Actual source code: ex17.c
2: static char help[] = "Solves a linear system with KSP. This problem is\n\
3: intended to test the complex numbers version of various solvers.\n\n";
5: #include <petscksp.h>
7: typedef enum {TEST_1,TEST_2,TEST_3,HELMHOLTZ_1,HELMHOLTZ_2} TestType;
8: extern PetscErrorCode FormTestMatrix(Mat,PetscInt,TestType);
10: int main(int argc,char **args)
11: {
12: Vec x,b,u; /* approx solution, RHS, exact solution */
13: Mat A; /* linear system matrix */
14: KSP ksp; /* KSP context */
15: PetscInt n = 10,its, dim,p = 1,use_random;
16: PetscScalar none = -1.0,pfive = 0.5;
17: PetscReal norm;
18: PetscRandom rctx;
19: TestType type;
20: PetscBool flg;
22: PetscInitialize(&argc,&args,(char*)0,help);
23: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
24: PetscOptionsGetInt(NULL,NULL,"-p",&p,NULL);
25: switch (p) {
26: case 1: type = TEST_1; dim = n; break;
27: case 2: type = TEST_2; dim = n; break;
28: case 3: type = TEST_3; dim = n; break;
29: case 4: type = HELMHOLTZ_1; dim = n*n; break;
30: case 5: type = HELMHOLTZ_2; dim = n*n; break;
31: default: type = TEST_1; dim = n;
32: }
34: /* Create vectors */
35: VecCreate(PETSC_COMM_WORLD,&x);
36: VecSetSizes(x,PETSC_DECIDE,dim);
37: VecSetFromOptions(x);
38: VecDuplicate(x,&b);
39: VecDuplicate(x,&u);
41: use_random = 1;
42: flg = PETSC_FALSE;
43: PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
44: if (flg) {
45: use_random = 0;
46: VecSet(u,pfive);
47: } else {
48: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
49: PetscRandomSetFromOptions(rctx);
50: VecSetRandom(u,rctx);
51: }
53: /* Create and assemble matrix */
54: MatCreate(PETSC_COMM_WORLD,&A);
55: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
56: MatSetFromOptions(A);
57: MatSetUp(A);
58: FormTestMatrix(A,n,type);
59: MatMult(A,u,b);
60: flg = PETSC_FALSE;
61: PetscOptionsGetBool(NULL,NULL,"-printout",&flg,NULL);
62: if (flg) {
63: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
64: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
65: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
66: }
68: /* Create KSP context; set operators and options; solve linear system */
69: KSPCreate(PETSC_COMM_WORLD,&ksp);
70: KSPSetOperators(ksp,A,A);
71: KSPSetFromOptions(ksp);
72: KSPSolve(ksp,b,x);
73: /* KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD); */
75: /* Check error */
76: VecAXPY(x,none,u);
77: VecNorm(x,NORM_2,&norm);
78: KSPGetIterationNumber(ksp,&its);
79: if (norm >= 1.e-12) {
80: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
81: } else {
82: PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12, Iterations %D\n",its);
83: }
85: /* Free work space */
86: VecDestroy(&x)); PetscCall(VecDestroy(&u);
87: VecDestroy(&b)); PetscCall(MatDestroy(&A);
88: if (use_random) PetscRandomDestroy(&rctx);
89: KSPDestroy(&ksp);
90: PetscFinalize();
91: return 0;
92: }
94: PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
95: {
96: PetscScalar val[5];
97: PetscInt i,j,Ii,J,col[5],Istart,Iend;
99: MatGetOwnershipRange(A,&Istart,&Iend);
100: if (type == TEST_1) {
101: val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
102: for (i=1; i<n-1; i++) {
103: col[0] = i-1; col[1] = i; col[2] = i+1;
104: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
105: }
106: i = n-1; col[0] = n-2; col[1] = n-1;
107: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
108: i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
109: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
110: } else if (type == TEST_2) {
111: val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
112: for (i=2; i<n-1; i++) {
113: col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
114: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
115: }
116: i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
117: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
118: i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
119: MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
120: i = 0;
121: MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
122: } else if (type == TEST_3) {
123: val[0] = PETSC_i * 2.0;
124: val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
125: for (i=1; i<n-3; i++) {
126: col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
127: MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
128: }
129: i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
130: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
131: i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
132: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
133: i = n-1; col[0] = n-2; col[1] = n-1;
134: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
135: i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
136: MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
137: } else if (type == HELMHOLTZ_1) {
138: /* Problem domain: unit square: (0,1) x (0,1)
139: Solve Helmholtz equation:
140: -delta u - sigma1*u + i*sigma2*u = f,
141: where delta = Laplace operator
142: Dirichlet b.c.'s on all sides
143: */
144: PetscRandom rctx;
145: PetscReal h2,sigma1 = 5.0;
146: PetscScalar sigma2;
147: PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
148: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
149: PetscRandomSetFromOptions(rctx);
150: PetscRandomSetInterval(rctx,0.0,PETSC_i);
151: h2 = 1.0/((n+1)*(n+1));
152: for (Ii=Istart; Ii<Iend; Ii++) {
153: *val = -1.0; i = Ii/n; j = Ii - i*n;
154: if (i>0) {
155: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
156: }
157: if (i<n-1) {
158: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
159: }
160: if (j>0) {
161: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
162: }
163: if (j<n-1) {
164: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
165: }
166: PetscRandomGetValue(rctx,&sigma2);
167: *val = 4.0 - sigma1*h2 + sigma2*h2;
168: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
169: }
170: PetscRandomDestroy(&rctx);
171: } else if (type == HELMHOLTZ_2) {
172: /* Problem domain: unit square: (0,1) x (0,1)
173: Solve Helmholtz equation:
174: -delta u - sigma1*u = f,
175: where delta = Laplace operator
176: Dirichlet b.c.'s on 3 sides
177: du/dn = i*alpha*u on (1,y), 0<y<1
178: */
179: PetscReal h2,sigma1 = 200.0;
180: PetscScalar alpha_h;
181: PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
182: h2 = 1.0/((n+1)*(n+1));
183: alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
184: for (Ii=Istart; Ii<Iend; Ii++) {
185: *val = -1.0; i = Ii/n; j = Ii - i*n;
186: if (i>0) {
187: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
188: }
189: if (i<n-1) {
190: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
191: }
192: if (j>0) {
193: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
194: }
195: if (j<n-1) {
196: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
197: }
198: *val = 4.0 - sigma1*h2;
199: if (!((Ii+1)%n)) *val += alpha_h;
200: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
201: }
202: } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_USER_INPUT,"FormTestMatrix: unknown test matrix type");
204: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
205: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
207: return 0;
208: }
210: /*TEST
212: build:
213: requires: complex
215: test:
216: args: -ksp_gmres_cgs_refinement_type refine_always -n 6 -ksp_monitor_short -p 5 -norandom -ksp_type gmres -pc_type jacobi -ksp_max_it 15
217: requires: complex
219: test:
220: suffix: 2
221: nsize: 3
222: requires: complex
223: args: -ksp_gmres_cgs_refinement_type refine_always -n 6 -ksp_monitor_short -p 5 -norandom -ksp_type gmres -pc_type jacobi -ksp_max_it 15
224: output_file: output/ex17_1.out
226: test:
227: suffix: superlu_dist
228: requires: superlu_dist complex
229: args: -n 6 -p 5 -norandom -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_colperm MMD_ATA
231: test:
232: suffix: superlu_dist_2
233: requires: superlu_dist complex
234: nsize: 3
235: output_file: output/ex17_superlu_dist.out
236: args: -n 6 -p 5 -norandom -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_colperm MMD_ATA
238: TEST*/