Date: 2022-08-02T03:14:46+00:00

Actual source code: ex6.c

      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 */
     13:   PetscInt       i,col[3],its,rstart,rend,N=10,num_numfac;
     14:   PetscScalar    value[3];

     16:   PetscInitialize(&argc,&args,(char*)0,help);
     17:   PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);

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

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

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

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

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

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

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

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

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

     86:   PetscFinalize();
     87:   return 0;
     88: }

     90: /*TEST

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

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

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

    106: TEST*/