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.
23: This matrix in this linear system arises from the discretized Laplacian,
24: and thus is not very interesting in terms of experimenting with variants
25: of the GASM preconditioner.
26: */
28: /*T
29: Concepts: KSP^Additive Schwarz Method (GASM) with user-defined subdomains
30: Processors: n
31: T*/
33: /*
34: Include "petscksp.h" so that we can use KSP solvers. Note that this file
35: automatically includes:
36: petscsys.h - base PETSc routines petscvec.h - vectors
37: petscmat.h - matrices
38: petscis.h - index sets petscksp.h - Krylov subspace methods
39: petscviewer.h - viewers petscpc.h - preconditioners
40: */
41: #include <petscksp.h>
42: #include <petscmat.h>
44: int main(int argc,char **args)
45: {
46: Vec x,b,u; /* approx solution, RHS, exact solution */
47: Mat A,perA; /* linear system matrix */
48: KSP ksp; /* linear solver context */
49: PC pc; /* PC context */
50: PetscInt overlap; /* width of subdomain overlap */
51: PetscInt m,n; /* mesh dimensions in x- and y- directions */
52: PetscInt M,N; /* number of subdomains in x- and y- directions */
53: PetscInt i,j,Ii,J,Istart,Iend;
55: PetscMPIInt size;
56: PetscBool flg;
57: PetscBool user_set_subdomains;
58: PetscScalar v, one = 1.0;
59: MatPartitioning part;
60: IS coarseparts,fineparts;
61: IS is,isn,isrows;
62: MPI_Comm comm;
63: PetscReal e;
65: PetscInitialize(&argc,&args,(char*)0,help);
66: comm = PETSC_COMM_WORLD;
67: MPI_Comm_size(comm,&size);
68: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PC");
69: m = 15;
70: PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
71: n = 17;
72: PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
73: user_set_subdomains = PETSC_FALSE;
74: PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
75: M = 2;
76: PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
77: N = 1;
78: PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
79: overlap = 1;
80: PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
81: PetscOptionsEnd();
83: /* -------------------------------------------------------------------
84: Compute the matrix and right-hand-side vector that define
85: the linear system, Ax = b.
86: ------------------------------------------------------------------- */
88: /*
89: Assemble the matrix for the five point stencil, YET AGAIN
90: */
91: MatCreate(comm,&A);
92: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
93: MatSetFromOptions(A);
94: MatSetUp(A);
95: MatGetOwnershipRange(A,&Istart,&Iend);
96: for (Ii=Istart; Ii<Iend; Ii++) {
97: v = -1.0; i = Ii/n; j = Ii - i*n;
98: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
99: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
100: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
101: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
102: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
103: }
104: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
105: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
107: /*
108: Partition the graph of the matrix
109: */
110: MatPartitioningCreate(comm,&part);
111: MatPartitioningSetAdjacency(part,A);
112: MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
113: MatPartitioningHierarchicalSetNcoarseparts(part,2);
114: MatPartitioningHierarchicalSetNfineparts(part,2);
115: MatPartitioningSetFromOptions(part);
116: /* get new processor owner number of each vertex */
117: MatPartitioningApply(part,&is);
118: /* get coarse parts according to which we rearrange the matrix */
119: MatPartitioningHierarchicalGetCoarseparts(part,&coarseparts);
120: /* fine parts are used with coarse parts */
121: MatPartitioningHierarchicalGetFineparts(part,&fineparts);
122: /* get new global number of each old global number */
123: ISPartitioningToNumbering(is,&isn);
124: ISBuildTwoSided(is,NULL,&isrows);
125: MatCreateSubMatrix(A,isrows,isrows,MAT_INITIAL_MATRIX,&perA);
126: MatCreateVecs(perA,&b,NULL);
127: VecSetFromOptions(b);
128: VecDuplicate(b,&u);
129: VecDuplicate(b,&x);
130: VecSet(u,one);
131: MatMult(perA,u,b);
132: KSPCreate(comm,&ksp);
133: /*
134: Set operators. Here the matrix that defines the linear system
135: also serves as the preconditioning matrix.
136: */
137: KSPSetOperators(ksp,perA,perA);
139: /*
140: Set the default preconditioner for this program to be GASM
141: */
142: KSPGetPC(ksp,&pc);
143: PCSetType(pc,PCGASM);
144: KSPSetFromOptions(ksp);
145: /* -------------------------------------------------------------------
146: Solve the linear system
147: ------------------------------------------------------------------- */
149: KSPSolve(ksp,b,x);
150: /* -------------------------------------------------------------------
151: Compare result to the exact solution
152: ------------------------------------------------------------------- */
153: VecAXPY(x,-1.0,u);
154: VecNorm(x,NORM_INFINITY, &e);
156: flg = PETSC_FALSE;
157: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
158: if (flg) {
159: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
160: }
161: /*
162: Free work space. All PETSc objects should be destroyed when they
163: are no longer needed.
164: */
165: KSPDestroy(&ksp);
166: VecDestroy(&u);
167: VecDestroy(&x);
168: VecDestroy(&b);
169: MatDestroy(&A);
170: MatDestroy(&perA);
171: ISDestroy(&is);
172: ISDestroy(&coarseparts);
173: ISDestroy(&fineparts);
174: ISDestroy(&isrows);
175: ISDestroy(&isn);
176: MatPartitioningDestroy(&part);
177: PetscFinalize();
178: return 0;
179: }
181: /*TEST
183: test:
184: nsize: 4
185: requires: superlu_dist parmetis
186: args: -ksp_monitor -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -pc_gasm_total_subdomains 2
188: TEST*/