Actual source code: loaded_string.c

slepc-3.15.2 2021-09-20
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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: */

 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;

 43:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 46:   PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);
 47:   PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL);
 48:   sigma = kappa/m;
 49:   PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%D 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:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 58:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
 59:     MatSetFromOptions(A[i]);
 60:     MatSetUp(A[i]);
 61:   }
 62:   MatGetOwnershipRange(A[0],&Istart,&Iend);

 64:   /* A0 */
 65:   for (i=Istart;i<Iend;i++) {
 66:     MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES);
 67:     if (i>0) { MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES); }
 68:     if (i<n-1) { MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES); }
 69:   }

 71:   /* A1 */
 72:   for (i=Istart;i<Iend;i++) {
 73:     MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES);
 74:     if (i>0) { MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES); }
 75:     if (i<n-1) { MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES); }
 76:   }

 78:   /* A2 */
 79:   if (Istart<=n-1 && n-1<Iend) {
 80:     MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);
 81:   }

 83:   /* assemble matrices */
 84:   for (i=0;i<NMAT;i++) {
 85:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
 86:   }
 87:   for (i=0;i<NMAT;i++) {
 88:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
 89:   }

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:                        Create the problem functions
 93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 95:   /* f1=1 */
 96:   FNCreate(PETSC_COMM_WORLD,&f[0]);
 97:   FNSetType(f[0],FNRATIONAL);
 98:   numer[0] = 1.0;
 99:   FNRationalSetNumerator(f[0],1,numer);

101:   /* f2=-lambda */
102:   FNCreate(PETSC_COMM_WORLD,&f[1]);
103:   FNSetType(f[1],FNRATIONAL);
104:   numer[0] = -1.0; numer[1] = 0.0;
105:   FNRationalSetNumerator(f[1],2,numer);

107:   /* f3=lambda/(lambda-sigma) */
108:   FNCreate(PETSC_COMM_WORLD,&f[2]);
109:   FNSetType(f[2],FNRATIONAL);
110:   numer[0] = 1.0; numer[1] = 0.0;
111:   denom[0] = 1.0; denom[1] = -sigma;
112:   FNRationalSetNumerator(f[2],2,numer);
113:   FNRationalSetDenominator(f[2],2,denom);

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:                 Create the eigensolver and solve the problem
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

119:   NEPCreate(PETSC_COMM_WORLD,&nep);
120:   NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
121:   NEPSetProblemType(nep,NEP_RATIONAL);
122:   NEPSetFromOptions(nep);
123:   NEPSolve(nep);

125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126:                     Display solution and clean up
127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

129:   /* show detailed info unless -terse option is given by user */
130:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
131:   if (terse) {
132:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
133:   } else {
134:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
135:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
136:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
137:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
138:   }
139:   NEPDestroy(&nep);
140:   for (i=0;i<NMAT;i++) {
141:     MatDestroy(&A[i]);
142:     FNDestroy(&f[i]);
143:   }
144:   SlepcFinalize();
145:   return ierr;
146: }

148: /*TEST

150:    test:
151:       suffix: 1
152:       args: -nep_type rii -nep_target 4 -terse
153:       requires: !single
154:       filter: sed -e "s/[+-]0\.0*i//g"

156:    testset:
157:       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
158:       requires: !single
159:       output_file: output/loaded_string_2.out
160:       test:
161:          suffix: 2
162:          args: -nep_refine_scheme {{schur explicit}}
163:       test:
164:          suffix: 2_mbe
165:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type lu

167:    testset:
168:       nsize: 2
169:       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
170:       requires: !single
171:       output_file: output/loaded_string_2.out
172:       timeoutfactor: 2
173:       test:
174:          suffix: 3_explicit
175:          args: -nep_refine_scheme explicit
176:       test:
177:          suffix: 3_mbe
178:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type cholesky

180:    test:
181:       suffix: 4
182:       nsize: 4
183:       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
184:       requires: !single
185:       output_file: output/loaded_string_2.out
186:       timeoutfactor: 4

188:    test:
189:       suffix: 5
190:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
191:       filter: sed -e "s/[+-]0\.0*i//g"
192:       requires: !single

194:    test:
195:       suffix: 6
196:       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
197:       requires: !complex !single

199:    test:
200:       suffix: 6_complex
201:       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
202:       filter: sed -e "s/[+-]0\.0*i//g"
203:       requires: complex !single
204:       output_file: output/loaded_string_6.out

206:    test:
207:       suffix: 7
208:       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
209:       requires: !complex double

211:    test:
212:       suffix: 7_complex
213:       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
214:       requires: complex double
215:       output_file: output/loaded_string_7.out

217:    testset:
218:       args: -nep_target 10 -nep_nev 3 -nep_tol 5e-10 -terse
219:       requires: !single
220:       output_file: output/loaded_string_8.out
221:       filter: sed -e "s/[+-]0\.0*i//g"
222:       test:
223:          suffix: 8
224:          args: -nep_type {{rii slp narnoldi}}
225:       test:
226:          suffix: 8_rii_thres
227:          args: -nep_type rii -nep_rii_deflation_threshold 5e-10
228:       test:
229:          suffix: 8_slp_thres
230:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10

232:       test:
233:          suffix: 8_slp_two_thres
234:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10 -nep_two_sided
235: TEST*/