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: /*T
26: Concepts: KSP^Additive Schwarz Method (ASM) with user-defined subdomains
27: Processors: n
28: T*/
30: /*
31: Include "petscksp.h" so that we can use KSP solvers. Note that this file
32: automatically includes:
33: petscsys.h - base PETSc routines petscvec.h - vectors
34: petscmat.h - matrices
35: petscis.h - index sets petscksp.h - Krylov subspace methods
36: petscviewer.h - viewers petscpc.h - preconditioners
37: */
38: #include <petscksp.h>
40: int main(int argc,char **args)
41: {
42: Vec x,b,u; /* approx solution, RHS, exact solution */
43: Mat A; /* linear system matrix */
44: KSP ksp; /* linear solver context */
45: PC pc; /* PC context */
46: IS *is,*is_local; /* array of index sets that define the subdomains */
47: PetscInt overlap = 1; /* width of subdomain overlap */
48: PetscInt Nsub; /* number of subdomains */
49: PetscInt m = 15,n = 17; /* mesh dimensions in x- and y- directions */
50: PetscInt M = 2,N = 1; /* number of subdomains in x- and y- directions */
51: PetscInt i,j,Ii,J,Istart,Iend;
53: PetscMPIInt size;
54: PetscBool flg;
55: PetscBool user_subdomains = PETSC_FALSE;
56: PetscScalar v, one = 1.0;
57: PetscReal e;
59: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
60: MPI_Comm_size(PETSC_COMM_WORLD,&size);
61: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
62: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
63: PetscOptionsGetInt(NULL,NULL,"-Mdomains",&M,NULL);
64: PetscOptionsGetInt(NULL,NULL,"-Ndomains",&N,NULL);
65: PetscOptionsGetInt(NULL,NULL,"-overlap",&overlap,NULL);
66: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomains",&user_subdomains,NULL);
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,&A);
77: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
78: MatSetFromOptions(A);
79: MatSetUp(A);
80: MatGetOwnershipRange(A,&Istart,&Iend);
81: for (Ii=Istart; Ii<Iend; Ii++) {
82: v = -1.0; i = Ii/n; j = Ii - i*n;
83: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
84: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
85: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
86: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
87: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
88: }
89: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
92: /*
93: Create and set vectors
94: */
95: MatCreateVecs(A,&u,&b);
96: VecDuplicate(u,&x);
97: VecSet(u,one);
98: MatMult(A,u,b);
100: /*
101: Create linear solver context
102: */
103: KSPCreate(PETSC_COMM_WORLD,&ksp);
105: /*
106: Set operators. Here the matrix that defines the linear system
107: also serves as the preconditioning matrix.
108: */
109: KSPSetOperators(ksp,A,A);
111: /*
112: Set the default preconditioner for this program to be ASM
113: */
114: KSPGetPC(ksp,&pc);
115: PCSetType(pc,PCASM);
117: /* -------------------------------------------------------------------
118: Define the problem decomposition
119: ------------------------------------------------------------------- */
121: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122: Basic method, should be sufficient for the needs of many users.
123: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Set the overlap, using the default PETSc decomposition via
126: PCASMSetOverlap(pc,overlap);
127: Could instead use the option -pc_asm_overlap <ovl>
129: Set the total number of blocks via -pc_asm_blocks <blks>
130: Note: The ASM default is to use 1 block per processor. To
131: experiment on a single processor with various overlaps, you
132: must specify use of multiple blocks!
133: */
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: More advanced method, setting user-defined subdomains
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Firstly, create index sets that define the subdomains. The utility
140: routine PCASMCreateSubdomains2D() is a simple example (that currently
141: supports 1 processor only!). More generally, the user should write
142: a custom routine for a particular problem geometry.
144: Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
145: to set the subdomains for the ASM preconditioner.
146: */
148: if (!user_subdomains) { /* basic version */
149: PCASMSetOverlap(pc,overlap);
150: } else { /* advanced version */
151: if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PCASMCreateSubdomains2D() is currently a uniprocessor routine only!");
152: PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
153: PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
154: flg = PETSC_FALSE;
155: PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
156: if (flg) {
157: 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);
158: PetscPrintf(PETSC_COMM_SELF,"IS:\n");
159: for (i=0; i<Nsub; i++) {
160: PetscPrintf(PETSC_COMM_SELF," IS[%D]\n",i);
161: ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
162: }
163: PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
164: for (i=0; i<Nsub; i++) {
165: PetscPrintf(PETSC_COMM_SELF," IS_local[%D]\n",i);
166: ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
167: }
168: }
169: }
171: /* -------------------------------------------------------------------
172: Set the linear solvers for the subblocks
173: ------------------------------------------------------------------- */
175: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: Basic method, should be sufficient for the needs of most users.
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: By default, the ASM preconditioner uses the same solver on each
180: block of the problem. To set the same solver options on all blocks,
181: use the prefix -sub before the usual PC and KSP options, e.g.,
182: -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
184: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Advanced method, setting different solvers for various blocks.
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: Note that each block's KSP context is completely independent of
189: the others, and the full range of uniprocessor KSP options is
190: available for each block.
192: - Use PCASMGetSubKSP() to extract the array of KSP contexts for
193: the local blocks.
194: - See ex7.c for a simple example of setting different linear solvers
195: for the individual blocks for the block Jacobi method (which is
196: equivalent to the ASM method with zero overlap).
197: */
199: flg = PETSC_FALSE;
200: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
201: if (flg) {
202: KSP *subksp; /* array of KSP contexts for local subblocks */
203: PetscInt nlocal,first; /* number of local subblocks, first local subblock */
204: PC subpc; /* PC context for subblock */
205: PetscBool isasm;
207: PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");
209: /*
210: Set runtime options
211: */
212: KSPSetFromOptions(ksp);
214: /*
215: Flag an error if PCTYPE is changed from the runtime options
216: */
217: PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
218: if (!isasm) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");
220: /*
221: Call KSPSetUp() to set the block Jacobi data structures (including
222: creation of an internal KSP context for each block).
224: Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
225: */
226: KSPSetUp(ksp);
228: /*
229: Extract the array of KSP contexts for the local blocks
230: */
231: PCASMGetSubKSP(pc,&nlocal,&first,&subksp);
233: /*
234: Loop over the local blocks, setting various KSP options
235: for each block.
236: */
237: for (i=0; i<nlocal; i++) {
238: KSPGetPC(subksp[i],&subpc);
239: PCSetType(subpc,PCILU);
240: KSPSetType(subksp[i],KSPGMRES);
241: KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
242: }
243: } else {
244: /*
245: Set runtime options
246: */
247: KSPSetFromOptions(ksp);
248: }
250: /* -------------------------------------------------------------------
251: Solve the linear system
252: ------------------------------------------------------------------- */
254: KSPSolve(ksp,b,x);
256: /* -------------------------------------------------------------------
257: Compare result to the exact solution
258: ------------------------------------------------------------------- */
259: VecAXPY(x,-1.0,u);
260: VecNorm(x,NORM_INFINITY, &e);
262: flg = PETSC_FALSE;
263: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
264: if (flg) {
265: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
266: }
268: /*
269: Free work space. All PETSc objects should be destroyed when they
270: are no longer needed.
271: */
273: if (user_subdomains) {
274: for (i=0; i<Nsub; i++) {
275: ISDestroy(&is[i]);
276: ISDestroy(&is_local[i]);
277: }
278: PetscFree(is);
279: PetscFree(is_local);
280: }
281: KSPDestroy(&ksp);
282: VecDestroy(&u);
283: VecDestroy(&x);
284: VecDestroy(&b);
285: MatDestroy(&A);
286: PetscFinalize();
287: return ierr;
288: }
290: /*TEST
292: test:
293: suffix: 1
294: args: -print_error
296: TEST*/