Date: 2013-07-02T14:48:38+00:00

Actual source code: ex3.c
petsc-3.4.2 2013-07-02

      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: /*T
      8:    Concepts: KSP^basic parallel example
      9:    Concepts: Matrices^inserting elements by blocks
     10:    Processors: n
     11: T*/

     13: /*
     14:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     15:   automatically includes:
     16:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     17:      petscmat.h - matrices
     18:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     19:      petscviewer.h - viewers               petscpc.h  - preconditioners
     20: */
     21: #include <petscksp.h>

     23: /* Declare user-defined routines */
     24: extern PetscErrorCode FormElementStiffness(PetscReal,PetscScalar*);
     25: extern PetscErrorCode FormElementRhs(PetscReal,PetscReal,PetscReal,PetscScalar*);

     29: int main(int argc,char **args)
     30: {
     31:   Vec            u,b,ustar; /* approx solution, RHS, exact solution */
     32:   Mat            A;           /* linear system matrix */
     33:   KSP            ksp;         /* Krylov subspace method context */
     34:   PetscInt       N;           /* dimension of system (global) */
     35:   PetscInt       M;           /* number of elements (global) */
     36:   PetscMPIInt    rank;        /* processor rank */
     37:   PetscMPIInt    size;        /* size of communicator */
     38:   PetscScalar    Ke[16];      /* element matrix */
     39:   PetscScalar    r[4];        /* element vector */
     40:   PetscReal      h;           /* mesh width */
     41:   PetscReal      norm;        /* norm of solution error */
     42:   PetscReal      x,y;
     43:   PetscScalar    val;
     45:   PetscInt       idx[4],count,*rows,i,m = 5,start,end,its;

     47:   PetscInitialize(&argc,&args,(char*)0,help);
     48:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
     49:   N    = (m+1)*(m+1);
     50:   M    = m*m;
     51:   h    = 1.0/m;
     52:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     53:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     56:          Compute the matrix and right-hand-side vector that define
     57:          the linear system, Au = b.
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     60:   /*
     61:      Create stiffness matrix
     62:   */
     63:   MatCreate(PETSC_COMM_WORLD,&A);
     64:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     65:   MatSetFromOptions(A);
     66:   MatSeqAIJSetPreallocation(A,9,NULL);
     67:   MatMPIAIJSetPreallocation(A,9,NULL,5,NULL); /* More than necessary */
     68:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
     69:   end   = start + M/size + ((M%size) > rank);

     71:   /*
     72:      Assemble matrix
     73:   */
     74:   FormElementStiffness(h*h,Ke);
     75:   for (i=start; i<end; i++) {
     76:     /* location of lower left corner of element */
     77:     x = h*(i % m); y = h*(i/m);
     78:     /* node numbers for the four corners of element */
     79:     idx[0] = (m+1)*(i/m) + (i % m);
     80:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
     81:     MatSetValues(A,4,idx,4,idx,Ke,ADD_VALUES);
     82:   }
     83:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     86:   /*
     87:      Create right-hand-side and solution vectors
     88:   */
     89:   VecCreate(PETSC_COMM_WORLD,&u);
     90:   VecSetSizes(u,PETSC_DECIDE,N);
     91:   VecSetFromOptions(u);
     92:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
     93:   VecDuplicate(u,&b);
     94:   PetscObjectSetName((PetscObject)b,"Right hand side");
     95:   VecDuplicate(b,&ustar);
     96:   VecSet(u,0.0);
     97:   VecSet(b,0.0);

     99:   /*
    100:      Assemble right-hand-side vector
    101:   */
    102:   for (i=start; i<end; i++) {
    103:     /* location of lower left corner of element */
    104:     x = h*(i % m); y = h*(i/m);
    105:     /* node numbers for the four corners of element */
    106:     idx[0] = (m+1)*(i/m) + (i % m);
    107:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
    108:     FormElementRhs(x,y,h*h,r);
    109:     VecSetValues(b,4,idx,r,ADD_VALUES);
    110:   }
    111:   VecAssemblyBegin(b);
    112:   VecAssemblyEnd(b);

    114:   /*
    115:      Modify matrix and right-hand-side for Dirichlet boundary conditions
    116:   */
    117:   PetscMalloc(4*m*sizeof(PetscInt),&rows);
    118:   for (i=0; i<m+1; i++) {
    119:     rows[i] = i; /* bottom */
    120:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
    121:   }
    122:   count = m+1; /* left side */
    123:   for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
    124:   count = 2*m; /* left side */
    125:   for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
    126:   for (i=0; i<4*m; i++) {
    127:     x    = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
    128:     val  = y;
    129:     VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
    130:     VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
    131:   }
    132:   MatZeroRows(A,4*m,rows,1.0,0,0);
    133:   PetscFree(rows);

    135:   VecAssemblyBegin(u);
    136:   VecAssemblyEnd(u);
    137:   VecAssemblyBegin(b);
    138:   VecAssemblyEnd(b);

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:                 Create the linear solver and set various options
    142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    144:   KSPCreate(PETSC_COMM_WORLD,&ksp);
    145:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
    146:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
    147:   KSPSetFromOptions(ksp);

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:                       Solve the linear system
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    153:   KSPSolve(ksp,b,u);

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:                       Check solution and clean up
    157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    159:   /* Check error */
    160:   VecGetOwnershipRange(ustar,&start,&end);
    161:   for (i=start; i<end; i++) {
    162:     x    = h*(i % (m+1)); y = h*(i/(m+1));
    163:     val  = y;
    164:     VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
    165:   }
    166:   VecAssemblyBegin(ustar);
    167:   VecAssemblyEnd(ustar);
    168:   VecAXPY(u,-1.0,ustar);
    169:   VecNorm(u,NORM_2,&norm);
    170:   KSPGetIterationNumber(ksp,&its);
    171:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G Iterations %D\n",norm*h,its);

    173:   /*
    174:      Free work space.  All PETSc objects should be destroyed when they
    175:      are no longer needed.
    176:   */
    177:   KSPDestroy(&ksp); VecDestroy(&u);
    178:   VecDestroy(&ustar); VecDestroy(&b);
    179:   MatDestroy(&A);

    181:   /*
    182:      Always call PetscFinalize() before exiting a program.  This routine
    183:        - finalizes the PETSc libraries as well as MPI
    184:        - provides summary and diagnostic information if certain runtime
    185:          options are chosen (e.g., -log_summary).
    186:   */
    187:   PetscFinalize();
    188:   return 0;
    189: }

    191: /* --------------------------------------------------------------------- */
    194: /* element stiffness for Laplacian */
    195: PetscErrorCode FormElementStiffness(PetscReal H,PetscScalar *Ke)
    196: {
    198:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
    199:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
    200:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
    201:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
    202:   return(0);
    203: }
    204: /* --------------------------------------------------------------------- */
    207: PetscErrorCode FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
    208: {
    210:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
    211:   return(0);
    212: }