Actual source code: ex11.c
1: /*$Id: ex11.c,v 1.37 2001/08/07 21:30:54 bsmith Exp $*/
3: static char help[] = "Solves a linear system in parallel with SLES.nn";
5: /*T
6: Concepts: SLES^solving a Helmholtz equation
7: Concepts: complex numbers;
8: Concepts: Helmholtz equation
9: Processors: n
10: T*/
12: /*
13: Description: Solves a complex linear system in parallel with SLES.
15: The model problem:
16: Solve Helmholtz equation on the unit square: (0,1) x (0,1)
17: -delta u - sigma1*u + i*sigma2*u = f,
18: where delta = Laplace operator
19: Dirichlet b.c.'s on all sides
20: Use the 2-D, five-point finite difference stencil.
22: Compiling the code:
23: This code uses the complex numbers version of PETSc, so one of the
24: following values of BOPT must be used for compiling the PETSc libraries
25: and this example:
26: BOPT=g_complex - debugging version
27: BOPT=O_complex - optimized version
28: BOPT=Opg_complex - profiling version
29: */
31: /*
32: Include "petscsles.h" so that we can use SLES solvers. Note that this file
33: automatically includes:
34: petsc.h - base PETSc routines petscvec.h - vectors
35: petscsys.h - system routines petscmat.h - matrices
36: petscis.h - index sets petscksp.h - Krylov subspace methods
37: petscviewer.h - viewers petscpc.h - preconditioners
38: */
39: #include petscsles.h
41: int main(int argc,char **args)
42: {
43: Vec x,b,u; /* approx solution, RHS, exact solution */
44: Mat A; /* linear system matrix */
45: SLES sles; /* linear solver context */
46: PetscReal norm; /* norm of solution error */
47: int dim,i,j,I,J,Istart,Iend,ierr,n = 6,its,use_random;
48: PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
49: PetscRandom rctx;
50: PetscReal h2,sigma1 = 100.0;
51: PetscTruth flg;
53: PetscInitialize(&argc,&args,(char *)0,help);
54: #if !defined(PETSC_USE_COMPLEX)
55: SETERRQ(1,"This example requires complex numbers");
56: #endif
58: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
59: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
60: dim = n*n;
62: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
63: Compute the matrix and right-hand-side vector that define
64: the linear system, Ax = b.
65: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
66: /*
67: Create parallel matrix, specifying only its global dimensions.
68: When using MatCreate(), the matrix format can be specified at
69: runtime. Also, the parallel partitioning of the matrix is
70: determined by PETSc at runtime.
71: */
72: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,dim,dim,&A);
73: MatSetFromOptions(A);
75: /*
76: Currently, all PETSc parallel matrix formats are partitioned by
77: contiguous chunks of rows across the processors. Determine which
78: rows of the matrix are locally owned.
79: */
80: MatGetOwnershipRange(A,&Istart,&Iend);
82: /*
83: Set matrix elements in parallel.
84: - Each processor needs to insert only elements that it owns
85: locally (but any non-local elements will be sent to the
86: appropriate processor during matrix assembly).
87: - Always specify global rows and columns of matrix entries.
88: */
90: PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);
91: if (flg) use_random = 0;
92: else use_random = 1;
93: if (use_random) {
94: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT_IMAGINARY,&rctx);
95: } else {
96: sigma2 = 10.0*PETSC_i;
97: }
98: h2 = 1.0/((n+1)*(n+1));
99: for (I=Istart; I<Iend; I++) {
100: v = -1.0; i = I/n; j = I - i*n;
101: if (i>0) {
102: J = I-n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
103: if (i<n-1) {
104: J = I+n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
105: if (j>0) {
106: J = I-1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
107: if (j<n-1) {
108: J = I+1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
109: if (use_random) {PetscRandomGetValue(rctx,&sigma2);}
110: v = 4.0 - sigma1*h2 + sigma2*h2;
111: MatSetValues(A,1,&I,1,&I,&v,ADD_VALUES);
112: }
113: if (use_random) {PetscRandomDestroy(rctx);}
115: /*
116: Assemble matrix, using the 2-step process:
117: MatAssemblyBegin(), MatAssemblyEnd()
118: Computations can be done while messages are in transition
119: by placing code between these two statements.
120: */
121: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
122: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
124: /*
125: Create parallel vectors.
126: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
127: we specify only the vector's global
128: dimension; the parallel partitioning is determined at runtime.
129: - Note: We form 1 vector from scratch and then duplicate as needed.
130: */
131: VecCreate(PETSC_COMM_WORLD,&u);
132: VecSetSizes(u,PETSC_DECIDE,dim);
133: VecSetFromOptions(u);
134: VecDuplicate(u,&b);
135: VecDuplicate(b,&x);
137: /*
138: Set exact solution; then compute right-hand-side vector.
139: */
140:
141: if (use_random) {
142: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
143: VecSetRandom(rctx,u);
144: } else {
145: VecSet(&pfive,u);
146: }
147: MatMult(A,u,b);
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Create the linear solver and set various options
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: /*
154: Create linear solver context
155: */
156: SLESCreate(PETSC_COMM_WORLD,&sles);
158: /*
159: Set operators. Here the matrix that defines the linear system
160: also serves as the preconditioning matrix.
161: */
162: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
164: /*
165: Set runtime options, e.g.,
166: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
167: */
168: SLESSetFromOptions(sles);
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Solve the linear system
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174: SLESSolve(sles,b,x,&its);
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Check solution and clean up
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: /*
181: Print the first 3 entries of x; this demonstrates extraction of the
182: real and imaginary components of the complex vector, x.
183: */
184: PetscOptionsHasName(PETSC_NULL,"-print_x3",&flg);
185: if (flg) {
186: VecGetArray(x,&xa);
187: PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:n");
188: for (i=0; i<3; i++){
189: PetscPrintf(PETSC_COMM_WORLD,"x[%d] = %g + %g in",i,PetscRealPart(xa[i]),PetscImaginaryPart(xa[i]));
190: }
191: VecRestoreArray(x,&xa);
192: }
194: /*
195: Check the error
196: */
197: VecAXPY(&none,u,x);
198: VecNorm(x,NORM_2,&norm);
199: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %dn",norm,its);
201: /*
202: Free work space. All PETSc objects should be destroyed when they
203: are no longer needed.
204: */
205: SLESDestroy(sles);
206: if (use_random) {PetscRandomDestroy(rctx);}
207: VecDestroy(u); VecDestroy(x);
208: VecDestroy(b); MatDestroy(A);
209: PetscFinalize();
210: return 0;
211: }