Date: 2022-03-04T17:39:12+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: /*T
      9:    Concepts: KSP^basic parallel example;
     10:    Concepts: KSP^Laplacian, 2d
     11:    Concepts: Laplacian, 2d
     12:    Processors: n
     13: T*/

     15: /*
     16:   Include "petscksp.h" so that we can use KSP solvers.
     17: */
     18: #include <petscksp.h>

     20: int main(int argc,char **args)
     21: {
     22:   Vec            x,b,u;    /* approx solution, RHS, exact solution */
     23:   Mat            A;        /* linear system matrix */
     24:   KSP            ksp;      /* linear solver context */
     25:   PetscReal      norm;     /* norm of solution error */
     26:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
     28:   PetscBool      flg;
     29:   PetscScalar    v;

     31:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     33:   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:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     38:   /*
     39:      Create parallel matrix, specifying only its global dimensions.
     40:      When using MatCreate(), the matrix format can be specified at
     41:      runtime. Also, the parallel partitioning of the matrix is
     42:      determined by PETSc at runtime.

     44:      Performance tuning note:  For problems of substantial size,
     45:      preallocation of matrix memory is crucial for attaining good
     46:      performance. See the matrix chapter of the users manual for details.
     47:   */
     48:   MatCreate(PETSC_COMM_WORLD,&A);
     49:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     50:   MatSetFromOptions(A);
     51:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     52:   MatSeqAIJSetPreallocation(A,5,NULL);
     53:   MatSeqSBAIJSetPreallocation(A,1,5,NULL);
     54:   MatMPISBAIJSetPreallocation(A,1,5,NULL,5,NULL);
     55:   MatMPISELLSetPreallocation(A,5,NULL,5,NULL);
     56:   MatSeqSELLSetPreallocation(A,5,NULL);

     58:   /*
     59:      Currently, all PETSc parallel matrix formats are partitioned by
     60:      contiguous chunks of rows across the processors.  Determine which
     61:      rows of the matrix are locally owned.
     62:   */
     63:   MatGetOwnershipRange(A,&Istart,&Iend);

     65:   /*
     66:      Set matrix elements for the 2-D, five-point stencil in parallel.
     67:       - Each processor needs to insert only elements that it owns
     68:         locally (but any non-local elements will be sent to the
     69:         appropriate processor during matrix assembly).
     70:       - Always specify global rows and columns of matrix entries.

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

     77:    */
     78:   for (Ii=Istart; Ii<Iend; Ii++) {
     79:     v = -1.0; i = Ii/n; j = Ii - i*n;
     80:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     81:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     82:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     83:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     84:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
     85:   }

     87:   /*
     88:      Assemble matrix, using the 2-step process:
     89:        MatAssemblyBegin(), MatAssemblyEnd()
     90:      Computations can be done while messages are in transition
     91:      by placing code between these two statements.
     92:   */
     93:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     94:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

     99:   /*
    100:      Create parallel vectors.
    101:       - We form 1 vector from scratch and then duplicate as needed.
    102:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
    103:         in this example, we specify only the
    104:         vector's global dimension; the parallel partitioning is determined
    105:         at runtime.
    106:       - When solving a linear system, the vectors and matrices MUST
    107:         be partitioned accordingly.  PETSc automatically generates
    108:         appropriately partitioned matrices and vectors when MatCreate()
    109:         and VecCreate() are used with the same communicator.
    110:       - The user can alternatively specify the local vector and matrix
    111:         dimensions when more sophisticated partitioning is needed
    112:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
    113:         below).
    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:      By default we use an exact solution of a vector with all
    124:      elements of 1.0;
    125:   */
    126:   VecSet(u,1.0);
    127:   MatMult(A,u,b);

    129:   /*
    130:      View the exact solution vector if desired
    131:   */
    132:   flg  = PETSC_FALSE;
    133:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
    134:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:                 Create the linear solver and set various options
    138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    139:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    141:   /*
    142:      Set operators. Here the matrix that defines the linear system
    143:      also serves as the preconditioning matrix.
    144:   */
    145:   KSPSetOperators(ksp,A,A);

    147:   /*
    148:      Set linear solver defaults for this problem (optional).
    149:      - By extracting the KSP and PC contexts from the KSP context,
    150:        we can then directly call any KSP and PC routines to set
    151:        various options.
    152:      - The following two statements are optional; all of these
    153:        parameters could alternatively be specified at runtime via
    154:        KSPSetFromOptions().  All of these defaults can be
    155:        overridden at runtime, as indicated below.
    156:   */
    157:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,PETSC_DEFAULT);

    159:   /*
    160:     Set runtime options, e.g.,
    161:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    162:     These options will override those specified above as long as
    163:     KSPSetFromOptions() is called _after_ any other customization
    164:     routines.
    165:   */
    166:   KSPSetFromOptions(ksp);

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:                       Solve the linear system
    170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    172:   KSPSolve(ksp,b,x);

    174:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    175:                       Check the solution and clean up
    176:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    177:   VecAXPY(x,-1.0,u);
    178:   VecNorm(x,NORM_2,&norm);
    179:   KSPGetIterationNumber(ksp,&its);

    181:   /*
    182:      Print convergence information.  PetscPrintf() produces a single
    183:      print statement from all processes that share a communicator.
    184:      An alternative is PetscFPrintf(), which prints to a file.
    185:   */
    186:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

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

    196:   /*
    197:      Always call PetscFinalize() before exiting a program.  This routine
    198:        - finalizes the PETSc libraries as well as MPI
    199:        - provides summary and diagnostic information if certain runtime
    200:          options are chosen (e.g., -log_view).
    201:   */
    202:   PetscFinalize();
    203:   return ierr;
    204: }

    206: /*TEST

    208:    build:
    209:       requires: !single

    211:    test:
    212:       suffix: chebyest_1
    213:       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

    215:    test:
    216:       suffix: chebyest_2
    217:       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

    219:    test:
    220:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

    222:    test:
    223:       suffix: 2
    224:       nsize: 2
    225:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

    227:    test:
    228:       suffix: 3
    229:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    231:    test:
    232:       suffix: 4
    233:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    235:    test:
    236:       suffix: 5
    237:       nsize: 2
    238:       args: -ksp_monitor_short -m 5 -n 5 -mat_view draw -ksp_gmres_cgs_refinement_type refine_always -nox
    239:       output_file: output/ex2_2.out

    241:    test:
    242:       suffix: bjacobi
    243:       nsize: 4
    244:       args: -pc_type bjacobi -pc_bjacobi_blocks 1 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

    246:    test:
    247:       suffix: bjacobi_2
    248:       nsize: 4
    249:       args: -pc_type bjacobi -pc_bjacobi_blocks 2 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres -ksp_view

    251:    test:
    252:       suffix: bjacobi_3
    253:       nsize: 4
    254:       args: -pc_type bjacobi -pc_bjacobi_blocks 4 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

    256:    test:
    257:       suffix: fbcgs
    258:       args: -ksp_type fbcgs -pc_type ilu

    260:    test:
    261:       suffix: fbcgs_2
    262:       nsize: 3
    263:       args: -ksp_type fbcgsr -pc_type bjacobi

    265:    test:
    266:       suffix: groppcg
    267:       args: -ksp_monitor_short -ksp_type groppcg -m 9 -n 9

    269:    test:
    270:       suffix: mkl_pardiso_cholesky
    271:       requires: mkl_pardiso
    272:       args: -ksp_type preonly -pc_type cholesky -mat_type sbaij -pc_factor_mat_solver_type mkl_pardiso

    274:    test:
    275:       suffix: mkl_pardiso_lu
    276:       requires: mkl_pardiso
    277:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mkl_pardiso

    279:    test:
    280:       suffix: pipebcgs
    281:       args: -ksp_monitor_short -ksp_type pipebcgs -m 9 -n 9

    283:    test:
    284:       suffix: pipecg
    285:       args: -ksp_monitor_short -ksp_type pipecg -m 9 -n 9

    287:    test:
    288:       suffix: pipecgrr
    289:       args: -ksp_monitor_short -ksp_type pipecgrr -m 9 -n 9

    291:    test:
    292:       suffix: pipecr
    293:       args: -ksp_monitor_short -ksp_type pipecr -m 9 -n 9

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

    300:    test:
    301:       suffix: sell
    302:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -m 9 -n 9 -mat_type sell

    304:    test:
    305:       requires: mumps
    306:       suffix: sell_mumps
    307:       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

    309:    test:
    310:       suffix: telescope
    311:       nsize: 4
    312:       args: -m 100 -n 100 -ksp_converged_reason -pc_type telescope -pc_telescope_reduction_factor 4 -telescope_pc_type bjacobi

    314:    test:
    315:       suffix: umfpack
    316:       requires: suitesparse
    317:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type umfpack

    319:    test:
    320:       suffix: spqr
    321:       requires: suitesparse
    322:       args: -ksp_type preonly -pc_type qr -pc_factor_mat_solver_type spqr

    324:    test:
    325:      suffix: pc_symmetric
    326:      args: -m 10 -n 9 -ksp_converged_reason -ksp_type gmres -ksp_pc_side symmetric -pc_type cholesky

    328:    test:
    329:       suffix: pipeprcg
    330:       args: -ksp_monitor_short -ksp_type pipeprcg -m 9 -n 9

    332:    test:
    333:       suffix: pipeprcg_rcw
    334:       args: -ksp_monitor_short -ksp_type pipeprcg -recompute_w false -m 9 -n 9

    336:    test:
    337:       suffix: pipecg2
    338:       args: -ksp_monitor_short -ksp_type pipecg2 -m 9 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

    340:    test:
    341:       suffix: pipecg2_2
    342:       nsize: 4
    343:       args: -ksp_monitor_short -ksp_type pipecg2 -m 15 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

    345:  TEST*/