Actual source code: ex20.c


  2: static char help[] = "Bilinear elements on the unit square for Laplacian.  To test the parallel\n\
  3: matrix assembly,the matrix is intentionally laid out across processors\n\
  4: differently from the way it is assembled.  Input arguments are:\n\
  5:   -m <size> : problem size\n\n";

  7: #include <petscksp.h>

  9: int FormElementStiffness(PetscReal H, PetscScalar *Ke)
 10: {
 11:   Ke[0]  = H / 6.0;
 12:   Ke[1]  = -.125 * H;
 13:   Ke[2]  = H / 12.0;
 14:   Ke[3]  = -.125 * H;
 15:   Ke[4]  = -.125 * H;
 16:   Ke[5]  = H / 6.0;
 17:   Ke[6]  = -.125 * H;
 18:   Ke[7]  = H / 12.0;
 19:   Ke[8]  = H / 12.0;
 20:   Ke[9]  = -.125 * H;
 21:   Ke[10] = H / 6.0;
 22:   Ke[11] = -.125 * H;
 23:   Ke[12] = -.125 * H;
 24:   Ke[13] = H / 12.0;
 25:   Ke[14] = -.125 * H;
 26:   Ke[15] = H / 6.0;
 27:   return 0;
 28: }

 30: int main(int argc, char **args)
 31: {
 32:   Mat          C;
 33:   PetscMPIInt  rank, size;
 34:   PetscInt     i, m = 5, N, start, end, M;
 35:   PetscInt     idx[4];
 36:   PetscScalar  Ke[16];
 37:   PetscReal    h;
 38:   Vec          u, b;
 39:   KSP          ksp;
 40:   MatNullSpace nullsp;

 43:   PetscInitialize(&argc, &args, (char *)0, help);
 44:   PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL);
 45:   N = (m + 1) * (m + 1); /* dimension of matrix */
 46:   M = m * m;             /* number of elements */
 47:   h = 1.0 / m;           /* mesh width */
 48:   MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
 49:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

 51:   /* Create stiffness matrix */
 52:   MatCreate(PETSC_COMM_WORLD, &C);
 53:   MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, N, N);
 54:   MatSetFromOptions(C);
 55:   MatSetUp(C);
 56:   start = rank * (M / size) + ((M % size) < rank ? (M % size) : rank);
 57:   end   = start + M / size + ((M % size) > rank);

 59:   /* Assemble matrix */
 60:   FormElementStiffness(h * h, Ke); /* element stiffness for Laplacian */
 61:   for (i = start; i < end; i++) {
 62:     /* location of lower left corner of element */
 63:     /* node numbers for the four corners of element */
 64:     idx[0] = (m + 1) * (i / m) + (i % m);
 65:     idx[1] = idx[0] + 1;
 66:     idx[2] = idx[1] + m + 1;
 67:     idx[3] = idx[2] - 1;
 68:     MatSetValues(C, 4, idx, 4, idx, Ke, ADD_VALUES);
 69:   }
 70:   MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY);
 71:   MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY);

 73:   /* Create right-hand-side and solution vectors */
 74:   VecCreate(PETSC_COMM_WORLD, &u);
 75:   VecSetSizes(u, PETSC_DECIDE, N);
 76:   VecSetFromOptions(u);
 77:   PetscObjectSetName((PetscObject)u, "Approx. Solution");
 78:   VecDuplicate(u, &b);
 79:   PetscObjectSetName((PetscObject)b, "Right hand side");

 81:   VecSet(b, 1.0);
 82:   VecSetValue(b, 0, 1.2, ADD_VALUES);
 83:   VecSet(u, 0.0);

 85:   /* Solve linear system */
 86:   KSPCreate(PETSC_COMM_WORLD, &ksp);
 87:   KSPSetOperators(ksp, C, C);
 88:   KSPSetFromOptions(ksp);
 89:   KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);

 91:   MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, NULL, &nullsp);
 92:   /*
 93:      The KSP solver will remove this nullspace from the solution at each iteration
 94:   */
 95:   MatSetNullSpace(C, nullsp);
 96:   /*
 97:      The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
 98:   */
 99:   MatSetTransposeNullSpace(C, nullsp);
100:   MatNullSpaceDestroy(&nullsp);

102:   KSPSolve(ksp, b, u);

104:   /* Free work space */
105:   KSPDestroy(&ksp);
106:   VecDestroy(&u);
107:   VecDestroy(&b);
108:   MatDestroy(&C);
109:   PetscFinalize();
110:   return 0;
111: }

113: /*TEST

115:     test:
116:       args: -ksp_monitor_short

118: TEST*/