Actual source code: ex64.c
1: /*
2: *
3: * Created on: Aug 10, 2015
4: * Author: Fande Kong <fdkong.jd@gmail.com>
5: */
7: static char help[] = "Illustrates use of the preconditioner GASM.\n \
8: using hierarchical partitioning and MatIncreaseOverlapSplit \
9: -pc_gasm_total_subdomains\n \
10: -pc_gasm_print_subdomains\n \n";
12: /*
13: Note: This example focuses on setting the subdomains for the GASM
14: preconditioner for a problem on a 2D rectangular grid. See ex1.c
15: and ex2.c for more detailed comments on the basic usage of KSP
16: (including working with matrices and vectors).
18: The GASM preconditioner is fully parallel. The user-space routine
19: CreateSubdomains2D that computes the domain decomposition is also parallel
20: and attempts to generate both subdomains straddling processors and multiple
21: domains per processor.
24: This matrix in this linear system arises from the discretized Laplacian,
25: and thus is not very interesting in terms of experimenting with variants
26: of the GASM preconditioner.
27: */
29: /*T
30: Concepts: KSP^Additive Schwarz Method (GASM) with user-defined subdomains
31: Processors: n
32: T*/
34: /*
35: Include "petscksp.h" so that we can use KSP solvers. Note that this file
36: automatically includes:
37: petscsys.h - base PETSc routines petscvec.h - vectors
38: petscmat.h - matrices
39: petscis.h - index sets petscksp.h - Krylov subspace methods
40: petscviewer.h - viewers petscpc.h - preconditioners
41: */
42: #include <petscksp.h>
43: #include <petscmat.h>
46: int main(int argc,char **args)
47: {
48: Vec x,b,u; /* approx solution, RHS, exact solution */
49: Mat A,perA; /* linear system matrix */
50: KSP ksp; /* linear solver context */
51: PC pc; /* PC context */
52: PetscInt overlap; /* width of subdomain overlap */
53: PetscInt m,n; /* mesh dimensions in x- and y- directions */
54: PetscInt M,N; /* number of subdomains in x- and y- directions */
55: PetscInt i,j,Ii,J,Istart,Iend;
57: PetscMPIInt size;
58: PetscBool flg;
59: PetscBool user_set_subdomains;
60: PetscScalar v, one = 1.0;
61: MatPartitioning part;
62: IS coarseparts,fineparts;
63: IS is,isn,isrows;
64: MPI_Comm comm;
65: PetscReal e;
67: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
68: comm = PETSC_COMM_WORLD;
69: MPI_Comm_size(comm,&size);
70: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PC");
71: m = 15;
72: PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
73: n = 17;
74: PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
75: user_set_subdomains = PETSC_FALSE;
76: PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
77: M = 2;
78: PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
79: N = 1;
80: PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
81: overlap = 1;
82: PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
83: PetscOptionsEnd();
85: /* -------------------------------------------------------------------
86: Compute the matrix and right-hand-side vector that define
87: the linear system, Ax = b.
88: ------------------------------------------------------------------- */
90: /*
91: Assemble the matrix for the five point stencil, YET AGAIN
92: */
93: MatCreate(comm,&A);
94: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
95: MatSetFromOptions(A);
96: MatSetUp(A);
97: MatGetOwnershipRange(A,&Istart,&Iend);
98: for (Ii=Istart; Ii<Iend; Ii++) {
99: v = -1.0; i = Ii/n; j = Ii - i*n;
100: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
101: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
102: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
103: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
104: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
105: }
106: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
107: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
109: /*
110: Partition the graph of the matrix
111: */
112: MatPartitioningCreate(comm,&part);
113: MatPartitioningSetAdjacency(part,A);
114: MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
115: MatPartitioningHierarchicalSetNcoarseparts(part,2);
116: MatPartitioningHierarchicalSetNfineparts(part,2);
117: MatPartitioningSetFromOptions(part);
118: /* get new processor owner number of each vertex */
119: MatPartitioningApply(part,&is);
120: /* get coarse parts according to which we rearrange the matrix */
121: MatPartitioningHierarchicalGetCoarseparts(part,&coarseparts);
122: /* fine parts are used with coarse parts */
123: MatPartitioningHierarchicalGetFineparts(part,&fineparts);
124: /* get new global number of each old global number */
125: ISPartitioningToNumbering(is,&isn);
126: ISBuildTwoSided(is,NULL,&isrows);
127: MatCreateSubMatrix(A,isrows,isrows,MAT_INITIAL_MATRIX,&perA);
128: MatCreateVecs(perA,&b,NULL);
129: VecSetFromOptions(b);
130: VecDuplicate(b,&u);
131: VecDuplicate(b,&x);
132: VecSet(u,one);
133: MatMult(perA,u,b);
134: KSPCreate(comm,&ksp);
135: /*
136: Set operators. Here the matrix that defines the linear system
137: also serves as the preconditioning matrix.
138: */
139: KSPSetOperators(ksp,perA,perA);
141: /*
142: Set the default preconditioner for this program to be GASM
143: */
144: KSPGetPC(ksp,&pc);
145: PCSetType(pc,PCGASM);
146: KSPSetFromOptions(ksp);
147: /* -------------------------------------------------------------------
148: Solve the linear system
149: ------------------------------------------------------------------- */
151: KSPSolve(ksp,b,x);
152: /* -------------------------------------------------------------------
153: Compare result to the exact solution
154: ------------------------------------------------------------------- */
155: VecAXPY(x,-1.0,u);
156: VecNorm(x,NORM_INFINITY, &e);
158: flg = PETSC_FALSE;
159: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
160: if (flg) {
161: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
162: }
163: /*
164: Free work space. All PETSc objects should be destroyed when they
165: are no longer needed.
166: */
167: KSPDestroy(&ksp);
168: VecDestroy(&u);
169: VecDestroy(&x);
170: VecDestroy(&b);
171: MatDestroy(&A);
172: MatDestroy(&perA);
173: ISDestroy(&is);
174: ISDestroy(&coarseparts);
175: ISDestroy(&fineparts);
176: ISDestroy(&isrows);
177: ISDestroy(&isn);
178: MatPartitioningDestroy(&part);
179: PetscFinalize();
180: return ierr;
181: }
184: /*TEST
186: test:
187: nsize: 4
188: requires: superlu_dist parmetis
189: args: -ksp_monitor -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -pc_gasm_total_subdomains 2
191: TEST*/