Actual source code: ex20.c

petsc-3.12.0 2019-09-29
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  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;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
 12:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
 13:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
 14:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
 15:   return 0;
 16: }

 18: int main(int argc,char **args)
 19: {
 21:   Mat            C;
 22:   PetscMPIInt    rank,size;
 23:   PetscInt       i,m = 5,N,start,end,M;
 24:   PetscInt       idx[4];
 25:   PetscScalar    Ke[16];
 26:   PetscReal      h;
 27:   Vec            u,b;
 28:   KSP            ksp;
 29:   MatNullSpace   nullsp;

 31:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 33:   N    = (m+1)*(m+1); /* dimension of matrix */
 34:   M    = m*m; /* number of elements */
 35:   h    = 1.0/m;    /* mesh width */
 36:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 37:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 39:   /* Create stiffness matrix */
 40:   MatCreate(PETSC_COMM_WORLD,&C);
 41:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 42:   MatSetFromOptions(C);
 43:   MatSetUp(C);
 44:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 45:   end   = start + M/size + ((M%size) > rank);

 47:   /* Assemble matrix */
 48:   FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
 49:   for (i=start; i<end; i++) {
 50:     /* location of lower left corner of element */
 51:     /* node numbers for the four corners of element */
 52:     idx[0] = (m+1)*(i/m) + (i % m);
 53:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 54:     MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
 55:   }
 56:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 57:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 59:   /* Create right-hand-side and solution vectors */
 60:   VecCreate(PETSC_COMM_WORLD,&u);
 61:   VecSetSizes(u,PETSC_DECIDE,N);
 62:   VecSetFromOptions(u);
 63:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 64:   VecDuplicate(u,&b);
 65:   PetscObjectSetName((PetscObject)b,"Right hand side");

 67:   VecSet(b,1.0);
 68:   VecSetValue(b,0,1.2,ADD_VALUES);
 69:   VecSet(u,0.0);

 71:   /* Solve linear system */
 72:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 73:   KSPSetOperators(ksp,C,C);
 74:   KSPSetFromOptions(ksp);
 75:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);

 77:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);
 78:   /*
 79:      The KSP solver will remove this nullspace from the solution at each iteration
 80:   */
 81:   MatSetNullSpace(C,nullsp);
 82:   /*
 83:      The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
 84:   */
 85:   MatSetTransposeNullSpace(C,nullsp);
 86:   MatNullSpaceDestroy(&nullsp);

 88:   KSPSolve(ksp,b,u);


 91:   /* Free work space */
 92:   KSPDestroy(&ksp);
 93:   VecDestroy(&u);
 94:   VecDestroy(&b);
 95:   MatDestroy(&C);
 96:   PetscFinalize();
 97:   return ierr;
 98: }

100: /*TEST

102:     test:
103:       args: -ksp_monitor_short

105: TEST*/