Date: 2022-08-02T03:14:46+00:00

Actual source code: ex12.c

      2: static char help[] = "Solves a linear system in parallel with KSP,\n\
      3: demonstrating how to register a new preconditioner (PC) type.\n\
      4: Input parameters include:\n\
      5:   -m <mesh_x>       : number of mesh points in x-direction\n\
      6:   -n <mesh_y>       : number of mesh points in y-direction\n\n";

      8: /*
      9:    Demonstrates registering a new preconditioner (PC) type.

     11:    To register a PC type whose code is linked into the executable,
     12:    use PCRegister(). To register a PC type in a dynamic library use PCRegister()

     14:    Also provide the prototype for your PCCreate_XXX() function. In
     15:    this example we use the PETSc implementation of the Jacobi method,
     16:    PCCreate_Jacobi() just as an example.

     18:    See the file src/ksp/pc/impls/jacobi/jacobi.c for details on how to
     19:    write a new PC component.

     21:    See the manual page PCRegister() for details on how to register a method.
     22: */

     24: /*
     25:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     26:   automatically includes:
     27:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     28:      petscmat.h - matrices
     29:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     30:      petscviewer.h - viewers               petscpc.h  - preconditioners
     31: */
     32: #include <petscksp.h>

     34: PETSC_EXTERN PetscErrorCode PCCreate_Jacobi(PC);

     36: int main(int argc,char **args)
     37: {
     38:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
     39:   Mat            A;        /* linear system matrix */
     40:   KSP            ksp;     /* linear solver context */
     41:   PetscReal      norm;     /* norm of solution error */
     42:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
     43:   PetscScalar    v,one = 1.0;
     44:   PC             pc;      /* preconditioner context */

     46:   PetscInitialize(&argc,&args,(char*)0,help);
     47:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     48:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:          Compute the matrix and right-hand-side vector that define
     52:          the linear system, Ax = b.
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     54:   /*
     55:      Create parallel matrix, specifying only its global dimensions.
     56:      When using MatCreate(), the matrix format can be specified at
     57:      runtime. Also, the parallel partitioning of the matrix can be
     58:      determined by PETSc at runtime.
     59:   */
     60:   MatCreate(PETSC_COMM_WORLD,&A);
     61:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     62:   MatSetFromOptions(A);
     63:   MatSetUp(A);

     65:   /*
     66:      Currently, all PETSc parallel matrix formats are partitioned by
     67:      contiguous chunks of rows across the processors.  Determine which
     68:      rows of the matrix are locally owned.
     69:   */
     70:   MatGetOwnershipRange(A,&Istart,&Iend);

     72:   /*
     73:      Set matrix elements for the 2-D, five-point stencil in parallel.
     74:       - Each processor needs to insert only elements that it owns
     75:         locally (but any non-local elements will be sent to the
     76:         appropriate processor during matrix assembly).
     77:       - Always specify global rows and columns of matrix entries.
     78:    */
     79:   for (Ii=Istart; Ii<Iend; Ii++) {
     80:     v = -1.0; i = Ii/n; j = Ii - i*n;
     81:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     82:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     83:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     84:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     85:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     86:   }

     88:   /*
     89:      Assemble matrix, using the 2-step process:
     90:        MatAssemblyBegin(), MatAssemblyEnd()
     91:      Computations can be done while messages are in transition
     92:      by placing code between these two statements.
     93:   */
     94:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     95:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     97:   /*
     98:      Create parallel vectors.
     99:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
    100:       we specify only the vector's global
    101:         dimension; the parallel partitioning is determined at runtime.
    102:       - When solving a linear system, the vectors and matrices MUST
    103:         be partitioned accordingly.  PETSc automatically generates
    104:         appropriately partitioned matrices and vectors when MatCreate()
    105:         and VecCreate() are used with the same communicator.
    106:       - Note: We form 1 vector from scratch and then duplicate as needed.
    107:   */
    108:   VecCreate(PETSC_COMM_WORLD,&u);
    109:   VecSetSizes(u,PETSC_DECIDE,m*n);
    110:   VecSetFromOptions(u);
    111:   VecDuplicate(u,&b);
    112:   VecDuplicate(b,&x);

    114:   /*
    115:      Set exact solution; then compute right-hand-side vector.
    116:      Use an exact solution of a vector with all elements of 1.0;
    117:   */
    118:   VecSet(u,one);
    119:   MatMult(A,u,b);

    121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    122:                 Create the linear solver and set various options
    123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    125:   /*
    126:      Create linear solver context
    127:   */
    128:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    130:   /*
    131:      Set operators. Here the matrix that defines the linear system
    132:      also serves as the preconditioning matrix.
    133:   */
    134:   KSPSetOperators(ksp,A,A);

    136:   /*
    137:        First register a new PC type with the command PCRegister()
    138:   */
    139:   PCRegister("ourjacobi",PCCreate_Jacobi);

    141:   /*
    142:      Set the PC type to be the new method
    143:   */
    144:   KSPGetPC(ksp,&pc);
    145:   PCSetType(pc,"ourjacobi");

    147:   /*
    148:     Set runtime options, e.g.,
    149:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    150:     These options will override those specified above as long as
    151:     KSPSetFromOptions() is called _after_ any other customization
    152:     routines.
    153:   */
    154:   KSPSetFromOptions(ksp);

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:                       Solve the linear system
    158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    160:   KSPSolve(ksp,b,x);

    162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    163:                       Check solution and clean up
    164:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    166:   /*
    167:      Check the error
    168:   */
    169:   VecAXPY(x,-1.0,u);
    170:   VecNorm(x,NORM_2,&norm);
    171:   KSPGetIterationNumber(ksp,&its);

    173:   /*
    174:      Print convergence information.  PetscPrintf() produces a single
    175:      print statement from all processes that share a communicator.
    176:   */
    177:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

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

    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 0;
    195: }

    197: /*TEST

    199:    test:
    200:       args: -ksp_gmres_cgs_refinement_type refine_always

    202: TEST*/