slepc-3.21.1 2024-04-26
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```  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.
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: */

22: static char help[] = "Finite element model of a loaded vibrating string.\n\n"
23:   "The command line options are:\n"
24:   "  -n <n>, dimension of the matrices.\n"
25:   "  -kappa <kappa>, stiffness of elastic spring.\n"
26:   "  -mass <m>, mass of the attached load.\n\n";

28: #include <slepcnep.h>

30: #define NMAT 3

32: int main(int argc,char **argv)
33: {
34:   Mat            A[NMAT];         /* problem matrices */
35:   FN             f[NMAT];         /* functions to define the nonlinear operator */
36:   NEP            nep;             /* nonlinear eigensolver context */
37:   PetscInt       n=100,Istart,Iend,i;
38:   PetscReal      kappa=1.0,m=1.0;
39:   PetscScalar    sigma,numer[2],denom[2];
40:   PetscBool      terse;

42:   PetscFunctionBeginUser;
43:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
46:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
47:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
48:   sigma = kappa/m;
49:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m));

51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
52:                        Build the problem matrices
53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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:   }

62:   /* A0 */
63:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
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:   PetscCall(MatGetOwnershipRange(A[1],&Istart,&Iend));
72:   for (i=Istart;i<Iend;i++) {
73:     PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
74:     if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
75:     if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
76:   }

78:   /* A2 */
79:   PetscCall(MatGetOwnershipRange(A[2],&Istart,&Iend));
80:   if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));

82:   /* assemble matrices */
83:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
84:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87:                        Create the problem functions
88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

90:   /* f1=1 */
91:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
92:   PetscCall(FNSetType(f[0],FNRATIONAL));
93:   numer[0] = 1.0;
94:   PetscCall(FNRationalSetNumerator(f[0],1,numer));

96:   /* f2=-lambda */
97:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
98:   PetscCall(FNSetType(f[1],FNRATIONAL));
99:   numer[0] = -1.0; numer[1] = 0.0;
100:   PetscCall(FNRationalSetNumerator(f[1],2,numer));

102:   /* f3=lambda/(lambda-sigma) */
103:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2]));
104:   PetscCall(FNSetType(f[2],FNRATIONAL));
105:   numer[0] = 1.0; numer[1] = 0.0;
106:   denom[0] = 1.0; denom[1] = -sigma;
107:   PetscCall(FNRationalSetNumerator(f[2],2,numer));
108:   PetscCall(FNRationalSetDenominator(f[2],2,denom));

110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111:                 Create the eigensolver and solve the problem
112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

114:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
115:   PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN));
116:   PetscCall(NEPSetProblemType(nep,NEP_RATIONAL));
117:   PetscCall(NEPSetFromOptions(nep));
118:   PetscCall(NEPSolve(nep));

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:                     Display solution and clean up
122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

124:   /* show detailed info unless -terse option is given by user */
125:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
126:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
127:   else {
128:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
129:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
130:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
131:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
132:   }
133:   PetscCall(NEPDestroy(&nep));
134:   for (i=0;i<NMAT;i++) {
135:     PetscCall(MatDestroy(&A[i]));
136:     PetscCall(FNDestroy(&f[i]));
137:   }
138:   PetscCall(SlepcFinalize());
139:   return 0;
140: }

142: /*TEST

144:    test:
145:       suffix: 1
146:       args: -nep_type rii -nep_target 4 -terse
147:       requires: !single
148:       filter: sed -e "s/[+-]0\.0*i//g"

150:    testset:
151:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 12 -nep_refine simple -terse
152:       requires: !single
154:       test:
155:          suffix: 2
156:          args: -nep_refine_scheme {{schur explicit}}
157:       test:
158:          suffix: 2_mbe
159:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type lu

161:    testset:
162:       nsize: 2
163:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 12 -nep_refine simple -nep_refine_partitions 2 -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type bjacobi -terse
164:       requires: !single
166:       timeoutfactor: 2
167:       test:
168:          suffix: 3_explicit
169:          args: -nep_refine_scheme explicit
170:       test:
171:          suffix: 3_mbe
172:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type cholesky

174:    test:
175:       suffix: 4
176:       nsize: 4
177:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 10 -nep_refine simple -nep_refine_partitions 2 -nep_refine_scheme explicit -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type bjacobi -terse -log_exclude nep,pep,fn
178:       requires: !single
180:       timeoutfactor: 4

182:    test:
183:       suffix: 5
184:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
185:       filter: sed -e "s/[+-]0\.0*i//g"
186:       requires: !single

188:    test:
189:       suffix: 6
190:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 100,700 -nep_nev 5 -nep_tol 1e-9 -nep_target 140 -nep_nleigs_interpolation_degree 15 -nep_general -terse
191:       requires: !complex !single

193:    test:
194:       suffix: 6_complex
195:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 100,700,-.1,.1 -nep_nev 5 -nep_tol 1e-9 -nep_target 140 -nep_nleigs_interpolation_degree 15 -nep_general -terse
196:       filter: sed -e "s/[+-]0\.0*i//g"
197:       requires: complex !single

200:    test:
201:       suffix: 7
202:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700 -nep_nev 5 -nep_target 100 -nep_interpol_interpolation_degree 20 -nep_ncv 20 -n 20 -nep_refine simple -nep_refine_its 1 -terse
203:       requires: !complex double

205:    test:
206:       suffix: 7_complex
207:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 5 -nep_target 100 -nep_interpol_interpolation_degree 20 -nep_ncv 20 -n 20 -nep_refine simple -nep_refine_its 1 -terse
208:       requires: complex double

211:    testset:
212:       args: -nep_target 10 -nep_nev 3 -nep_tol 5e-10 -terse
213:       requires: !single
215:       filter: sed -e "s/[+-]0\.0*i//g"
216:       test:
217:          suffix: 8
218:          args: -nep_type {{rii slp narnoldi}}
219:       test:
220:          suffix: 8_rii_thres
221:          args: -nep_type rii -nep_rii_deflation_threshold 5e-10
222:       test:
223:          suffix: 8_slp_thres
224:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10

226:       test:
227:          suffix: 8_slp_two_thres
228:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10 -nep_two_sided

230:    test:
231:       suffix: 9
232:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 500 -rg_ellipse_radius 500 -rg_ellipse_vscale .1 -nep_ciss_moments 4 -nep_ciss_blocksize 5 -terse
233:       requires: complex double

235: TEST*/
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