Actual source code: loaded_string.c
slepc-3.22.1 2024-10-28
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: */
10: /*
11: This example implements one of the problems found at
12: NLEVP: A Collection of Nonlinear Eigenvalue Problems,
13: The University of Manchester.
14: The details of the collection can be found at:
15: [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
16: Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.
18: The loaded_string problem is a rational eigenvalue problem for the
19: finite element model of a loaded vibrating string.
20: This example solves the loaded_string problem by first transforming
21: it to a quadratic eigenvalue problem.
22: */
24: static char help[] = "Finite element model of a loaded vibrating string.\n\n"
25: "The command line options are:\n"
26: " -n <n>, dimension of the matrices.\n"
27: " -kappa <kappa>, stiffness of elastic spring.\n"
28: " -mass <m>, mass of the attached load.\n\n";
30: #include <slepcpep.h>
32: #define NMAT 3
34: int main(int argc,char **argv)
35: {
36: Mat A[3],M; /* problem matrices */
37: PEP pep; /* polynomial eigenproblem solver context */
38: PetscInt n=100,Istart,Iend,i;
39: PetscBool terse;
40: PetscReal kappa=1.0,m=1.0;
41: PetscScalar sigma;
43: PetscFunctionBeginUser;
44: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
46: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
47: PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
48: PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
49: sigma = kappa/m;
50: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string (QEP), n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m));
52: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
54: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: /* initialize matrices */
56: for (i=0;i<NMAT;i++) {
57: PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
58: PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
59: PetscCall(MatSetFromOptions(A[i]));
60: }
61: PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
63: /* A0 */
64: for (i=Istart;i<Iend;i++) {
65: PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES));
66: if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES));
67: if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES));
68: }
70: /* A1 */
71: for (i=Istart;i<Iend;i++) {
72: PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
73: if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
74: if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
75: }
77: /* A2 */
78: if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));
80: /* assemble matrices */
81: for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
82: for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));
84: /* build matrices for the QEP */
85: PetscCall(MatAXPY(A[2],1.0,A[0],DIFFERENT_NONZERO_PATTERN));
86: PetscCall(MatAXPY(A[2],sigma,A[1],SAME_NONZERO_PATTERN));
87: PetscCall(MatScale(A[2],-1.0));
88: PetscCall(MatScale(A[0],sigma));
89: M = A[1];
90: A[1] = A[2];
91: A[2] = M;
93: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: Create the eigensolver and solve the problem
95: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
98: PetscCall(PEPSetOperators(pep,3,A));
99: PetscCall(PEPSetFromOptions(pep));
100: PetscCall(PEPSolve(pep));
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Display solution and clean up
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: /* show detailed info unless -terse option is given by user */
107: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
108: if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
109: else {
110: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
111: PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
112: PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
113: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
114: }
115: PetscCall(PEPDestroy(&pep));
116: for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
117: PetscCall(SlepcFinalize());
118: return 0;
119: }
121: /*TEST
123: test:
124: suffix: 1
125: args: -pep_hyperbolic -pep_interval 4,900 -pep_type stoar -st_type sinvert -st_pc_type cholesky -terse
126: requires: !single
128: TEST*/