Actual source code: ex11.c
2: static char help[] = "Solves a linear system in parallel with KSP.\n\n";
4: /*T
5: Concepts: KSP^solving a Helmholtz equation
6: Concepts: complex numbers;
7: Concepts: Helmholtz equation
8: Processors: n
9: T*/
11: /*
12: Description: Solves a complex linear system in parallel with KSP.
14: The model problem:
15: Solve Helmholtz equation on the unit square: (0,1) x (0,1)
16: -delta u - sigma1*u + i*sigma2*u = f,
17: where delta = Laplace operator
18: Dirichlet b.c.'s on all sides
19: Use the 2-D, five-point finite difference stencil.
21: Compiling the code:
22: This code uses the complex numbers version of PETSc, so configure
23: must be run to enable this
24: */
26: /*
27: Include "petscksp.h" so that we can use KSP solvers. Note that this file
28: automatically includes:
29: petsc.h - base PETSc routines petscvec.h - vectors
30: petscsys.h - system routines petscmat.h - matrices
31: petscis.h - index sets petscksp.h - Krylov subspace methods
32: petscviewer.h - viewers petscpc.h - preconditioners
33: */
34: #include petscksp.h
38: int main(int argc,char **args)
39: {
40: Vec x,b,u; /* approx solution, RHS, exact solution */
41: Mat A; /* linear system matrix */
42: KSP ksp; /* linear solver context */
43: PetscReal norm; /* norm of solution error */
44: PetscInt dim,i,j,I,J,Istart,Iend,n = 6,its,use_random;
46: PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
47: PetscRandom rctx;
48: PetscReal h2,sigma1 = 100.0;
49: PetscTruth flg;
51: PetscInitialize(&argc,&args,(char *)0,help);
52: #if !defined(PETSC_USE_COMPLEX)
53: SETERRQ(1,"This example requires complex numbers");
54: #endif
56: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
57: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
58: dim = n*n;
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Compute the matrix and right-hand-side vector that define
62: the linear system, Ax = b.
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: /*
65: Create parallel matrix, specifying only its global dimensions.
66: When using MatCreate(), the matrix format can be specified at
67: runtime. Also, the parallel partitioning of the matrix is
68: determined by PETSc at runtime.
69: */
70: MatCreate(PETSC_COMM_WORLD,&A);
71: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
72: MatSetFromOptions(A);
74: /*
75: Currently, all PETSc parallel matrix formats are partitioned by
76: contiguous chunks of rows across the processors. Determine which
77: rows of the matrix are locally owned.
78: */
79: MatGetOwnershipRange(A,&Istart,&Iend);
81: /*
82: Set matrix elements in parallel.
83: - Each processor needs to insert only elements that it owns
84: locally (but any non-local elements will be sent to the
85: appropriate processor during matrix assembly).
86: - Always specify global rows and columns of matrix entries.
87: */
89: PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);
90: if (flg) use_random = 0;
91: else use_random = 1;
92: if (use_random) {
93: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT_IMAGINARY,&rctx);
94: } else {
95: sigma2 = 10.0*PETSC_i;
96: }
97: h2 = 1.0/((n+1)*(n+1));
98: for (I=Istart; I<Iend; I++) {
99: v = -1.0; i = I/n; j = I - i*n;
100: if (i>0) {
101: J = I-n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
102: if (i<n-1) {
103: J = I+n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
104: if (j>0) {
105: J = I-1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
106: if (j<n-1) {
107: J = I+1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
108: if (use_random) {PetscRandomGetValue(rctx,&sigma2);}
109: v = 4.0 - sigma1*h2 + sigma2*h2;
110: MatSetValues(A,1,&I,1,&I,&v,ADD_VALUES);
111: }
112: if (use_random) {PetscRandomDestroy(rctx);}
114: /*
115: Assemble matrix, using the 2-step process:
116: MatAssemblyBegin(), MatAssemblyEnd()
117: Computations can be done while messages are in transition
118: by placing code between these two statements.
119: */
120: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
121: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
123: /*
124: Create parallel vectors.
125: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
126: we specify only the vector's global
127: dimension; the parallel partitioning is determined at runtime.
128: - Note: We form 1 vector from scratch and then duplicate as needed.
129: */
130: VecCreate(PETSC_COMM_WORLD,&u);
131: VecSetSizes(u,PETSC_DECIDE,dim);
132: VecSetFromOptions(u);
133: VecDuplicate(u,&b);
134: VecDuplicate(b,&x);
136: /*
137: Set exact solution; then compute right-hand-side vector.
138: */
139:
140: if (use_random) {
141: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
142: VecSetRandom(u,rctx);
143: } else {
144: VecSet(u,pfive);
145: }
146: MatMult(A,u,b);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Create the linear solver and set various options
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: /*
153: Create linear solver context
154: */
155: KSPCreate(PETSC_COMM_WORLD,&ksp);
157: /*
158: Set operators. Here the matrix that defines the linear system
159: also serves as the preconditioning matrix.
160: */
161: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
163: /*
164: Set runtime options, e.g.,
165: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
166: */
167: KSPSetFromOptions(ksp);
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Solve the linear system
171: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: KSPSolve(ksp,b,x);
175: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: Check solution and clean up
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: /*
180: Print the first 3 entries of x; this demonstrates extraction of the
181: real and imaginary components of the complex vector, x.
182: */
183: PetscOptionsHasName(PETSC_NULL,"-print_x3",&flg);
184: if (flg) {
185: VecGetArray(x,&xa);
186: PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
187: for (i=0; i<3; i++){
188: PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %G + %G i\n",i,PetscRealPart(xa[i]),PetscImaginaryPart(xa[i]));
189: }
190: VecRestoreArray(x,&xa);
191: }
193: /*
194: Check the error
195: */
196: VecAXPY(x,none,u);
197: VecNorm(x,NORM_2,&norm);
198: KSPGetIterationNumber(ksp,&its);
199: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",norm,its);
201: /*
202: Free work space. All PETSc objects should be destroyed when they
203: are no longer needed.
204: */
205: KSPDestroy(ksp);
206: if (use_random) {PetscRandomDestroy(rctx);}
207: VecDestroy(u); VecDestroy(x);
208: VecDestroy(b); MatDestroy(A);
209: PetscFinalize();
210: return 0;
211: }