Actual source code: ex8.c
petsc-3.8.4 2018-03-24
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: VecCreate(PETSC_COMM_WORLD,&b);
96: VecSetSizes(b,PETSC_DECIDE,m*n);
97: VecSetFromOptions(b);
98: VecDuplicate(b,&u);
99: VecDuplicate(b,&x);
100: VecSet(u,one);
101: MatMult(A,u,b);
103: /*
104: Create linear solver context
105: */
106: KSPCreate(PETSC_COMM_WORLD,&ksp);
108: /*
109: Set operators. Here the matrix that defines the linear system
110: also serves as the preconditioning matrix.
111: */
112: KSPSetOperators(ksp,A,A);
114: /*
115: Set the default preconditioner for this program to be ASM
116: */
117: KSPGetPC(ksp,&pc);
118: PCSetType(pc,PCASM);
120: /* -------------------------------------------------------------------
121: Define the problem decomposition
122: ------------------------------------------------------------------- */
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Basic method, should be sufficient for the needs of many users.
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Set the overlap, using the default PETSc decomposition via
129: PCASMSetOverlap(pc,overlap);
130: Could instead use the option -pc_asm_overlap <ovl>
132: Set the total number of blocks via -pc_asm_blocks <blks>
133: Note: The ASM default is to use 1 block per processor. To
134: experiment on a single processor with various overlaps, you
135: must specify use of multiple blocks!
136: */
138: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: More advanced method, setting user-defined subdomains
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Firstly, create index sets that define the subdomains. The utility
143: routine PCASMCreateSubdomains2D() is a simple example (that currently
144: supports 1 processor only!). More generally, the user should write
145: a custom routine for a particular problem geometry.
147: Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
148: to set the subdomains for the ASM preconditioner.
149: */
151: if (!user_subdomains) { /* basic version */
152: PCASMSetOverlap(pc,overlap);
153: } else { /* advanced version */
154: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"PCASMCreateSubdomains2D() is currently a uniprocessor routine only!");
155: PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
156: PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
157: flg = PETSC_FALSE;
158: PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
159: if (flg) {
160: 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);
161: PetscPrintf(PETSC_COMM_SELF,"IS:\n");
162: for (i=0; i<Nsub; i++) {
163: PetscPrintf(PETSC_COMM_SELF," IS[%D]\n",i);
164: ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
165: }
166: PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
167: for (i=0; i<Nsub; i++) {
168: PetscPrintf(PETSC_COMM_SELF," IS_local[%D]\n",i);
169: ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
170: }
171: }
172: }
174: /* -------------------------------------------------------------------
175: Set the linear solvers for the subblocks
176: ------------------------------------------------------------------- */
178: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: Basic method, should be sufficient for the needs of most users.
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: By default, the ASM preconditioner uses the same solver on each
183: block of the problem. To set the same solver options on all blocks,
184: use the prefix -sub before the usual PC and KSP options, e.g.,
185: -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: Advanced method, setting different solvers for various blocks.
189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Note that each block's KSP context is completely independent of
192: the others, and the full range of uniprocessor KSP options is
193: available for each block.
195: - Use PCASMGetSubKSP() to extract the array of KSP contexts for
196: the local blocks.
197: - See ex7.c for a simple example of setting different linear solvers
198: for the individual blocks for the block Jacobi method (which is
199: equivalent to the ASM method with zero overlap).
200: */
202: flg = PETSC_FALSE;
203: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
204: if (flg) {
205: KSP *subksp; /* array of KSP contexts for local subblocks */
206: PetscInt nlocal,first; /* number of local subblocks, first local subblock */
207: PC subpc; /* PC context for subblock */
208: PetscBool isasm;
210: PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");
212: /*
213: Set runtime options
214: */
215: KSPSetFromOptions(ksp);
217: /*
218: Flag an error if PCTYPE is changed from the runtime options
219: */
220: PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
221: if (!isasm) SETERRQ(PETSC_COMM_WORLD,1,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");
223: /*
224: Call KSPSetUp() to set the block Jacobi data structures (including
225: creation of an internal KSP context for each block).
227: Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
228: */
229: KSPSetUp(ksp);
231: /*
232: Extract the array of KSP contexts for the local blocks
233: */
234: PCASMGetSubKSP(pc,&nlocal,&first,&subksp);
236: /*
237: Loop over the local blocks, setting various KSP options
238: for each block.
239: */
240: for (i=0; i<nlocal; i++) {
241: KSPGetPC(subksp[i],&subpc);
242: PCSetType(subpc,PCILU);
243: KSPSetType(subksp[i],KSPGMRES);
244: KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
245: }
246: } else {
247: /*
248: Set runtime options
249: */
250: KSPSetFromOptions(ksp);
251: }
253: /* -------------------------------------------------------------------
254: Solve the linear system
255: ------------------------------------------------------------------- */
257: KSPSolve(ksp,b,x);
259: /* -------------------------------------------------------------------
260: Compare result to the exact solution
261: ------------------------------------------------------------------- */
262: VecAXPY(x,-1.0,u);
263: VecNorm(x,NORM_INFINITY, &e);
265: flg = PETSC_FALSE;
266: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
267: if (flg) {
268: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
269: }
271: /*
272: Free work space. All PETSc objects should be destroyed when they
273: are no longer needed.
274: */
276: if (user_subdomains) {
277: for (i=0; i<Nsub; i++) {
278: ISDestroy(&is[i]);
279: ISDestroy(&is_local[i]);
280: }
281: PetscFree(is);
282: PetscFree(is_local);
283: }
284: KSPDestroy(&ksp);
285: VecDestroy(&u);
286: VecDestroy(&x);
287: VecDestroy(&b);
288: MatDestroy(&A);
289: PetscFinalize();
290: return ierr;
291: }