Actual source code: damped_beam.c
slepc-3.23.1 2025-05-01
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 damped_beam problem is a QEP from the vibrarion analysis of a beam
19: simply supported at both ends and damped in the middle.
20: */
22: static char help[] = "Quadratic eigenproblem from the vibrarion analysis of a beam.\n\n"
23: "The command line options are:\n"
24: " -n <n> ... dimension of the matrices.\n\n";
26: #include <slepcpep.h>
28: int main(int argc,char **argv)
29: {
30: Mat M,Mo,C,K,Ko,A[3]; /* problem matrices */
31: PEP pep; /* polynomial eigenproblem solver context */
32: IS isf,isbc,is;
33: PetscInt n=200,nele,Istart,Iend,i,j,mloc,nloc,bc[2];
34: PetscReal width=0.05,height=0.005,glength=1.0,dlen,EI,area,rho;
35: PetscScalar K1[4],K2[4],K2t[4],K3[4],M1[4],M2[4],M2t[4],M3[4],damp=5.0;
36: PetscBool terse;
38: PetscFunctionBeginUser;
39: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
41: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
42: nele = n/2;
43: n = 2*nele;
44: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSimply supported beam damped in the middle, n=%" PetscInt_FMT " (nele=%" PetscInt_FMT ")\n\n",n,nele));
46: dlen = glength/nele;
47: EI = 7e10*width*height*height*height/12.0;
48: area = width*height;
49: rho = 0.674/(area*glength);
51: K1[0] = 12; K1[1] = 6*dlen; K1[2] = 6*dlen; K1[3] = 4*dlen*dlen;
52: K2[0] = -12; K2[1] = 6*dlen; K2[2] = -6*dlen; K2[3] = 2*dlen*dlen;
53: K2t[0] = -12; K2t[1] = -6*dlen; K2t[2] = 6*dlen; K2t[3] = 2*dlen*dlen;
54: K3[0] = 12; K3[1] = -6*dlen; K3[2] = -6*dlen; K3[3] = 4*dlen*dlen;
55: M1[0] = 156; M1[1] = 22*dlen; M1[2] = 22*dlen; M1[3] = 4*dlen*dlen;
56: M2[0] = 54; M2[1] = -13*dlen; M2[2] = 13*dlen; M2[3] = -3*dlen*dlen;
57: M2t[0] = 54; M2t[1] = 13*dlen; M2t[2] = -13*dlen; M2t[3] = -3*dlen*dlen;
58: M3[0] = 156; M3[1] = -22*dlen; M3[2] = -22*dlen; M3[3] = 4*dlen*dlen;
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: /* K is block-tridiagonal */
65: PetscCall(MatCreate(PETSC_COMM_WORLD,&Ko));
66: PetscCall(MatSetSizes(Ko,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2));
67: PetscCall(MatSetBlockSize(Ko,2));
68: PetscCall(MatSetFromOptions(Ko));
70: PetscCall(MatGetOwnershipRange(Ko,&Istart,&Iend));
71: for (i=Istart/2;i<Iend/2;i++) {
72: if (i>0) {
73: j = i-1;
74: PetscCall(MatSetValuesBlocked(Ko,1,&i,1,&j,K2t,ADD_VALUES));
75: PetscCall(MatSetValuesBlocked(Ko,1,&i,1,&i,K3,ADD_VALUES));
76: }
77: if (i<nele) {
78: j = i+1;
79: PetscCall(MatSetValuesBlocked(Ko,1,&i,1,&j,K2,ADD_VALUES));
80: PetscCall(MatSetValuesBlocked(Ko,1,&i,1,&i,K1,ADD_VALUES));
81: }
82: }
83: PetscCall(MatAssemblyBegin(Ko,MAT_FINAL_ASSEMBLY));
84: PetscCall(MatAssemblyEnd(Ko,MAT_FINAL_ASSEMBLY));
85: PetscCall(MatScale(Ko,EI/(dlen*dlen*dlen)));
87: /* M is block-tridiagonal */
88: PetscCall(MatCreate(PETSC_COMM_WORLD,&Mo));
89: PetscCall(MatSetSizes(Mo,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2));
90: PetscCall(MatSetBlockSize(Mo,2));
91: PetscCall(MatSetFromOptions(Mo));
93: PetscCall(MatGetOwnershipRange(Mo,&Istart,&Iend));
94: for (i=Istart/2;i<Iend/2;i++) {
95: if (i>0) {
96: j = i-1;
97: PetscCall(MatSetValuesBlocked(Mo,1,&i,1,&j,M2t,ADD_VALUES));
98: PetscCall(MatSetValuesBlocked(Mo,1,&i,1,&i,M3,ADD_VALUES));
99: }
100: if (i<nele) {
101: j = i+1;
102: PetscCall(MatSetValuesBlocked(Mo,1,&i,1,&j,M2,ADD_VALUES));
103: PetscCall(MatSetValuesBlocked(Mo,1,&i,1,&i,M1,ADD_VALUES));
104: }
105: }
106: PetscCall(MatAssemblyBegin(Mo,MAT_FINAL_ASSEMBLY));
107: PetscCall(MatAssemblyEnd(Mo,MAT_FINAL_ASSEMBLY));
108: PetscCall(MatScale(Mo,rho*area*dlen/420));
110: /* remove rows/columns from K and M corresponding to boundary conditions */
111: PetscCall(ISCreateStride(PETSC_COMM_WORLD,Iend-Istart,Istart,1,&isf));
112: bc[0] = 0; bc[1] = n;
113: PetscCall(ISCreateGeneral(PETSC_COMM_SELF,2,bc,PETSC_USE_POINTER,&isbc));
114: PetscCall(ISDifference(isf,isbc,&is));
115: PetscCall(MatCreateSubMatrix(Ko,is,is,MAT_INITIAL_MATRIX,&K));
116: PetscCall(MatCreateSubMatrix(Mo,is,is,MAT_INITIAL_MATRIX,&M));
117: PetscCall(MatGetLocalSize(M,&mloc,&nloc));
119: /* C is zero except for the (nele,nele)-entry */
120: PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
121: PetscCall(MatSetSizes(C,mloc,nloc,PETSC_DECIDE,PETSC_DECIDE));
122: PetscCall(MatSetFromOptions(C));
124: PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
125: if (nele-1>=Istart && nele-1<Iend) PetscCall(MatSetValue(C,nele-1,nele-1,damp,INSERT_VALUES));
126: PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
127: PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Create the eigensolver and solve the problem
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
134: A[0] = K; A[1] = C; A[2] = M;
135: PetscCall(PEPSetOperators(pep,3,A));
136: PetscCall(PEPSetFromOptions(pep));
137: PetscCall(PEPSolve(pep));
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Display solution and clean up
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: /* show detailed info unless -terse option is given by user */
144: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
145: if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
146: else {
147: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
148: PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
149: PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
150: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
151: }
152: PetscCall(PEPDestroy(&pep));
153: PetscCall(ISDestroy(&isf));
154: PetscCall(ISDestroy(&isbc));
155: PetscCall(ISDestroy(&is));
156: PetscCall(MatDestroy(&M));
157: PetscCall(MatDestroy(&C));
158: PetscCall(MatDestroy(&K));
159: PetscCall(MatDestroy(&Ko));
160: PetscCall(MatDestroy(&Mo));
161: PetscCall(SlepcFinalize());
162: return 0;
163: }
165: /*TEST
167: testset:
168: args: -pep_nev 2 -pep_ncv 12 -pep_target 0 -terse
169: requires: !single
170: output_file: output/damped_beam_1.out
171: test:
172: suffix: 1
173: args: -pep_type {{toar linear}} -st_type sinvert
174: test:
175: suffix: 1_qarnoldi
176: args: -pep_type qarnoldi -pep_qarnoldi_locking 0 -st_type sinvert
177: test:
178: suffix: 1_jd
179: args: -pep_type jd
180: filter: sed -e "s/23066i/23065i/"
182: testset:
183: args: -pep_nev 2 -pep_ncv 12 -pep_target 1i -terse
184: requires: complex !single
185: output_file: output/damped_beam_1.out
186: test:
187: suffix: 1_complex
188: args: -pep_type {{toar linear}} -st_type sinvert
189: test:
190: suffix: 1_qarnoldi_complex
191: args: -pep_type qarnoldi -pep_qarnoldi_locking 0 -st_type sinvert
192: test:
193: suffix: 1_jd_complex
194: args: -pep_type jd
196: TEST*/