Date: 2021-03-03T22:27:33+00:00

Actual source code: ex53.c
petsc-3.14.5 2021-03-03
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      2: static char help[] = "Solves a tridiagonal linear system with KSP. \n\
      3:                       Modified from ex1.c to illustrate reuse of preconditioner \n\
      4:                       Written as requested by [petsc-maint #63875] \n\n";

      6: #include <petscksp.h>

      8: int main(int argc,char **args)
      9: {
     10:   Vec            x,x2,b,u;     /* approx solution, RHS, exact solution */
     11:   Mat            A;            /* linear system matrix */
     12:   KSP            ksp;          /* linear solver context */
     13:   PC             pc;           /* preconditioner context */
     14:   PetscReal      norm,tol=100.*PETSC_MACHINE_EPSILON; /* norm of solution error */
     16:   PetscInt       i,n = 10,col[3],its;
     17:   PetscMPIInt    rank,size;
     18:   PetscScalar    one = 1.0,value[3];

     20:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     21:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     22:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     23:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     25:   /* Create vectors.*/
     26:   VecCreate(PETSC_COMM_WORLD,&x);
     27:   PetscObjectSetName((PetscObject) x, "Solution");
     28:   VecSetSizes(x,PETSC_DECIDE,n);
     29:   VecSetFromOptions(x);
     30:   VecDuplicate(x,&b);
     31:   VecDuplicate(x,&u);
     32:   VecDuplicate(x,&x2);

     34:   /* Create matrix. Only proc[0] sets values - not efficient for parallel processing!
     35:      See ex23.c for efficient parallel assembly matrix */
     36:   MatCreate(PETSC_COMM_WORLD,&A);
     37:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     38:   MatSetFromOptions(A);
     39:   MatSetUp(A);

     41:   if (!rank) {
     42:     value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     43:     for (i=1; i<n-1; i++) {
     44:       col[0] = i-1; col[1] = i; col[2] = i+1;
     45:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
     46:     }
     47:     i    = n - 1; col[0] = n - 2; col[1] = n - 1;
     48:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     49:     i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     50:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);

     52:     i    = 0; col[0] = n-1; value[0] = 0.5; /* make A non-symmetric */
     53:     MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
     54:   }
     55:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     56:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     58:   /* Set exact solution */
     59:   VecSet(u,one);

     61:   /* Create linear solver context */
     62:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     63:   KSPSetOperators(ksp,A,A);
     64:   KSPGetPC(ksp,&pc);
     65:   PCSetType(pc,PCLU);
     66: #if defined(PETSC_HAVE_MUMPS)
     67:   if (size > 1) {
     68:     PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
     69:   }
     70: #endif
     71:   KSPSetFromOptions(ksp);

     73:   /* 1. Solve linear system A x = b */
     74:   MatMult(A,u,b);
     75:   KSPSolve(ksp,b,x);

     77:   /* Check the error */
     78:   VecAXPY(x,-1.0,u);
     79:   VecNorm(x,NORM_2,&norm);
     80:   KSPGetIterationNumber(ksp,&its);
     81:   if (norm > tol) {
     82:     PetscPrintf(PETSC_COMM_WORLD,"1. Norm of error for Ax=b: %g, Iterations %D\n",(double)norm,its);
     83:   }

     85:   /* 2. Solve linear system A^T x = b*/
     86:   MatMultTranspose(A,u,b);
     87:   KSPSolveTranspose(ksp,b,x2);

     89:   /* Check the error */
     90:   VecAXPY(x2,-1.0,u);
     91:   VecNorm(x2,NORM_2,&norm);
     92:   KSPGetIterationNumber(ksp,&its);
     93:   if (norm > tol) {
     94:     PetscPrintf(PETSC_COMM_WORLD,"2. Norm of error for A^T x=b: %g, Iterations %D\n",(double)norm,its);
     95:   }

     97:   /* 3. Change A and solve A x = b with an iterative solver using A=LU as a preconditioner*/
     98:   if (!rank) {
     99:     i    = 0; col[0] = n-1; value[0] = 1.e-2;
    100:     MatSetValues(A,1,&i,1,col,value,ADD_VALUES);
    101:   }
    102:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    103:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    105:   MatMult(A,u,b);
    106:   KSPSolve(ksp,b,x);

    108:   /* Check the error */
    109:   VecAXPY(x,-1.0,u);
    110:   VecNorm(x,NORM_2,&norm);
    111:   KSPGetIterationNumber(ksp,&its);
    112:   if (norm > tol) {
    113:     PetscPrintf(PETSC_COMM_WORLD,"3. Norm of error for (A+Delta) x=b: %g, Iterations %D\n",(double)norm,its);
    114:   }

    116:   /* Free work space. */
    117:   VecDestroy(&x);
    118:   VecDestroy(&u);
    119:   VecDestroy(&x2);
    120:   VecDestroy(&b);
    121:   MatDestroy(&A);
    122:   KSPDestroy(&ksp);

    124:   PetscFinalize();
    125:   return ierr;
    126: }

    129: /*TEST

    131:    test:
    132:       requires: mumps

    134:    test:
    135:       suffix: 2
    136:       nsize: 2
    137:       requires: mumps
    138:       output_file: output/ex53.out

    140: TEST*/