Actual source code: ex17.c
1: /*$Id: ex17.c,v 1.43 2001/08/07 21:30:50 bsmith Exp $*/
3: static char help[] = "Solves a linear system with SLES. This problem is\n\
4: intended to test the complex numbers version of various solvers.\n\n";
6: #include petscsles.h
8: typedef enum {TEST_1,TEST_2,TEST_3,HELMHOLTZ_1,HELMHOLTZ_2} TestType;
9: extern int FormTestMatrix(Mat,int,TestType);
13: int main(int argc,char **args)
14: {
15: Vec x,b,u; /* approx solution, RHS, exact solution */
16: Mat A; /* linear system matrix */
17: SLES sles; /* SLES context */
18: int ierr,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: PetscTruth flg;
25: PetscInitialize(&argc,&args,(char *)0,help);
26: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
27: PetscOptionsGetInt(PETSC_NULL,"-p",&p,PETSC_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: PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);
46: if (flg) {
47: use_random = 0;
48: VecSet(&pfive,u);
49: } else {
50: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
51: VecSetRandom(rctx,u);
52: }
54: /* Create and assemble matrix */
55: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,dim,dim,&A);
56: MatSetFromOptions(A);
57: FormTestMatrix(A,n,type);
58: MatMult(A,u,b);
59: PetscOptionsHasName(PETSC_NULL,"-printout",&flg);
60: if (flg) {
61: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
62: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
63: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
64: }
66: /* Create SLES context; set operators and options; solve linear system */
67: SLESCreate(PETSC_COMM_WORLD,&sles);
68: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
69:
70: SLESSetFromOptions(sles);
71: SLESSolve(sles,b,x,&its);
72: SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
74: /* Check error */
75: VecAXPY(&none,u,x);
76: VecNorm(x,NORM_2,&norm);
77: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A,Iterations %d\n",norm,its);
79: /* Free work space */
80: VecDestroy(x); VecDestroy(u);
81: VecDestroy(b); MatDestroy(A);
82: if (use_random) {PetscRandomDestroy(rctx);}
83: SLESDestroy(sles);
84: PetscFinalize();
85: return 0;
86: }
90: int FormTestMatrix(Mat A,int n,TestType type)
91: {
92: #if !defined(PETSC_USE_COMPLEX)
93: SETERRQ(1,"FormTestMatrix: These problems require complex numbers.");
94: #else
96: PetscScalar val[5];
97: int i,j,I,J,ierr,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: }
111: else if (type == TEST_2) {
112: val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
113: for (i=2; i<n-1; i++) {
114: col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
115: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
116: }
117: i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
118: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
119: i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
120: MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
121: i = 0;
122: MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
123: }
124: else if (type == TEST_3) {
125: val[0] = PETSC_i * 2.0;
126: val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
127: for (i=1; i<n-3; i++) {
128: col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
129: MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
130: }
131: i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
132: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
133: i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
134: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
135: i = n-1; col[0] = n-2; col[1] = n-1;
136: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
137: i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
138: MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
139: }
140: else if (type == HELMHOLTZ_1) {
141: /* Problem domain: unit square: (0,1) x (0,1)
142: Solve Helmholtz equation:
143: -delta u - sigma1*u + i*sigma2*u = f,
144: where delta = Laplace operator
145: Dirichlet b.c.'s on all sides
146: */
147: PetscRandom rctx;
148: PetscReal h2,sigma1 = 5.0;
149: PetscScalar sigma2;
150: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
151: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT_IMAGINARY,&rctx);
152: h2 = 1.0/((n+1)*(n+1));
153: for (I=Istart; I<Iend; I++) {
154: *val = -1.0; i = I/n; j = I - i*n;
155: if (i>0) {
156: J = I-n; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
157: if (i<n-1) {
158: J = I+n; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
159: if (j>0) {
160: J = I-1; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
161: if (j<n-1) {
162: J = I+1; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
163: PetscRandomGetValue(rctx,&sigma2);
164: *val = 4.0 - sigma1*h2 + sigma2*h2;
165: MatSetValues(A,1,&I,1,&I,val,ADD_VALUES);
166: }
167: PetscRandomDestroy(rctx);
168: }
169: else if (type == HELMHOLTZ_2) {
170: /* Problem domain: unit square: (0,1) x (0,1)
171: Solve Helmholtz equation:
172: -delta u - sigma1*u = f,
173: where delta = Laplace operator
174: Dirichlet b.c.'s on 3 sides
175: du/dn = i*alpha*u on (1,y), 0<y<1
176: */
177: PetscReal h2,sigma1 = 200.0;
178: PetscScalar alpha_h;
179: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
180: h2 = 1.0/((n+1)*(n+1));
181: alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
182: for (I=Istart; I<Iend; I++) {
183: *val = -1.0; i = I/n; j = I - i*n;
184: if (i>0) {
185: J = I-n; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
186: if (i<n-1) {
187: J = I+n; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
188: if (j>0) {
189: J = I-1; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
190: if (j<n-1) {
191: J = I+1; MatSetValues(A,1,&I,1,&J,val,ADD_VALUES);}
192: *val = 4.0 - sigma1*h2;
193: if (!((I+1)%n)) *val += alpha_h;
194: MatSetValues(A,1,&I,1,&I,val,ADD_VALUES);
195: }
196: }
197: else SETERRQ(1,"FormTestMatrix: unknown test matrix type");
199: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
200: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
201: #endif
203: return 0;
204: }