Actual source code: ex26.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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;
28: PetscBool flag;
30: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
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=%D (%Dx%D 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) {
101: PetscPrintf(PETSC_COMM_WORLD," Error norm is less than the requested tolerance\n\n");
102: } else {
103: PetscPrintf(PETSC_COMM_WORLD," Error norm larger than tolerance: %3.1e\n\n",(double)norm);
104: }
106: /*
107: Free work space
108: */
109: MFNDestroy(&mfn);
110: MatDestroy(&A);
111: VecDestroy(&v);
112: VecDestroy(&y);
113: VecDestroy(&z);
114: SlepcFinalize();
115: return ierr;
116: }
118: /*TEST
120: test:
121: suffix: 1
122: args: -mfn_tol 1e-5
124: TEST*/