Actual source code: ex8.c
1: /*$Id: ex8.c,v 1.50 2001/08/07 03:04:00 balay Exp $*/
3: static char help[] = "Illustrates use of the preconditioner ASM.n
4: The Additive Schwarz Method for solving a linear system in parallel with SLES. Then
5: code indicates the procedure for setting user-defined subdomains. Inputn
6: parameters include:n
7: -user_set_subdomain_solvers: User explicitly sets subdomain solversn
8: -user_set_subdomains: Activate user-defined subdomainsnn";
10: /*
11: Note: This example focuses on setting the subdomains for the ASM
12: preconditioner for a problem on a 2D rectangular grid. See ex1.c
13: and ex2.c for more detailed comments on the basic usage of SLES
14: (including working with matrices and vectors).
16: The ASM preconditioner is fully parallel, but currently the routine
17: PCASMCreateSubDomains2D(), which is used in this example to demonstrate
18: user-defined subdomains (activated via -user_set_subdomains), is
19: uniprocessor only.
21: This matrix in this linear system arises from the discretized Laplacian,
22: and thus is not very interesting in terms of experimenting with variants
23: of the ASM preconditioner.
24: */
26: /*T
27: Concepts: SLES^Additive Schwarz Method (ASM) with user-defined subdomains
28: Processors: n
29: T*/
31: /*
32: Include "petscsles.h" so that we can use SLES solvers. Note that this file
33: automatically includes:
34: petsc.h - base PETSc routines petscvec.h - vectors
35: petscsys.h - system routines petscmat.h - matrices
36: petscis.h - index sets petscksp.h - Krylov subspace methods
37: petscviewer.h - viewers petscpc.h - preconditioners
38: */
39: #include petscsles.h
41: #undef __FUNCT__
43: int main(int argc,char **args)
44: {
45: Vec x,b,u; /* approx solution, RHS, exact solution */
46: Mat A; /* linear system matrix */
47: SLES sles; /* linear solver context */
48: PC pc; /* PC context */
49: IS *is; /* array of index sets that define the subdomains */
50: int overlap = 1; /* width of subdomain overlap */
51: int Nsub; /* number of subdomains */
52: int m = 15,n = 17; /* mesh dimensions in x- and y- directions */
53: int M = 2,N = 1; /* number of subdomains in x- and y- directions */
54: int i,j,its,I,J,ierr,Istart,Iend,size;
55: PetscTruth flg;
56: PetscTruth user_subdomains; /* flag - 1 indicates user-defined subdomains */
57: PetscScalar v, one = 1.0;
59: PetscInitialize(&argc,&args,(char *)0,help);
60: MPI_Comm_size(PETSC_COMM_WORLD,&size);
61: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
62: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
63: PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);
64: PetscOptionsGetInt(PETSC_NULL,"-N",&N,PETSC_NULL);
65: PetscOptionsGetInt(PETSC_NULL,"-overlap",&overlap,PETSC_NULL);
66: PetscOptionsHasName(PETSC_NULL,"-user_set_subdomains",&user_subdomains);
68: /* -------------------------------------------------------------------
69: Compute the matrix and right-hand-side vector that define
70: the linear system, Ax = b.
71: ------------------------------------------------------------------- */
73: /*
74: Assemble the matrix for the five point stencil, YET AGAIN
75: */
76: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
77: MatSetFromOptions(A);
78: MatGetOwnershipRange(A,&Istart,&Iend);
79: for (I=Istart; I<Iend; I++) {
80: v = -1.0; i = I/n; j = I - i*n;
81: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
82: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
83: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
84: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
85: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
86: }
87: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
88: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
90: /*
91: Create and set vectors
92: */
93: VecCreate(PETSC_COMM_WORLD,&b);
94: VecSetSizes(b,PETSC_DECIDE,m*n);
95: VecSetFromOptions(b);
96: VecDuplicate(b,&u);
97: VecDuplicate(b,&x);
98: VecSet(&one,u);
99: MatMult(A,u,b);
101: /*
102: Create linear solver context
103: */
104: SLESCreate(PETSC_COMM_WORLD,&sles);
106: /*
107: Set operators. Here the matrix that defines the linear system
108: also serves as the preconditioning matrix.
109: */
110: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
112: /*
113: Set the default preconditioner for this program to be ASM
114: */
115: SLESGetPC(sles,&pc);
116: PCSetType(pc,PCASM);
118: /* -------------------------------------------------------------------
119: Define the problem decomposition
120: ------------------------------------------------------------------- */
122: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123: Basic method, should be sufficient for the needs of many users.
124: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Set the overlap, using the default PETSc decomposition via
127: PCASMSetOverlap(pc,overlap);
128: Could instead use the option -pc_asm_overlap <ovl>
130: Set the total number of blocks via -pc_asm_blocks <blks>
131: Note: The ASM default is to use 1 block per processor. To
132: experiment on a single processor with various overlaps, you
133: must specify use of multiple blocks!
134: */
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: More advanced method, setting user-defined subdomains
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Firstly, create index sets that define the subdomains. The utility
141: routine PCASMCreateSubdomains2D() is a simple example (that currently
142: supports 1 processor only!). More generally, the user should write
143: a custom routine for a particular problem geometry.
145: Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
146: to set the subdomains for the ASM preconditioner.
147: */
149: if (!user_subdomains) { /* basic version */
150: PCASMSetOverlap(pc,overlap);
151: } else { /* advanced version */
152: if (size != 1) SETERRQ(1,"PCASMCreateSubdomains() is currently a uniprocessor routine only!");
153: PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is);
154: PCASMSetLocalSubdomains(pc,Nsub,is);
155: }
157: /* -------------------------------------------------------------------
158: Set the linear solvers for the subblocks
159: ------------------------------------------------------------------- */
161: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: Basic method, should be sufficient for the needs of most users.
163: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: By default, the ASM preconditioner 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 SLES context is completely independent of
175: the others, and the full range of uniprocessor SLES options is
176: available for each block.
178: - Use PCASMGetSubSLES() to extract the array of SLES contexts for
179: the local blocks.
180: - See ex7.c for a simple example of setting different linear solvers
181: for the individual blocks for the block Jacobi method (which is
182: equivalent to the ASM method with zero overlap).
183: */
185: PetscOptionsHasName(PETSC_NULL,"-user_set_subdomain_solvers",&flg);
186: if (flg) {
187: SLES *subsles; /* array of SLES contexts for local subblocks */
188: int nlocal,first; /* number of local subblocks, first local subblock */
189: KSP subksp; /* KSP context for subblock */
190: PC subpc; /* PC context for subblock */
191: PetscTruth isasm;
193: PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.n");
195: /*
196: Set runtime options
197: */
198: SLESSetFromOptions(sles);
200: /*
201: Flag an error if PCTYPE is changed from the runtime options
202: */
203: PetscTypeCompare((PetscObject)pc,PCASM,&isasm);
204: if (isasm) {
205: SETERRQ(1,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");
206: }
207: /*
208: Call SLESSetUp() to set the block Jacobi data structures (including
209: creation of an internal SLES context for each block).
211: Note: SLESSetUp() MUST be called before PCASMGetSubSLES().
212: */
213: SLESSetUp(sles,b,x);
215: /*
216: Extract the array of SLES contexts for the local blocks
217: */
218: PCASMGetSubSLES(pc,&nlocal,&first,&subsles);
220: /*
221: Loop over the local blocks, setting various SLES options
222: for each block.
223: */
224: for (i=0; i<nlocal; i++) {
225: SLESGetPC(subsles[i],&subpc);
226: SLESGetKSP(subsles[i],&subksp);
227: PCSetType(subpc,PCILU);
228: KSPSetType(subksp,KSPGMRES);
229: KSPSetTolerances(subksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
230: }
231: } else {
232: /*
233: Set runtime options
234: */
235: SLESSetFromOptions(sles);
236: }
238: /* -------------------------------------------------------------------
239: Solve the linear system
240: ------------------------------------------------------------------- */
242: SLESSolve(sles,b,x,&its);
244: /*
245: Free work space. All PETSc objects should be destroyed when they
246: are no longer needed.
247: */
249: if (user_subdomains) {
250: for (i=0; i<Nsub; i++) {
251: ISDestroy(is[i]);
252: }
253: PetscFree(is);
254: }
255: SLESDestroy(sles);
256: VecDestroy(u);
257: VecDestroy(x);
258: VecDestroy(b);
259: MatDestroy(A);
260: PetscFinalize();
261: return 0;
262: }