Actual source code: ex17.c
petsc-3.4.2 2013-07-02
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);
12: int main(int argc,char **args)
13: {
14: Vec x,b,u; /* approx solution, RHS, exact solution */
15: Mat A; /* linear system matrix */
16: KSP ksp; /* KSP context */
18: PetscInt n = 10,its, dim,p = 1,use_random;
19: PetscScalar none = -1.0,pfive = 0.5;
20: PetscReal norm;
21: PetscRandom rctx;
22: TestType type;
23: PetscBool flg;
25: PetscInitialize(&argc,&args,(char*)0,help);
26: PetscOptionsGetInt(NULL,"-n",&n,NULL);
27: PetscOptionsGetInt(NULL,"-p",&p,NULL);
28: switch (p) {
29: case 1: type = TEST_1; dim = n; break;
30: case 2: type = TEST_2; dim = n; break;
31: case 3: type = TEST_3; dim = n; break;
32: case 4: type = HELMHOLTZ_1; dim = n*n; break;
33: case 5: type = HELMHOLTZ_2; dim = n*n; break;
34: default: type = TEST_1; dim = n;
35: }
37: /* Create vectors */
38: VecCreate(PETSC_COMM_WORLD,&x);
39: VecSetSizes(x,PETSC_DECIDE,dim);
40: VecSetFromOptions(x);
41: VecDuplicate(x,&b);
42: VecDuplicate(x,&u);
44: use_random = 1;
45: flg = PETSC_FALSE;
46: PetscOptionsGetBool(NULL,"-norandom",&flg,NULL);
47: if (flg) {
48: use_random = 0;
49: VecSet(u,pfive);
50: } else {
51: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
52: PetscRandomSetFromOptions(rctx);
53: VecSetRandom(u,rctx);
54: }
56: /* Create and assemble matrix */
57: MatCreate(PETSC_COMM_WORLD,&A);
58: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
59: MatSetFromOptions(A);
60: MatSetUp(A);
61: FormTestMatrix(A,n,type);
62: MatMult(A,u,b);
63: flg = PETSC_FALSE;
64: PetscOptionsGetBool(NULL,"-printout",&flg,NULL);
65: if (flg) {
66: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
67: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
68: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
69: }
71: /* Create KSP context; set operators and options; solve linear system */
72: KSPCreate(PETSC_COMM_WORLD,&ksp);
73: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
74: KSPSetFromOptions(ksp);
75: KSPSolve(ksp,b,x);
76: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
78: /* Check error */
79: VecAXPY(x,none,u);
80: VecNorm(x,NORM_2,&norm);
81: KSPGetIterationNumber(ksp,&its);
82: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G,Iterations %D\n",norm,its);
84: /* Free work space */
85: VecDestroy(&x); VecDestroy(&u);
86: VecDestroy(&b); MatDestroy(&A);
87: if (use_random) {PetscRandomDestroy(&rctx);}
88: KSPDestroy(&ksp);
89: PetscFinalize();
90: return 0;
91: }
95: PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
96: {
97: #if !defined(PETSC_USE_COMPLEX)
98: SETERRQ(PetscObjectComm((PetscObject)A),1,"FormTestMatrix: These problems require complex numbers.");
99: #else
101: PetscScalar val[5];
103: PetscInt i,j,Ii,J,col[5],Istart,Iend;
105: MatGetOwnershipRange(A,&Istart,&Iend);
106: if (type == TEST_1) {
107: val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
108: for (i=1; i<n-1; i++) {
109: col[0] = i-1; col[1] = i; col[2] = i+1;
110: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
111: }
112: i = n-1; col[0] = n-2; col[1] = n-1;
113: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
114: i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
115: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
116: } else if (type == TEST_2) {
117: val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
118: for (i=2; i<n-1; i++) {
119: col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
120: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
121: }
122: i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
123: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
124: i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
125: MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
126: i = 0;
127: MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
128: } else if (type == TEST_3) {
129: val[0] = PETSC_i * 2.0;
130: val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
131: for (i=1; i<n-3; i++) {
132: col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
133: MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
134: }
135: i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
136: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
137: i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
138: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
139: i = n-1; col[0] = n-2; col[1] = n-1;
140: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
141: i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
142: MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
143: } else if (type == HELMHOLTZ_1) {
144: /* Problem domain: unit square: (0,1) x (0,1)
145: Solve Helmholtz equation:
146: -delta u - sigma1*u + i*sigma2*u = f,
147: where delta = Laplace operator
148: Dirichlet b.c.'s on all sides
149: */
150: PetscRandom rctx;
151: PetscReal h2,sigma1 = 5.0;
152: PetscScalar sigma2;
153: PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);
154: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
155: PetscRandomSetFromOptions(rctx);
156: PetscRandomSetInterval(rctx,0.0,PETSC_i);
157: h2 = 1.0/((n+1)*(n+1));
158: for (Ii=Istart; Ii<Iend; Ii++) {
159: *val = -1.0; i = Ii/n; j = Ii - i*n;
160: if (i>0) {
161: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
162: }
163: if (i<n-1) {
164: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
165: }
166: if (j>0) {
167: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
168: }
169: if (j<n-1) {
170: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
171: }
172: PetscRandomGetValue(rctx,&sigma2);
173: *val = 4.0 - sigma1*h2 + sigma2*h2;
174: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
175: }
176: PetscRandomDestroy(&rctx);
177: } else if (type == HELMHOLTZ_2) {
178: /* Problem domain: unit square: (0,1) x (0,1)
179: Solve Helmholtz equation:
180: -delta u - sigma1*u = f,
181: where delta = Laplace operator
182: Dirichlet b.c.'s on 3 sides
183: du/dn = i*alpha*u on (1,y), 0<y<1
184: */
185: PetscReal h2,sigma1 = 200.0;
186: PetscScalar alpha_h;
187: PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);
188: h2 = 1.0/((n+1)*(n+1));
189: alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
190: for (Ii=Istart; Ii<Iend; Ii++) {
191: *val = -1.0; i = Ii/n; j = Ii - i*n;
192: if (i>0) {
193: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
194: }
195: if (i<n-1) {
196: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
197: }
198: if (j>0) {
199: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
200: }
201: if (j<n-1) {
202: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
203: }
204: *val = 4.0 - sigma1*h2;
205: if (!((Ii+1)%n)) *val += alpha_h;
206: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
207: }
208: } else SETERRQ(PetscObjectComm((PetscObject)A),1,"FormTestMatrix: unknown test matrix type");
210: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
211: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
212: #endif
214: return 0;
215: }