Actual source code: ex7.c
1: /*$Id: ex7.c,v 1.56 2001/04/10 19:36:40 bsmith Exp $*/
3: static char help[] = "Block Jacobi preconditioner for solving a linear system in parallel with SLES.n
4: The code indicates then
5: procedures for setting the particular block sizes and for using differentn
6: linear solvers on the individual blocks.nn";
8: /*
9: Note: This example focuses on ways to customize the block Jacobi
10: preconditioner. See ex1.c and ex2.c for more detailed comments on
11: the basic usage of SLES (including working with matrices and vectors).
13: Recall: The block Jacobi method is equivalent to the ASM preconditioner
14: with zero overlap.
15: */
17: /*T
18: Concepts: SLES^customizing the block Jacobi preconditioner
19: Processors: n
20: T*/
22: /*
23: Include "petscsles.h" so that we can use SLES solvers. Note that this file
24: automatically includes:
25: petsc.h - base PETSc routines petscvec.h - vectors
26: petscsys.h - system routines petscmat.h - matrices
27: petscis.h - index sets petscksp.h - Krylov subspace methods
28: petscviewer.h - viewers petscpc.h - preconditioners
29: */
30: #include "petscsles.h"
32: int main(int argc,char **args)
33: {
34: Vec x,b,u; /* approx solution, RHS, exact solution */
35: Mat A; /* linear system matrix */
36: SLES sles; /* SLES context */
37: SLES *subsles; /* array of local SLES contexts on this processor */
38: PC pc; /* PC context */
39: PC subpc; /* PC context for subdomain */
40: KSP subksp; /* KSP context for subdomain */
41: double norm; /* norm of solution error */
42: int i,j,I,J,ierr,*blks,m = 8,n;
43: int rank,size,its,nlocal,first,Istart,Iend;
44: Scalar v,one = 1.0,none = -1.0;
45: PetscTruth isbjacobi,flg;
47: PetscInitialize(&argc,&args,(char *)0,help);
48: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
49: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
50: MPI_Comm_size(PETSC_COMM_WORLD,&size);
51: n = m+2;
53: /* -------------------------------------------------------------------
54: Compute the matrix and right-hand-side vector that define
55: the linear system, Ax = b.
56: ------------------------------------------------------------------- */
58: /*
59: Create and assemble parallel matrix
60: */
61: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
62: MatSetFromOptions(A);
63: MatGetOwnershipRange(A,&Istart,&Iend);
64: for (I=Istart; I<Iend; I++) {
65: v = -1.0; i = I/n; j = I - i*n;
66: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
67: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
68: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
69: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
70: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,ADD_VALUES);
71: }
72: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
73: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
75: /*
76: Create parallel vectors
77: */
78: VecCreate(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,&u);
79: VecSetFromOptions(u);
80: VecDuplicate(u,&b);
81: VecDuplicate(b,&x);
83: /*
84: Set exact solution; then compute right-hand-side vector.
85: */
86: VecSet(&one,u);
87: MatMult(A,u,b);
89: /*
90: Create linear solver context
91: */
92: SLESCreate(PETSC_COMM_WORLD,&sles);
94: /*
95: Set operators. Here the matrix that defines the linear system
96: also serves as the preconditioning matrix.
97: */
98: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
100: /*
101: Set default preconditioner for this program to be block Jacobi.
102: This choice can be overridden at runtime with the option
103: -pc_type <type>
104: */
105: SLESGetPC(sles,&pc);
106: PCSetType(pc,PCBJACOBI);
109: /* -------------------------------------------------------------------
110: Define the problem decomposition
111: ------------------------------------------------------------------- */
113: /*
114: Call PCBJacobiSetTotalBlocks() to set individually the size of
115: each block in the preconditioner. This could also be done with
116: the runtime option
117: -pc_bjacobi_blocks <blocks>
118: Also, see the command PCBJacobiSetLocalBlocks() to set the
119: local blocks.
121: Note: The default decomposition is 1 block per processor.
122: */
123: PetscMalloc(m*sizeof(int),&blks);
124: for (i=0; i<m; i++) blks[i] = n;
125: PCBJacobiSetTotalBlocks(pc,m,blks);
126: PetscFree(blks);
129: /* -------------------------------------------------------------------
130: Set the linear solvers for the subblocks
131: ------------------------------------------------------------------- */
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Basic method, should be sufficient for the needs of most users.
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: By default, the block Jacobi method uses the same solver on each
138: block of the problem. To set the same solver options on all blocks,
139: use the prefix -sub before the usual PC and KSP options, e.g.,
140: -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
141: */
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Advanced method, setting different solvers for various blocks.
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Note that each block's SLES context is completely independent of
148: the others, and the full range of uniprocessor SLES options is
149: available for each block. The following section of code is intended
150: to be a simple illustration of setting different linear solvers for
151: the individual blocks. These choices are obviously not recommended
152: for solving this particular problem.
153: */
154: PetscTypeCompare((PetscObject)pc,PCBJACOBI,&isbjacobi);
155: if (isbjacobi) {
156: /*
157: Call SLESSetUp() to set the block Jacobi data structures (including
158: creation of an internal SLES context for each block).
160: Note: SLESSetUp() MUST be called before PCBJacobiGetSubSLES().
161: */
162: SLESSetUp(sles,x,b);
164: /*
165: Extract the array of SLES contexts for the local blocks
166: */
167: PCBJacobiGetSubSLES(pc,&nlocal,&first,&subsles);
169: /*
170: Loop over the local blocks, setting various SLES options
171: for each block.
172: */
173: for (i=0; i<nlocal; i++) {
174: SLESGetPC(subsles[i],&subpc);
175: SLESGetKSP(subsles[i],&subksp);
176: if (!rank) {
177: if (i%2) {
178: PCSetType(subpc,PCILU);
179: } else {
180: PCSetType(subpc,PCNONE);
181: KSPSetType(subksp,KSPBCGS);
182: KSPSetTolerances(subksp,1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
183: }
184: } else {
185: PCSetType(subpc,PCJACOBI);
186: KSPSetType(subksp,KSPGMRES);
187: KSPSetTolerances(subksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
188: }
189: }
190: }
192: /* -------------------------------------------------------------------
193: Solve the linear system
194: ------------------------------------------------------------------- */
196: /*
197: Set runtime options
198: */
199: SLESSetFromOptions(sles);
201: /*
202: Solve the linear system
203: */
204: SLESSolve(sles,b,x,&its);
206: /*
207: View info about the solver
208: */
209: PetscOptionsHasName(PETSC_NULL,"-noslesview",&flg);
210: if (!flg) {
211: SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
212: }
214: /* -------------------------------------------------------------------
215: Check solution and clean up
216: ------------------------------------------------------------------- */
218: /*
219: Check the error
220: */
221: VecAXPY(&none,u,x);
222: VecNorm(x,NORM_2,&norm);
223: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %dn",norm,its);
225: /*
226: Free work space. All PETSc objects should be destroyed when they
227: are no longer needed.
228: */
229: SLESDestroy(sles);
230: VecDestroy(u); VecDestroy(x);
231: VecDestroy(b); MatDestroy(A);
232: PetscFinalize();
233: return 0;
234: }