Actual source code: ex11.c
petsc-3.7.7 2017-09-25
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: petscsys.h - base PETSc routines petscvec.h - vectors
30: 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,Ii,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: PetscBool flg = PETSC_FALSE;
51: PetscInitialize(&argc,&args,(char*)0,help);
52: #if !defined(PETSC_USE_COMPLEX)
53: SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
54: #endif
56: PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
57: PetscOptionsGetInt(NULL,NULL,"-n",&n,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);
73: MatSetUp(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: PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
91: if (flg) use_random = 0;
92: else use_random = 1;
93: if (use_random) {
94: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
95: PetscRandomSetFromOptions(rctx);
96: PetscRandomSetInterval(rctx,0.0,PETSC_i);
97: } else {
98: sigma2 = 10.0*PETSC_i;
99: }
100: h2 = 1.0/((n+1)*(n+1));
101: for (Ii=Istart; Ii<Iend; Ii++) {
102: v = -1.0; i = Ii/n; j = Ii - i*n;
103: if (i>0) {
104: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
105: }
106: if (i<n-1) {
107: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
108: }
109: if (j>0) {
110: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
111: }
112: if (j<n-1) {
113: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
114: }
115: if (use_random) {PetscRandomGetValue(rctx,&sigma2);}
116: v = 4.0 - sigma1*h2 + sigma2*h2;
117: MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
118: }
119: if (use_random) {PetscRandomDestroy(&rctx);}
121: /*
122: Assemble matrix, using the 2-step process:
123: MatAssemblyBegin(), MatAssemblyEnd()
124: Computations can be done while messages are in transition
125: by placing code between these two statements.
126: */
127: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
128: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
130: /*
131: Create parallel vectors.
132: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
133: we specify only the vector's global
134: dimension; the parallel partitioning is determined at runtime.
135: - Note: We form 1 vector from scratch and then duplicate as needed.
136: */
137: VecCreate(PETSC_COMM_WORLD,&u);
138: VecSetSizes(u,PETSC_DECIDE,dim);
139: VecSetFromOptions(u);
140: VecDuplicate(u,&b);
141: VecDuplicate(b,&x);
143: /*
144: Set exact solution; then compute right-hand-side vector.
145: */
147: if (use_random) {
148: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
149: PetscRandomSetFromOptions(rctx);
150: VecSetRandom(u,rctx);
151: } else {
152: VecSet(u,pfive);
153: }
154: MatMult(A,u,b);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Create the linear solver and set various options
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: /*
161: Create linear solver context
162: */
163: KSPCreate(PETSC_COMM_WORLD,&ksp);
165: /*
166: Set operators. Here the matrix that defines the linear system
167: also serves as the preconditioning matrix.
168: */
169: KSPSetOperators(ksp,A,A);
171: /*
172: Set runtime options, e.g.,
173: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
174: */
175: KSPSetFromOptions(ksp);
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Solve the linear system
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: KSPSolve(ksp,b,x);
183: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: Check solution and clean up
185: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: /*
188: Print the first 3 entries of x; this demonstrates extraction of the
189: real and imaginary components of the complex vector, x.
190: */
191: flg = PETSC_FALSE;
192: PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
193: if (flg) {
194: VecGetArray(x,&xa);
195: PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
196: for (i=0; i<3; i++) {
197: PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
198: }
199: VecRestoreArray(x,&xa);
200: }
202: /*
203: Check the error
204: */
205: VecAXPY(x,none,u);
206: VecNorm(x,NORM_2,&norm);
207: KSPGetIterationNumber(ksp,&its);
208: if (norm < 1.e-12) {
209: PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
210: } else {
211: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
212: }
214: /*
215: Free work space. All PETSc objects should be destroyed when they
216: are no longer needed.
217: */
218: KSPDestroy(&ksp);
219: if (use_random) {PetscRandomDestroy(&rctx);}
220: VecDestroy(&u); VecDestroy(&x);
221: VecDestroy(&b); MatDestroy(&A);
222: PetscFinalize();
223: return 0;
224: }