Date: 2022-03-31T04:48:19+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: /*T
      9:    Concepts: KSP^solving a system of linear equations
     10:    Concepts: KSP^Laplacian, 2d
     11:    Concepts: PC^registering preconditioners
     12:    Processors: n
     13: T*/

     15: /*
     16:    Demonstrates registering a new preconditioner (PC) type.

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

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

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

     28:    See the manual page PCRegister() for details on how to register a method.
     29: */

     31: /*
     32:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     33:   automatically includes:
     34:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     35:      petscmat.h - matrices
     36:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     37:      petscviewer.h - viewers               petscpc.h  - preconditioners
     38: */
     39: #include <petscksp.h>

     41: PETSC_EXTERN PetscErrorCode PCCreate_Jacobi(PC);

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

     53:   PetscInitialize(&argc,&args,(char*)0,help);
     54:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     55:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:          Compute the matrix and right-hand-side vector that define
     59:          the linear system, Ax = b.
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     61:   /*
     62:      Create parallel matrix, specifying only its global dimensions.
     63:      When using MatCreate(), the matrix format can be specified at
     64:      runtime. Also, the parallel partitioning of the matrix can be
     65:      determined by PETSc at runtime.
     66:   */
     67:   MatCreate(PETSC_COMM_WORLD,&A);
     68:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     69:   MatSetFromOptions(A);
     70:   MatSetUp(A);

     72:   /*
     73:      Currently, all PETSc parallel matrix formats are partitioned by
     74:      contiguous chunks of rows across the processors.  Determine which
     75:      rows of the matrix are locally owned.
     76:   */
     77:   MatGetOwnershipRange(A,&Istart,&Iend);

     79:   /*
     80:      Set matrix elements for the 2-D, five-point stencil in parallel.
     81:       - Each processor needs to insert only elements that it owns
     82:         locally (but any non-local elements will be sent to the
     83:         appropriate processor during matrix assembly).
     84:       - Always specify global rows and columns of matrix entries.
     85:    */
     86:   for (Ii=Istart; Ii<Iend; Ii++) {
     87:     v = -1.0; i = Ii/n; j = Ii - i*n;
     88:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     89:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     90:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     91:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     92:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     93:   }

     95:   /*
     96:      Assemble matrix, using the 2-step process:
     97:        MatAssemblyBegin(), MatAssemblyEnd()
     98:      Computations can be done while messages are in transition
     99:      by placing code between these two statements.
    100:   */
    101:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    102:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    104:   /*
    105:      Create parallel vectors.
    106:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
    107:       we specify only the vector's global
    108:         dimension; the parallel partitioning is determined at runtime.
    109:       - When solving a linear system, the vectors and matrices MUST
    110:         be partitioned accordingly.  PETSc automatically generates
    111:         appropriately partitioned matrices and vectors when MatCreate()
    112:         and VecCreate() are used with the same communicator.
    113:       - Note: We form 1 vector from scratch and then duplicate as needed.
    114:   */
    115:   VecCreate(PETSC_COMM_WORLD,&u);
    116:   VecSetSizes(u,PETSC_DECIDE,m*n);
    117:   VecSetFromOptions(u);
    118:   VecDuplicate(u,&b);
    119:   VecDuplicate(b,&x);

    121:   /*
    122:      Set exact solution; then compute right-hand-side vector.
    123:      Use an exact solution of a vector with all elements of 1.0;
    124:   */
    125:   VecSet(u,one);
    126:   MatMult(A,u,b);

    128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    129:                 Create the linear solver and set various options
    130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    132:   /*
    133:      Create linear solver context
    134:   */
    135:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    137:   /*
    138:      Set operators. Here the matrix that defines the linear system
    139:      also serves as the preconditioning matrix.
    140:   */
    141:   KSPSetOperators(ksp,A,A);

    143:   /*
    144:        First register a new PC type with the command PCRegister()
    145:   */
    146:   PCRegister("ourjacobi",PCCreate_Jacobi);

    148:   /*
    149:      Set the PC type to be the new method
    150:   */
    151:   KSPGetPC(ksp,&pc);
    152:   PCSetType(pc,"ourjacobi");

    154:   /*
    155:     Set runtime options, e.g.,
    156:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    157:     These options will override those specified above as long as
    158:     KSPSetFromOptions() is called _after_ any other customization
    159:     routines.
    160:   */
    161:   KSPSetFromOptions(ksp);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:                       Solve the linear system
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    167:   KSPSolve(ksp,b,x);

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:                       Check solution and clean up
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    173:   /*
    174:      Check the error
    175:   */
    176:   VecAXPY(x,-1.0,u);
    177:   VecNorm(x,NORM_2,&norm);
    178:   KSPGetIterationNumber(ksp,&its);

    180:   /*
    181:      Print convergence information.  PetscPrintf() produces a single
    182:      print statement from all processes that share a communicator.
    183:   */
    184:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    186:   /*
    187:      Free work space.  All PETSc objects should be destroyed when they
    188:      are no longer needed.
    189:   */
    190:   KSPDestroy(&ksp);
    191:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
    192:   VecDestroy(&b));  PetscCall(MatDestroy(&A);

    194:   /*
    195:      Always call PetscFinalize() before exiting a program.  This routine
    196:        - finalizes the PETSc libraries as well as MPI
    197:        - provides summary and diagnostic information if certain runtime
    198:          options are chosen (e.g., -log_view).
    199:   */
    200:   PetscFinalize();
    201:   return 0;
    202: }

    204: /*TEST

    206:    test:
    207:       args: -ksp_gmres_cgs_refinement_type refine_always

    209: TEST*/