Date: 2026-01-20T11:35:15+00:00

Actual source code: ex26.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Computes the action of the square root of the 2-D Laplacian.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n"
     15:   "To draw the solution run with -mfn_view_solution draw -draw_pause -1\n\n";

     17: #include <slepcmfn.h>

     19: int main(int argc,char **argv)
     20: {
     21:   Mat            A;           /* problem matrix */
     22:   MFN            mfn;
     23:   FN             f;
     24:   PetscReal      norm,tol;
     25:   Vec            v,y,z;
     26:   PetscInt       N,n=10,m,Istart,Iend,i,j,II;
     27:   PetscBool      flag;

     29:   PetscFunctionBeginUser;
     30:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root of Laplacian y=sqrt(A)*e_1, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:                  Compute the discrete 2-D Laplacian, A
     40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     42:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     43:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     44:   PetscCall(MatSetFromOptions(A));

     46:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     47:   for (II=Istart;II<Iend;II++) {
     48:     i = II/n; j = II-i*n;
     49:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
     50:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
     51:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
     52:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
     53:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
     54:   }

     56:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     57:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

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

     62:   /* set v = e_1 */
     63:   PetscCall(MatCreateVecs(A,NULL,&v));
     64:   PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES));
     65:   PetscCall(VecAssemblyBegin(v));
     66:   PetscCall(VecAssemblyEnd(v));
     67:   PetscCall(VecDuplicate(v,&y));
     68:   PetscCall(VecDuplicate(v,&z));

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:              Create the solver, set the matrix and the function
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     73:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
     74:   PetscCall(MFNSetOperator(mfn,A));
     75:   PetscCall(MFNGetFN(mfn,&f));
     76:   PetscCall(FNSetType(f,FNSQRT));
     77:   PetscCall(MFNSetErrorIfNotConverged(mfn,PETSC_TRUE));
     78:   PetscCall(MFNSetFromOptions(mfn));

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:                       First solve: y=sqrt(A)*v
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     84:   PetscCall(MFNSolve(mfn,v,y));
     85:   PetscCall(VecNorm(y,NORM_2,&norm));
     86:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Intermediate vector has norm %g\n",(double)norm));

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:              Second solve: z=sqrt(A)*y and compare against A*v
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     92:   PetscCall(MFNSolve(mfn,y,z));
     93:   PetscCall(MFNGetTolerances(mfn,&tol,NULL));

     95:   PetscCall(MatMult(A,v,y));   /* overwrite y */
     96:   PetscCall(VecAXPY(y,-1.0,z));
     97:   PetscCall(VecNorm(y,NORM_2,&norm));

     99:   if (norm<tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm is less than the requested tolerance\n\n"));
    100:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm larger than tolerance: %3.1e\n\n",(double)norm));

    102:   /*
    103:      Free work space
    104:   */
    105:   PetscCall(MFNDestroy(&mfn));
    106:   PetscCall(MatDestroy(&A));
    107:   PetscCall(VecDestroy(&v));
    108:   PetscCall(VecDestroy(&y));
    109:   PetscCall(VecDestroy(&z));
    110:   PetscCall(SlepcFinalize());
    111:   return 0;
    112: }

    114: /*TEST

    116:    test:
    117:       suffix: 1
    118:       args: -mfn_tol 1e-4

    120: TEST*/