Actual source code: ex26.c

slepc-3.7.0 2016-05-16
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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: }