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

Actual source code: ex2.c

      2: static char help[] = "Solves a linear system in parallel with KSP.\n\
      3: Input parameters include:\n\
      4:   -view_exact_sol   : write exact solution vector to stdout\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:   Include "petscksp.h" so that we can use KSP solvers.
     10: */
     11: #include <petscksp.h>

     13: int main(int argc,char **args)
     14: {
     15:   Vec            x,b,u;    /* approx solution, RHS, exact solution */
     16:   Mat            A;        /* linear system matrix */
     17:   KSP            ksp;      /* linear solver context */
     18:   PetscReal      norm;     /* norm of solution error */
     19:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
     20:   PetscBool      flg;
     21:   PetscScalar    v;

     23:   PetscInitialize(&argc,&args,(char*)0,help);
     24:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     25:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     26:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     27:          Compute the matrix and right-hand-side vector that define
     28:          the linear system, Ax = b.
     29:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     30:   /*
     31:      Create parallel matrix, specifying only its global dimensions.
     32:      When using MatCreate(), the matrix format can be specified at
     33:      runtime. Also, the parallel partitioning of the matrix is
     34:      determined by PETSc at runtime.

     36:      Performance tuning note:  For problems of substantial size,
     37:      preallocation of matrix memory is crucial for attaining good
     38:      performance. See the matrix chapter of the users manual for details.
     39:   */
     40:   MatCreate(PETSC_COMM_WORLD,&A);
     41:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     42:   MatSetFromOptions(A);
     43:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     44:   MatSeqAIJSetPreallocation(A,5,NULL);
     45:   MatSeqSBAIJSetPreallocation(A,1,5,NULL);
     46:   MatMPISBAIJSetPreallocation(A,1,5,NULL,5,NULL);
     47:   MatMPISELLSetPreallocation(A,5,NULL,5,NULL);
     48:   MatSeqSELLSetPreallocation(A,5,NULL);

     50:   /*
     51:      Currently, all PETSc parallel matrix formats are partitioned by
     52:      contiguous chunks of rows across the processors.  Determine which
     53:      rows of the matrix are locally owned.
     54:   */
     55:   MatGetOwnershipRange(A,&Istart,&Iend);

     57:   /*
     58:      Set matrix elements for the 2-D, five-point stencil in parallel.
     59:       - Each processor needs to insert only elements that it owns
     60:         locally (but any non-local elements will be sent to the
     61:         appropriate processor during matrix assembly).
     62:       - Always specify global rows and columns of matrix entries.

     64:      Note: this uses the less common natural ordering that orders first
     65:      all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
     66:      instead of J = I +- m as you might expect. The more standard ordering
     67:      would first do all variables for y = h, then y = 2h etc.

     69:    */
     70:   for (Ii=Istart; Ii<Iend; Ii++) {
     71:     v = -1.0; i = Ii/n; j = Ii - i*n;
     72:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     73:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     74:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     75:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     76:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
     77:   }

     79:   /*
     80:      Assemble matrix, using the 2-step process:
     81:        MatAssemblyBegin(), MatAssemblyEnd()
     82:      Computations can be done while messages are in transition
     83:      by placing code between these two statements.
     84:   */
     85:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     86:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     88:   /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
     89:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

     91:   /*
     92:      Create parallel vectors.
     93:       - We form 1 vector from scratch and then duplicate as needed.
     94:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
     95:         in this example, we specify only the
     96:         vector's global dimension; the parallel partitioning is determined
     97:         at runtime.
     98:       - When solving a linear system, the vectors and matrices MUST
     99:         be partitioned accordingly.  PETSc automatically generates
    100:         appropriately partitioned matrices and vectors when MatCreate()
    101:         and VecCreate() are used with the same communicator.
    102:       - The user can alternatively specify the local vector and matrix
    103:         dimensions when more sophisticated partitioning is needed
    104:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
    105:         below).
    106:   */
    107:   VecCreate(PETSC_COMM_WORLD,&u);
    108:   VecSetSizes(u,PETSC_DECIDE,m*n);
    109:   VecSetFromOptions(u);
    110:   VecDuplicate(u,&b);
    111:   VecDuplicate(b,&x);

    113:   /*
    114:      Set exact solution; then compute right-hand-side vector.
    115:      By default we use an exact solution of a vector with all
    116:      elements of 1.0;
    117:   */
    118:   VecSet(u,1.0);
    119:   MatMult(A,u,b);

    121:   /*
    122:      View the exact solution vector if desired
    123:   */
    124:   flg  = PETSC_FALSE;
    125:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
    126:   if (flg) VecView(u,PETSC_VIEWER_STDOUT_WORLD);

    128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    129:                 Create the linear solver and set various options
    130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    131:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    133:   /*
    134:      Set operators. Here the matrix that defines the linear system
    135:      also serves as the preconditioning matrix.
    136:   */
    137:   KSPSetOperators(ksp,A,A);

    139:   /*
    140:      Set linear solver defaults for this problem (optional).
    141:      - By extracting the KSP and PC contexts from the KSP context,
    142:        we can then directly call any KSP and PC routines to set
    143:        various options.
    144:      - The following two statements are optional; all of these
    145:        parameters could alternatively be specified at runtime via
    146:        KSPSetFromOptions().  All of these defaults can be
    147:        overridden at runtime, as indicated below.
    148:   */
    149:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,PETSC_DEFAULT);

    151:   /*
    152:     Set runtime options, e.g.,
    153:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    154:     These options will override those specified above as long as
    155:     KSPSetFromOptions() is called _after_ any other customization
    156:     routines.
    157:   */
    158:   KSPSetFromOptions(ksp);

    160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    161:                       Solve the linear system
    162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    164:   KSPSolve(ksp,b,x);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:                       Check the solution and clean up
    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:      An alternative is PetscFPrintf(), which prints to a file.
    177:   */
    178:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

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

    188:   /*
    189:      Always call PetscFinalize() before exiting a program.  This routine
    190:        - finalizes the PETSc libraries as well as MPI
    191:        - provides summary and diagnostic information if certain runtime
    192:          options are chosen (e.g., -log_view).
    193:   */
    194:   PetscFinalize();
    195:   return 0;
    196: }

    198: /*TEST

    200:    build:
    201:       requires: !single

    203:    test:
    204:       suffix: chebyest_1
    205:       args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_monitor_short

    207:    test:
    208:       suffix: chebyest_2
    209:       args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_esteig_ksp_type cg -ksp_monitor_short

    211:    test:
    212:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

    214:    test:
    215:       suffix: 2
    216:       nsize: 2
    217:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

    219:    test:
    220:       suffix: 3
    221:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    223:    test:
    224:       suffix: 4
    225:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    227:    test:
    228:       suffix: 5
    229:       nsize: 2
    230:       args: -ksp_monitor_short -m 5 -n 5 -mat_view draw -ksp_gmres_cgs_refinement_type refine_always -nox
    231:       output_file: output/ex2_2.out

    233:    test:
    234:       suffix: bjacobi
    235:       nsize: 4
    236:       args: -pc_type bjacobi -pc_bjacobi_blocks 1 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

    238:    test:
    239:       suffix: bjacobi_2
    240:       nsize: 4
    241:       args: -pc_type bjacobi -pc_bjacobi_blocks 2 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres -ksp_view

    243:    test:
    244:       suffix: bjacobi_3
    245:       nsize: 4
    246:       args: -pc_type bjacobi -pc_bjacobi_blocks 4 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

    248:    test:
    249:       suffix: qmrcgs
    250:       args: -ksp_type qmrcgs -pc_type ilu
    251:       output_file: output/ex2_fbcgs.out

    253:    test:
    254:       suffix: qmrcgs_2
    255:       nsize: 3
    256:       args: -ksp_type qmrcgs -pc_type bjacobi
    257:       output_file: output/ex2_fbcgs_2.out

    259:    test:
    260:       suffix: fbcgs
    261:       args: -ksp_type fbcgs -pc_type ilu

    263:    test:
    264:       suffix: fbcgs_2
    265:       nsize: 3
    266:       args: -ksp_type fbcgsr -pc_type bjacobi

    268:    test:
    269:       suffix: groppcg
    270:       args: -ksp_monitor_short -ksp_type groppcg -m 9 -n 9

    272:    test:
    273:       suffix: mkl_pardiso_cholesky
    274:       requires: mkl_pardiso
    275:       args: -ksp_type preonly -pc_type cholesky -mat_type sbaij -pc_factor_mat_solver_type mkl_pardiso

    277:    test:
    278:       suffix: mkl_pardiso_lu
    279:       requires: mkl_pardiso
    280:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mkl_pardiso

    282:    test:
    283:       suffix: pipebcgs
    284:       args: -ksp_monitor_short -ksp_type pipebcgs -m 9 -n 9

    286:    test:
    287:       suffix: pipecg
    288:       args: -ksp_monitor_short -ksp_type pipecg -m 9 -n 9

    290:    test:
    291:       suffix: pipecgrr
    292:       args: -ksp_monitor_short -ksp_type pipecgrr -m 9 -n 9

    294:    test:
    295:       suffix: pipecr
    296:       args: -ksp_monitor_short -ksp_type pipecr -m 9 -n 9

    298:    test:
    299:       suffix: pipelcg
    300:       args: -ksp_monitor_short -ksp_type pipelcg -m 9 -n 9 -pc_type none -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmax 2
    301:       filter: grep -v "sqrt breakdown in iteration"

    303:    test:
    304:       suffix: sell
    305:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -m 9 -n 9 -mat_type sell

    307:    test:
    308:       requires: mumps
    309:       suffix: sell_mumps
    310:       args: -ksp_type preonly -m 9 -n 12 -mat_type sell -pc_type lu -pc_factor_mat_solver_type mumps -pc_factor_mat_ordering_type natural

    312:    test:
    313:       suffix: telescope
    314:       nsize: 4
    315:       args: -m 100 -n 100 -ksp_converged_reason -pc_type telescope -pc_telescope_reduction_factor 4 -telescope_pc_type bjacobi

    317:    test:
    318:       suffix: umfpack
    319:       requires: suitesparse
    320:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type umfpack

    322:    test:
    323:       suffix: spqr
    324:       requires: suitesparse
    325:       args: -ksp_type preonly -pc_type qr -pc_factor_mat_solver_type spqr

    327:    test:
    328:      suffix: pc_symmetric
    329:      args: -m 10 -n 9 -ksp_converged_reason -ksp_type gmres -ksp_pc_side symmetric -pc_type cholesky

    331:    test:
    332:       suffix: pipeprcg
    333:       args: -ksp_monitor_short -ksp_type pipeprcg -m 9 -n 9

    335:    test:
    336:       suffix: pipeprcg_rcw
    337:       args: -ksp_monitor_short -ksp_type pipeprcg -recompute_w false -m 9 -n 9

    339:    test:
    340:       suffix: pipecg2
    341:       args: -ksp_monitor_short -ksp_type pipecg2 -m 9 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

    343:    test:
    344:       suffix: pipecg2_2
    345:       nsize: 4
    346:       args: -ksp_monitor_short -ksp_type pipecg2 -m 15 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

    348:    test:
    349:       suffix: hpddm
    350:       nsize: 4
    351:       requires: hpddm
    352:       filter: sed -e "s/ iterations 9/ iterations 8/g"
    353:       args: -ksp_converged_reason -ksp_type hpddm -ksp_hpddm_precision {{single double}shared output} -ksp_pc_side {{left right}shared output}

    355:  TEST*/