Actual source code: ex26.c

slepc-3.17.1 2022-04-11
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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;

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

 31:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 33:   if (!flag) m=n;
 34:   N = n*m;
 35:   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);

 37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 38:                  Compute the discrete 2-D Laplacian, A
 39:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

 84:   MFNSolve(mfn,v,y);
 85:   VecNorm(y,NORM_2,&norm);
 86:   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:   MFNSolve(mfn,y,z);
 93:   MFNGetTolerances(mfn,&tol,NULL);

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

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

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

114: /*TEST

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

120: TEST*/