Date: 2022-10-01T06:40:47+00:00

Actual source code: ex26.c
slepc-3.18.0 2022-10-01
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      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;

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

     32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   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:   MatCreate(PETSC_COMM_WORLD,&A);
     43:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     44:   MatSetFromOptions(A);
     45:   MatSetUp(A);

     47:   MatGetOwnershipRange(A,&Istart,&Iend);
     48:   for (II=Istart;II<Iend;II++) {
     49:     i = II/n; j = II-i*n;
     50:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
     51:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
     52:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
     53:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
     54:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     55:   }

     57:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     58:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

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

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

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:                       First solve: y=sqrt(A)*v
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:              Second solve: z=sqrt(A)*y and compare against A*v
     91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

    103:   /*
    104:      Free work space
    105:   */
    106:   MFNDestroy(&mfn);
    107:   MatDestroy(&A);
    108:   VecDestroy(&v);
    109:   VecDestroy(&y);
    110:   VecDestroy(&z);
    111:   SlepcFinalize();
    112:   return 0;
    113: }

    115: /*TEST

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

    121: TEST*/