Actual source code: ex8.c
2: static char help[] = "Illustrates use of the preconditioner ASM.\n\
3: The Additive Schwarz Method for solving a linear system in parallel with KSP. The\n\
4: code indicates the procedure for setting user-defined subdomains. Input\n\
5: parameters include:\n\
6: -user_set_subdomain_solvers: User explicitly sets subdomain solvers\n\
7: -user_set_subdomains: Activate user-defined subdomains\n\n";
9: /*
10: Note: This example focuses on setting the subdomains for the ASM
11: preconditioner for a problem on a 2D rectangular grid. See ex1.c
12: and ex2.c for more detailed comments on the basic usage of KSP
13: (including working with matrices and vectors).
15: The ASM preconditioner is fully parallel, but currently the routine
16: PCASMCreateSubdomains2D(), which is used in this example to demonstrate
17: user-defined subdomains (activated via -user_set_subdomains), is
18: uniprocessor only.
20: This matrix in this linear system arises from the discretized Laplacian,
21: and thus is not very interesting in terms of experimenting with variants
22: of the ASM preconditioner.
23: */
25: /*
26: Include "petscksp.h" so that we can use KSP solvers. Note that this file
27: automatically includes:
28: petscsys.h - base PETSc routines petscvec.h - vectors
29: petscmat.h - matrices
30: petscis.h - index sets petscksp.h - Krylov subspace methods
31: petscviewer.h - viewers petscpc.h - preconditioners
32: */
33: #include <petscksp.h>
35: int main(int argc,char **args)
36: {
37: Vec x,b,u; /* approx solution, RHS, exact solution */
38: Mat A; /* linear system matrix */
39: KSP ksp; /* linear solver context */
40: PC pc; /* PC context */
41: IS *is,*is_local; /* array of index sets that define the subdomains */
42: PetscInt overlap = 1; /* width of subdomain overlap */
43: PetscInt Nsub; /* number of subdomains */
44: PetscInt m = 15,n = 17; /* mesh dimensions in x- and y- directions */
45: PetscInt M = 2,N = 1; /* number of subdomains in x- and y- directions */
46: PetscInt i,j,Ii,J,Istart,Iend;
47: PetscMPIInt size;
48: PetscBool flg;
49: PetscBool user_subdomains = PETSC_FALSE;
50: PetscScalar v, one = 1.0;
51: PetscReal e;
53: PetscInitialize(&argc,&args,(char*)0,help);
54: MPI_Comm_size(PETSC_COMM_WORLD,&size);
55: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
56: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
57: PetscOptionsGetInt(NULL,NULL,"-Mdomains",&M,NULL);
58: PetscOptionsGetInt(NULL,NULL,"-Ndomains",&N,NULL);
59: PetscOptionsGetInt(NULL,NULL,"-overlap",&overlap,NULL);
60: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomains",&user_subdomains,NULL);
62: /* -------------------------------------------------------------------
63: Compute the matrix and right-hand-side vector that define
64: the linear system, Ax = b.
65: ------------------------------------------------------------------- */
67: /*
68: Assemble the matrix for the five point stencil, YET AGAIN
69: */
70: MatCreate(PETSC_COMM_WORLD,&A);
71: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
72: MatSetFromOptions(A);
73: MatSetUp(A);
74: MatGetOwnershipRange(A,&Istart,&Iend);
75: for (Ii=Istart; Ii<Iend; Ii++) {
76: v = -1.0; i = Ii/n; j = Ii - i*n;
77: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
78: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
79: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
80: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
81: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
82: }
83: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
86: /*
87: Create and set vectors
88: */
89: MatCreateVecs(A,&u,&b);
90: VecDuplicate(u,&x);
91: VecSet(u,one);
92: MatMult(A,u,b);
94: /*
95: Create linear solver context
96: */
97: KSPCreate(PETSC_COMM_WORLD,&ksp);
99: /*
100: Set operators. Here the matrix that defines the linear system
101: also serves as the preconditioning matrix.
102: */
103: KSPSetOperators(ksp,A,A);
105: /*
106: Set the default preconditioner for this program to be ASM
107: */
108: KSPGetPC(ksp,&pc);
109: PCSetType(pc,PCASM);
111: /* -------------------------------------------------------------------
112: Define the problem decomposition
113: ------------------------------------------------------------------- */
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Basic method, should be sufficient for the needs of many users.
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Set the overlap, using the default PETSc decomposition via
120: PCASMSetOverlap(pc,overlap);
121: Could instead use the option -pc_asm_overlap <ovl>
123: Set the total number of blocks via -pc_asm_blocks <blks>
124: Note: The ASM default is to use 1 block per processor. To
125: experiment on a single processor with various overlaps, you
126: must specify use of multiple blocks!
127: */
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: More advanced method, setting user-defined subdomains
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Firstly, create index sets that define the subdomains. The utility
134: routine PCASMCreateSubdomains2D() is a simple example (that currently
135: supports 1 processor only!). More generally, the user should write
136: a custom routine for a particular problem geometry.
138: Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
139: to set the subdomains for the ASM preconditioner.
140: */
142: if (!user_subdomains) { /* basic version */
143: PCASMSetOverlap(pc,overlap);
144: } else { /* advanced version */
146: PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
147: PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
148: flg = PETSC_FALSE;
149: PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
150: if (flg) {
151: PetscPrintf(PETSC_COMM_SELF,"Nmesh points: %D x %D; subdomain partition: %D x %D; overlap: %D; Nsub: %D\n",m,n,M,N,overlap,Nsub);
152: PetscPrintf(PETSC_COMM_SELF,"IS:\n");
153: for (i=0; i<Nsub; i++) {
154: PetscPrintf(PETSC_COMM_SELF," IS[%D]\n",i);
155: ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
156: }
157: PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
158: for (i=0; i<Nsub; i++) {
159: PetscPrintf(PETSC_COMM_SELF," IS_local[%D]\n",i);
160: ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
161: }
162: }
163: }
165: /* -------------------------------------------------------------------
166: Set the linear solvers for the subblocks
167: ------------------------------------------------------------------- */
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Basic method, should be sufficient for the needs of most users.
171: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173: By default, the ASM preconditioner uses the same solver on each
174: block of the problem. To set the same solver options on all blocks,
175: use the prefix -sub before the usual PC and KSP options, e.g.,
176: -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Advanced method, setting different solvers for various blocks.
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: Note that each block's KSP context is completely independent of
183: the others, and the full range of uniprocessor KSP options is
184: available for each block.
186: - Use PCASMGetSubKSP() to extract the array of KSP contexts for
187: the local blocks.
188: - See ex7.c for a simple example of setting different linear solvers
189: for the individual blocks for the block Jacobi method (which is
190: equivalent to the ASM method with zero overlap).
191: */
193: flg = PETSC_FALSE;
194: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
195: if (flg) {
196: KSP *subksp; /* array of KSP contexts for local subblocks */
197: PetscInt nlocal,first; /* number of local subblocks, first local subblock */
198: PC subpc; /* PC context for subblock */
199: PetscBool isasm;
201: PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");
203: /*
204: Set runtime options
205: */
206: KSPSetFromOptions(ksp);
208: /*
209: Flag an error if PCTYPE is changed from the runtime options
210: */
211: PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
214: /*
215: Call KSPSetUp() to set the block Jacobi data structures (including
216: creation of an internal KSP context for each block).
218: Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
219: */
220: KSPSetUp(ksp);
222: /*
223: Extract the array of KSP contexts for the local blocks
224: */
225: PCASMGetSubKSP(pc,&nlocal,&first,&subksp);
227: /*
228: Loop over the local blocks, setting various KSP options
229: for each block.
230: */
231: for (i=0; i<nlocal; i++) {
232: KSPGetPC(subksp[i],&subpc);
233: PCSetType(subpc,PCILU);
234: KSPSetType(subksp[i],KSPGMRES);
235: KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
236: }
237: } else {
238: /*
239: Set runtime options
240: */
241: KSPSetFromOptions(ksp);
242: }
244: /* -------------------------------------------------------------------
245: Solve the linear system
246: ------------------------------------------------------------------- */
248: KSPSolve(ksp,b,x);
250: /* -------------------------------------------------------------------
251: Compare result to the exact solution
252: ------------------------------------------------------------------- */
253: VecAXPY(x,-1.0,u);
254: VecNorm(x,NORM_INFINITY, &e);
256: flg = PETSC_FALSE;
257: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
258: if (flg) {
259: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
260: }
262: /*
263: Free work space. All PETSc objects should be destroyed when they
264: are no longer needed.
265: */
267: if (user_subdomains) {
268: for (i=0; i<Nsub; i++) {
269: ISDestroy(&is[i]);
270: ISDestroy(&is_local[i]);
271: }
272: PetscFree(is);
273: PetscFree(is_local);
274: }
275: KSPDestroy(&ksp);
276: VecDestroy(&u);
277: VecDestroy(&x);
278: VecDestroy(&b);
279: MatDestroy(&A);
280: PetscFinalize();
281: return 0;
282: }
284: /*TEST
286: test:
287: suffix: 1
288: args: -print_error
290: TEST*/