Actual source code: ex26.c
slepc-3.17.1 2022-04-11
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*/