Date: 2022-03-31T04:48:20+00:00

Actual source code: ex23.c

      2: static char help[] = "Solves a tridiagonal linear system.\n\n";

      4: /*T
      5:    Concepts: KSP^basic parallel example;
      6:    Processors: n
      7: T*/

      9: /*
     10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     11:   automatically includes:
     12:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     13:      petscmat.h - matrices
     14:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     15:      petscviewer.h - viewers               petscpc.h  - preconditioners

     17:   Note:  The corresponding uniprocessor example is ex1.c
     18: */
     19: #include <petscksp.h>

     21: int main(int argc,char **args)
     22: {
     23:   Vec            x, b, u;          /* approx solution, RHS, exact solution */
     24:   Mat            A;                /* linear system matrix */
     25:   KSP            ksp;              /* linear solver context */
     26:   PC             pc;               /* preconditioner context */
     27:   PetscReal      norm,tol=1000.*PETSC_MACHINE_EPSILON;  /* norm of solution error */
     28:   PetscInt       i,n = 10,col[3],its,rstart,rend,nlocal;
     29:   PetscScalar    one = 1.0,value[3];

     31:   PetscInitialize(&argc,&args,(char*)0,help);
     32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35:          Compute the matrix and right-hand-side vector that define
     36:          the linear system, Ax = b.
     37:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     39:   /*
     40:      Create vectors.  Note that we form 1 vector from scratch and
     41:      then duplicate as needed. For this simple case let PETSc decide how
     42:      many elements of the vector are stored on each processor. The second
     43:      argument to VecSetSizes() below causes PETSc to decide.
     44:   */
     45:   VecCreate(PETSC_COMM_WORLD,&x);
     46:   VecSetSizes(x,PETSC_DECIDE,n);
     47:   VecSetFromOptions(x);
     48:   VecDuplicate(x,&b);
     49:   VecDuplicate(x,&u);

     51:   /* Identify the starting and ending mesh points on each
     52:      processor for the interior part of the mesh. We let PETSc decide
     53:      above. */

     55:   VecGetOwnershipRange(x,&rstart,&rend);
     56:   VecGetLocalSize(x,&nlocal);

     58:   /*
     59:      Create matrix.  When using MatCreate(), the matrix format can
     60:      be specified at runtime.

     62:      Performance tuning note:  For problems of substantial size,
     63:      preallocation of matrix memory is crucial for attaining good
     64:      performance. See the matrix chapter of the users manual for details.

     66:      We pass in nlocal as the "local" size of the matrix to force it
     67:      to have the same parallel layout as the vector created above.
     68:   */
     69:   MatCreate(PETSC_COMM_WORLD,&A);
     70:   MatSetSizes(A,nlocal,nlocal,n,n);
     71:   MatSetFromOptions(A);
     72:   MatSetUp(A);

     74:   /*
     75:      Assemble matrix.

     77:      The linear system is distributed across the processors by
     78:      chunks of contiguous rows, which correspond to contiguous
     79:      sections of the mesh on which the problem is discretized.
     80:      For matrix assembly, each processor contributes entries for
     81:      the part that it owns locally.
     82:   */

     84:   if (!rstart) {
     85:     rstart = 1;
     86:     i      = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     87:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     88:   }
     89:   if (rend == n) {
     90:     rend = n-1;
     91:     i    = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
     92:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     93:   }

     95:   /* Set entries corresponding to the mesh interior */
     96:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
     97:   for (i=rstart; i<rend; i++) {
     98:     col[0] = i-1; col[1] = i; col[2] = i+1;
     99:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
    100:   }

    102:   /* Assemble the matrix */
    103:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    104:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    106:   /*
    107:      Set exact solution; then compute right-hand-side vector.
    108:   */
    109:   VecSet(u,one);
    110:   MatMult(A,u,b);

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                 Create the linear solver and set various options
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    115:   /*
    116:      Create linear solver context
    117:   */
    118:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    120:   /*
    121:      Set operators. Here the matrix that defines the linear system
    122:      also serves as the preconditioning matrix.
    123:   */
    124:   KSPSetOperators(ksp,A,A);

    126:   /*
    127:      Set linear solver defaults for this problem (optional).
    128:      - By extracting the KSP and PC contexts from the KSP context,
    129:        we can then directly call any KSP and PC routines to set
    130:        various options.
    131:      - The following four statements are optional; all of these
    132:        parameters could alternatively be specified at runtime via
    133:        KSPSetFromOptions();
    134:   */
    135:   KSPGetPC(ksp,&pc);
    136:   PCSetType(pc,PCJACOBI);
    137:   KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    139:   /*
    140:     Set runtime options, e.g.,
    141:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    142:     These options will override those specified above as long as
    143:     KSPSetFromOptions() is called _after_ any other customization
    144:     routines.
    145:   */
    146:   KSPSetFromOptions(ksp);

    148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:                       Solve the linear system
    150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    151:   /*
    152:      Solve linear system
    153:   */
    154:   KSPSolve(ksp,b,x);

    156:   /*
    157:      View solver info; we could instead use the option -ksp_view to
    158:      print this info to the screen at the conclusion of KSPSolve().
    159:   */
    160:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

    162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    163:                       Check solution and clean up
    164:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    165:   /*
    166:      Check the error
    167:   */
    168:   VecAXPY(x,-1.0,u);
    169:   VecNorm(x,NORM_2,&norm);
    170:   KSPGetIterationNumber(ksp,&its);
    171:   if (norm > tol) {
    172:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    173:   }

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

    183:   /*
    184:      Always call PetscFinalize() before exiting a program.  This routine
    185:        - finalizes the PETSc libraries as well as MPI
    186:        - provides summary and diagnostic information if certain runtime
    187:          options are chosen (e.g., -log_view).
    188:   */
    189:   PetscFinalize();
    190:   return 0;
    191: }

    193: /*TEST

    195:    build:
    196:       requires: !complex !single

    198:    test:
    199:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    201:    test:
    202:       suffix: 2
    203:       nsize: 3
    204:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    206:    test:
    207:       suffix: 3
    208:       nsize: 2
    209:       args: -ksp_monitor_short -ksp_rtol 1e-6 -ksp_type pipefgmres

    211: TEST*/