Date: 2016-09-29T11:13:13+00:00

Actual source code: ex26.c
slepc-3.7.3 2016-09-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Computes the action of the square root of the 2-D Laplacian.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     25:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     27: #include <slepcmfn.h>

     31: int main(int argc,char **argv)
     32: {
     33:   Mat                A;           /* problem matrix */
     34:   MFN                mfn;
     35:   FN                 f;
     36:   PetscReal          norm;
     37:   Vec                v,y,z;
     38:   PetscInt           N,n=10,m,Istart,Iend,i,j,II;
     39:   PetscErrorCode     ierr;
     40:   PetscBool          flag,draw_sol;
     41:   MFNConvergedReason reason;

     43:   SlepcInitialize(&argc,&argv,(char*)0,help);

     45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     46:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     47:   if (!flag) m=n;
     48:   N = n*m;
     49:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root of Laplacian y=sqrt(A)*e_1, N=%D (%Dx%D grid)\n\n",N,n,m);

     51:   PetscOptionsHasName(NULL,NULL,"-draw_sol",&draw_sol);

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:                  Compute the discrete 2-D Laplacian, A
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   MatCreate(PETSC_COMM_WORLD,&A);
     58:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     59:   MatSetFromOptions(A);
     60:   MatSetUp(A);

     62:   MatGetOwnershipRange(A,&Istart,&Iend);
     63:   for (II=Istart;II<Iend;II++) {
     64:     i = II/n; j = II-i*n;
     65:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
     66:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
     67:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
     68:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
     69:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     70:   }

     72:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     73:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     75:   /* set symmetry flag so that solver can exploit it */
     76:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

     78:   /* set v = e_1 */
     79:   MatCreateVecs(A,NULL,&v);
     80:   VecSetValue(v,0,1.0,INSERT_VALUES);
     81:   VecAssemblyBegin(v);
     82:   VecAssemblyEnd(v);
     83:   VecDuplicate(v,&y);
     84:   VecDuplicate(v,&z);

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:              Create the solver, set the matrix and the function
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     89:   MFNCreate(PETSC_COMM_WORLD,&mfn);
     90:   MFNSetOperator(mfn,A);
     91:   MFNGetFN(mfn,&f);
     92:   FNSetType(f,FNSQRT);
     93:   MFNSetFromOptions(mfn);

     95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96:                       First solve: y=sqrt(A)*v
     97:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     99:   MFNSolve(mfn,v,y);
    100:   MFNGetConvergedReason(mfn,&reason);
    101:   if (reason<0) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");
    102:   VecNorm(y,NORM_2,&norm);
    103:
    104:   PetscPrintf(PETSC_COMM_WORLD," Intermediate vector has norm %g\n",(double)norm);
    105:   if (draw_sol) {
    106:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
    107:     VecView(y,PETSC_VIEWER_DRAW_WORLD);
    108:   }

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:              Second solve: z=sqrt(A)*y and compare against A*v
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   MFNSolve(mfn,y,z);
    115:   MFNGetConvergedReason(mfn,&reason);
    116:   if (reason<0) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");

    118:   MatMult(A,v,y);   /* overwrite y */
    119:   VecAXPY(y,-1.0,z);
    120:   VecNorm(y,NORM_2,&norm);
    121:
    122:   if (norm<100*PETSC_MACHINE_EPSILON) {
    123:     PetscPrintf(PETSC_COMM_WORLD," Error norm is less than 100*epsilon\n\n");
    124:   } else {
    125:     PetscPrintf(PETSC_COMM_WORLD," Error norm %3.1e\n\n",(double)norm);
    126:   }
    127:   if (draw_sol) {
    128:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
    129:     VecView(z,PETSC_VIEWER_DRAW_WORLD);
    130:   }

    132:   /*
    133:      Free work space
    134:   */
    135:   MFNDestroy(&mfn);
    136:   MatDestroy(&A);
    137:   VecDestroy(&v);
    138:   VecDestroy(&y);
    139:   VecDestroy(&z);
    140:   SlepcFinalize();
    141:   return ierr;
    142: }