Actual source code: ex26.c

slepc-3.8.2 2017-12-01
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2017, 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";

 16: #include <slepcmfn.h>

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

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

 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=%D (%Dx%D grid)\n\n",N,n,m);

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

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:                  Compute the discrete 2-D Laplacian, A
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 48:   MatGetOwnershipRange(A,&Istart,&Iend);
 49:   for (II=Istart;II<Iend;II++) {
 50:     i = II/n; j = II-i*n;
 51:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
 52:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
 53:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
 54:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
 55:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
 56:   }

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

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

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

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

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:                       First solve: y=sqrt(A)*v
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 86:   MFNSolve(mfn,v,y);
 87:   VecNorm(y,NORM_2,&norm);
 88:   PetscPrintf(PETSC_COMM_WORLD," Intermediate vector has norm %g\n",(double)norm);
 89:   if (draw_sol) {
 90:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
 91:     VecView(y,PETSC_VIEWER_DRAW_WORLD);
 92:   }

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95:              Second solve: z=sqrt(A)*y and compare against A*v
 96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 98:   MFNSolve(mfn,y,z);
 99:   MFNGetTolerances(mfn,&tol,NULL);

101:   MatMult(A,v,y);   /* overwrite y */
102:   VecAXPY(y,-1.0,z);
103:   VecNorm(y,NORM_2,&norm);

105:   if (norm<tol) {
106:     PetscPrintf(PETSC_COMM_WORLD," Error norm is less than the requested tolerance\n\n");
107:   } else {
108:     PetscPrintf(PETSC_COMM_WORLD," Error norm larger than tolerance: %3.1e\n\n",(double)norm);
109:   }
110:   if (draw_sol) {
111:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
112:     VecView(z,PETSC_VIEWER_DRAW_WORLD);
113:   }

115:   /*
116:      Free work space
117:   */
118:   MFNDestroy(&mfn);
119:   MatDestroy(&A);
120:   VecDestroy(&v);
121:   VecDestroy(&y);
122:   VecDestroy(&z);
123:   SlepcFinalize();
124:   return ierr;
125: }