Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
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.
17 :
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 : */
23 :
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";
29 :
30 : #include <slepcpep.h>
31 :
32 : #define NMAT 3
33 :
34 1 : int main(int argc,char **argv)
35 : {
36 1 : Mat A[3],M; /* problem matrices */
37 1 : PEP pep; /* polynomial eigenproblem solver context */
38 1 : PetscInt n=100,Istart,Iend,i;
39 1 : PetscBool terse;
40 1 : PetscReal kappa=1.0,m=1.0;
41 1 : PetscScalar sigma;
42 :
43 1 : PetscFunctionBeginUser;
44 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
45 :
46 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
47 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
48 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
49 1 : sigma = kappa/m;
50 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string (QEP), n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m));
51 :
52 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53 : Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
54 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55 : /* initialize matrices */
56 4 : for (i=0;i<NMAT;i++) {
57 3 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
58 3 : PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
59 3 : PetscCall(MatSetFromOptions(A[i]));
60 : }
61 1 : PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
62 :
63 : /* A0 */
64 101 : for (i=Istart;i<Iend;i++) {
65 100 : PetscCall(MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES));
66 100 : if (i>0) PetscCall(MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES));
67 100 : if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES));
68 : }
69 :
70 : /* A1 */
71 101 : for (i=Istart;i<Iend;i++) {
72 100 : PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
73 100 : if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
74 100 : if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
75 : }
76 :
77 : /* A2 */
78 1 : if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));
79 :
80 : /* assemble matrices */
81 4 : for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
82 4 : for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));
83 :
84 : /* build matrices for the QEP */
85 1 : PetscCall(MatAXPY(A[2],1.0,A[0],DIFFERENT_NONZERO_PATTERN));
86 1 : PetscCall(MatAXPY(A[2],sigma,A[1],SAME_NONZERO_PATTERN));
87 1 : PetscCall(MatScale(A[2],-1.0));
88 1 : PetscCall(MatScale(A[0],sigma));
89 1 : M = A[1];
90 1 : A[1] = A[2];
91 1 : A[2] = M;
92 :
93 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94 : Create the eigensolver and solve the problem
95 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
96 :
97 1 : PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
98 1 : PetscCall(PEPSetOperators(pep,3,A));
99 1 : PetscCall(PEPSetFromOptions(pep));
100 1 : PetscCall(PEPSolve(pep));
101 :
102 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103 : Display solution and clean up
104 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105 :
106 : /* show detailed info unless -terse option is given by user */
107 1 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
108 1 : if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
109 : else {
110 0 : PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
111 0 : PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
112 0 : PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
113 0 : PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
114 : }
115 1 : PetscCall(PEPDestroy(&pep));
116 4 : for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
117 1 : PetscCall(SlepcFinalize());
118 : return 0;
119 : }
120 :
121 : /*TEST
122 :
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
127 :
128 : TEST*/
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