Date: 2021-03-03T22:27:32+00:00

Actual source code: ex23.c
petsc-3.14.5 2021-03-03
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      2: static char help[] = "Solves a tridiagonal linear system.\n\n";

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

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

     19:   Note:  The corresponding uniprocessor example is ex1.c
     20: */
     21: #include <petscksp.h>

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

     34:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     35:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     38:          Compute the matrix and right-hand-side vector that define
     39:          the linear system, Ax = b.
     40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     54:   /* Identify the starting and ending mesh points on each
     55:      processor for the interior part of the mesh. We let PETSc decide
     56:      above. */

     58:   VecGetOwnershipRange(x,&rstart,&rend);
     59:   VecGetLocalSize(x,&nlocal);

     61:   /*
     62:      Create matrix.  When using MatCreate(), the matrix format can
     63:      be specified at runtime.

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

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

     77:   /*
     78:      Assemble matrix.

     80:      The linear system is distributed across the processors by
     81:      chunks of contiguous rows, which correspond to contiguous
     82:      sections of the mesh on which the problem is discretized.
     83:      For matrix assembly, each processor contributes entries for
     84:      the part that it owns locally.
     85:   */

     88:   if (!rstart) {
     89:     rstart = 1;
     90:     i      = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
     91:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     92:   }
     93:   if (rend == n) {
     94:     rend = n-1;
     95:     i    = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
     96:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
     97:   }

     99:   /* Set entries corresponding to the mesh interior */
    100:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
    101:   for (i=rstart; i<rend; i++) {
    102:     col[0] = i-1; col[1] = i; col[2] = i+1;
    103:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
    104:   }

    106:   /* Assemble the matrix */
    107:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    108:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    110:   /*
    111:      Set exact solution; then compute right-hand-side vector.
    112:   */
    113:   VecSet(u,one);
    114:   MatMult(A,u,b);

    116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    117:                 Create the linear solver and set various options
    118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    119:   /*
    120:      Create linear solver context
    121:   */
    122:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    124:   /*
    125:      Set operators. Here the matrix that defines the linear system
    126:      also serves as the preconditioning matrix.
    127:   */
    128:   KSPSetOperators(ksp,A,A);

    130:   /*
    131:      Set linear solver defaults for this problem (optional).
    132:      - By extracting the KSP and PC contexts from the KSP context,
    133:        we can then directly call any KSP and PC routines to set
    134:        various options.
    135:      - The following four statements are optional; all of these
    136:        parameters could alternatively be specified at runtime via
    137:        KSPSetFromOptions();
    138:   */
    139:   KSPGetPC(ksp,&pc);
    140:   PCSetType(pc,PCJACOBI);
    141:   KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

    143:   /*
    144:     Set runtime options, e.g.,
    145:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    146:     These options will override those specified above as long as
    147:     KSPSetFromOptions() is called _after_ any other customization
    148:     routines.
    149:   */
    150:   KSPSetFromOptions(ksp);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                       Solve the linear system
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    155:   /*
    156:      Solve linear system
    157:   */
    158:   KSPSolve(ksp,b,x);

    160:   /*
    161:      View solver info; we could instead use the option -ksp_view to
    162:      print this info to the screen at the conclusion of KSPSolve().
    163:   */
    164:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:                       Check solution and clean up
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    169:   /*
    170:      Check the error
    171:   */
    172:   VecAXPY(x,-1.0,u);
    173:   VecNorm(x,NORM_2,&norm);
    174:   KSPGetIterationNumber(ksp,&its);
    175:   if (norm > tol) {
    176:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
    177:   }

    179:   /*
    180:      Free work space.  All PETSc objects should be destroyed when they
    181:      are no longer needed.
    182:   */
    183:   VecDestroy(&x); VecDestroy(&u);
    184:   VecDestroy(&b); MatDestroy(&A);
    185:   KSPDestroy(&ksp);

    187:   /*
    188:      Always call PetscFinalize() before exiting a program.  This routine
    189:        - finalizes the PETSc libraries as well as MPI
    190:        - provides summary and diagnostic information if certain runtime
    191:          options are chosen (e.g., -log_view).
    192:   */
    193:   PetscFinalize();
    194:   return ierr;
    195: }

    198: /*TEST

    200:    build:
    201:       requires: !complex !single

    203:    test:
    204:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    206:    test:
    207:       suffix: 2
    208:       nsize: 3
    209:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    211:    test:
    212:       suffix: 3
    213:       nsize: 2
    214:       args: -ksp_monitor_short -ksp_rtol 1e-6 -ksp_type pipefgmres

    216: TEST*/