Actual source code: ex11.c
2: static char help[] = "Solves a linear system in parallel with KSP.\n\n";
4: /*
5: Description: Solves a complex linear system in parallel with KSP.
7: The model problem:
8: Solve Helmholtz equation on the unit square: (0,1) x (0,1)
9: -delta u - sigma1*u + i*sigma2*u = f,
10: where delta = Laplace operator
11: Dirichlet b.c.'s on all sides
12: Use the 2-D, five-point finite difference stencil.
14: Compiling the code:
15: This code uses the complex numbers version of PETSc, so configure
16: must be run to enable this
17: */
19: /*
20: Include "petscksp.h" so that we can use KSP solvers. Note that this file
21: automatically includes:
22: petscsys.h - base PETSc routines petscvec.h - vectors
23: petscmat.h - matrices
24: petscis.h - index sets petscksp.h - Krylov subspace methods
25: petscviewer.h - viewers petscpc.h - preconditioners
26: */
27: #include <petscksp.h>
29: int main(int argc,char **args)
30: {
31: Vec x,b,u; /* approx solution, RHS, exact solution */
32: Mat A; /* linear system matrix */
33: KSP ksp; /* linear solver context */
34: PetscReal norm; /* norm of solution error */
35: PetscInt dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
36: PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
37: PetscRandom rctx;
38: PetscReal h2,sigma1 = 100.0;
39: PetscBool flg = PETSC_FALSE;
41: PetscInitialize(&argc,&args,(char*)0,help);
42: PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
43: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
44: dim = n*n;
46: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: Compute the matrix and right-hand-side vector that define
48: the linear system, Ax = b.
49: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
50: /*
51: Create parallel matrix, specifying only its global dimensions.
52: When using MatCreate(), the matrix format can be specified at
53: runtime. Also, the parallel partitioning of the matrix is
54: determined by PETSc at runtime.
55: */
56: MatCreate(PETSC_COMM_WORLD,&A);
57: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
58: MatSetFromOptions(A);
59: MatSetUp(A);
61: /*
62: Currently, all PETSc parallel matrix formats are partitioned by
63: contiguous chunks of rows across the processors. Determine which
64: rows of the matrix are locally owned.
65: */
66: MatGetOwnershipRange(A,&Istart,&Iend);
68: /*
69: Set matrix elements in parallel.
70: - Each processor needs to insert only elements that it owns
71: locally (but any non-local elements will be sent to the
72: appropriate processor during matrix assembly).
73: - Always specify global rows and columns of matrix entries.
74: */
76: PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
77: if (flg) use_random = 0;
78: else use_random = 1;
79: if (use_random) {
80: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
81: PetscRandomSetFromOptions(rctx);
82: PetscRandomSetInterval(rctx,0.0,PETSC_i);
83: } else {
84: sigma2 = 10.0*PETSC_i;
85: }
86: h2 = 1.0/((n+1)*(n+1));
87: for (Ii=Istart; Ii<Iend; Ii++) {
88: v = -1.0; i = Ii/n; j = Ii - i*n;
89: if (i>0) {
90: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
91: }
92: if (i<n-1) {
93: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
94: }
95: if (j>0) {
96: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
97: }
98: if (j<n-1) {
99: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
100: }
101: if (use_random) PetscRandomGetValue(rctx,&sigma2);
102: v = 4.0 - sigma1*h2 + sigma2*h2;
103: MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
104: }
105: if (use_random) PetscRandomDestroy(&rctx);
107: /*
108: Assemble matrix, using the 2-step process:
109: MatAssemblyBegin(), MatAssemblyEnd()
110: Computations can be done while messages are in transition
111: by placing code between these two statements.
112: */
113: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
114: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
116: /*
117: Create parallel vectors.
118: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
119: we specify only the vector's global
120: dimension; the parallel partitioning is determined at runtime.
121: - Note: We form 1 vector from scratch and then duplicate as needed.
122: */
123: VecCreate(PETSC_COMM_WORLD,&u);
124: VecSetSizes(u,PETSC_DECIDE,dim);
125: VecSetFromOptions(u);
126: VecDuplicate(u,&b);
127: VecDuplicate(b,&x);
129: /*
130: Set exact solution; then compute right-hand-side vector.
131: */
133: if (use_random) {
134: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
135: PetscRandomSetFromOptions(rctx);
136: VecSetRandom(u,rctx);
137: } else {
138: VecSet(u,pfive);
139: }
140: MatMult(A,u,b);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Create the linear solver and set various options
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: /*
147: Create linear solver context
148: */
149: KSPCreate(PETSC_COMM_WORLD,&ksp);
151: /*
152: Set operators. Here the matrix that defines the linear system
153: also serves as the preconditioning matrix.
154: */
155: KSPSetOperators(ksp,A,A);
157: /*
158: Set runtime options, e.g.,
159: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
160: */
161: KSPSetFromOptions(ksp);
163: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: Solve the linear system
165: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: KSPSolve(ksp,b,x);
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Check solution and clean up
171: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: /*
174: Print the first 3 entries of x; this demonstrates extraction of the
175: real and imaginary components of the complex vector, x.
176: */
177: flg = PETSC_FALSE;
178: PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
179: if (flg) {
180: VecGetArray(x,&xa);
181: PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
182: for (i=0; i<3; i++) {
183: PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
184: }
185: VecRestoreArray(x,&xa);
186: }
188: /*
189: Check the error
190: */
191: VecAXPY(x,none,u);
192: VecNorm(x,NORM_2,&norm);
193: KSPGetIterationNumber(ksp,&its);
194: if (norm < 1.e-12) {
195: PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
196: } else {
197: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
198: }
200: /*
201: Free work space. All PETSc objects should be destroyed when they
202: are no longer needed.
203: */
204: KSPDestroy(&ksp);
205: if (use_random) PetscRandomDestroy(&rctx);
206: VecDestroy(&u)); PetscCall(VecDestroy(&x);
207: VecDestroy(&b)); PetscCall(MatDestroy(&A);
208: PetscFinalize();
209: return 0;
210: }
212: /*TEST
214: build:
215: requires: complex
217: test:
218: args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
220: testset:
221: suffix: deflation
222: args: -norandom -pc_type deflation -ksp_monitor_short
223: requires: superlu_dist
225: test:
226: nsize: 6
228: test:
229: nsize: 3
230: args: -pc_deflation_compute_space {{db2 aggregation}}
232: test:
233: suffix: pc_deflation_init_only-0
234: nsize: 4
235: args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
236: #TODO remove suffix and next test when this works
237: #args: -pc_deflation_init_only {{0 1}separate output}
238: args: -pc_deflation_init_only 0
240: test:
241: suffix: pc_deflation_init_only-1
242: nsize: 4
243: args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
244: args: -pc_deflation_init_only 1
246: TEST*/