Actual source code: ex6.c

petsc-master 2020-06-03
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```
2: static char help[] = "Solves a tridiagonal linear system with KSP. \n\
3: It illustrates how to do one symbolic factorization and multiple numeric factorizations using same matrix structure. \n\n";

5:  #include <petscksp.h>
6: int main(int argc,char **args)
7: {
8:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
9:   Mat            A;            /* linear system matrix */
10:   KSP            ksp;          /* linear solver context */
11:   PC             pc;           /* preconditioner context */
12:   PetscReal      norm;         /* norm of solution error */
14:   PetscInt       i,col[3],its,rstart,rend,N=10,num_numfac;
15:   PetscScalar    value[3];

17:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
18:   PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);

20:   /* Create and assemble matrix. */
21:   MatCreate(PETSC_COMM_WORLD,&A);
22:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
23:   MatSetFromOptions(A);
24:   MatSetUp(A);
25:   MatGetOwnershipRange(A,&rstart,&rend);

27:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
28:   for (i=rstart; i<rend; i++) {
29:     col[0] = i-1; col[1] = i; col[2] = i+1;
30:     if (i == 0) {
31:       MatSetValues(A,1,&i,2,col+1,value+1,INSERT_VALUES);
32:     } else if (i == N-1) {
33:       MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
34:     } else {
35:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
36:     }
37:   }
38:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
39:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
40:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

42:   /* Create vectors */
43:   MatCreateVecs(A,&x,&b);
44:   VecDuplicate(x,&u);

46:   /* Set exact solution; then compute right-hand-side vector. */
47:   VecSet(u,1.0);
48:   MatMult(A,u,b);

50:   /* Create the linear solver and set various options. */
51:   KSPCreate(PETSC_COMM_WORLD,&ksp);
52:   KSPGetPC(ksp,&pc);
53:   PCSetType(pc,PCJACOBI);
54:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
55:   KSPSetOperators(ksp,A,A);
56:   KSPSetFromOptions(ksp);

58:   num_numfac = 1;
59:   PetscOptionsGetInt(NULL,NULL,"-num_numfac",&num_numfac,NULL);
60:   while (num_numfac--) {
61:     /* An example on how to update matrix A for repeated numerical factorization and solve. */
62:     PetscScalar one=1.0;
63:     PetscInt    i = 0;
65:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
66:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
67:     /* Update b */
68:     MatMult(A,u,b);

70:     /* Solve the linear system */
71:     KSPSolve(ksp,b,x);

73:     /* Check the solution and clean up */
74:     VecAXPY(x,-1.0,u);
75:     VecNorm(x,NORM_2,&norm);
76:     KSPGetIterationNumber(ksp,&its);
77:     if (norm > 100*PETSC_MACHINE_EPSILON) {
78:       PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
79:     }
80:   }

82:   /* Free work space. */
83:   VecDestroy(&x); VecDestroy(&u);
84:   VecDestroy(&b); MatDestroy(&A);
85:   KSPDestroy(&ksp);

87:   PetscFinalize();
88:   return ierr;
89: }

91: /*TEST

93:     test:
94:       args: -num_numfac 2 -pc_type lu

96:     test:
97:       suffix: 2
98:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
99:       requires: mumps

101:     test:
102:       suffix: 3
103:       nsize: 3
104:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
105:       requires: mumps

107: TEST*/
```