: endif
221: end do
223: endif
225: !----------------------------------------------------------------
226: ! Solve the linear system
227: !-----------------------------------------------------------------
229: ! Set runtime options
231: call KSPSetFromOptions(ksp,ierr); CHKERRA(ierr)
233: ! Solve the linear system
235: call KSPSolve(ksp,b,x,ierr); CHKERRA(ierr)
237: ! -----------------------------------------------------------------
238: ! Check solution and clean up
239: !-------------------------------------------------------------------
241: ! -----------------------------------------------------------------
242: ! Check the error
243: ! -----------------------------------------------------------------
245: !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
247: call VecAXPY(x,myNone,u,ierr)
249: !call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
251: call VecNorm(x,NORM_2,norm,ierr); CHKERRA(ierr)
252: call KSPGetIterationNumber(ksp,its,ierr); CHKERRA(ierr)
253: write(outputString,*)'Norm of error',real(norm),'Iterations',its,'\n' ! PETScScalar might be of complex type
254: call PetscPrintf(PETSC_COMM_WORLD,outputString,ierr); CHKERRA(ierr)
256: ! Free work space. All PETSc objects should be destroyed when they
257: ! are no longer needed.
258: deallocate(subksp)
259: call KSPDestroy(ksp,ierr);CHKERRA(ierr)
260: call VecDestroy(u,ierr); CHKERRA(ierr)
261: call VecDestroy(b,ierr); CHKERRA(ierr)
262: call MatDestroy(A,ierr); CHKERRA(ierr)
263: call VecDestroy(x,ierr); CHKERRA(ierr)
264: call PetscFinalize(ierr); CHKERRA(ierr)
266: end program main
268: !/*TEST
269: !
270: ! test:
271: ! nsize: 2
272: ! args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
273: !
274: ! test:
275: ! suffix: 2
276: ! nsize: 2
277: ! args: -ksp_view ::ascii_info_detail
278: !
279: !TEST*/