Actual source code: test9.c

slepc-3.17.2 2022-08-09
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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.
  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[] = "Test the NLEIGS solver with FNCOMBINE.\n\n"
 23:   "This is based on loaded_string from the NLEVP collection.\n"
 24:   "The command line options are:\n"
 25:   "  -n <n>, dimension of the matrices.\n"
 26:   "  -kappa <kappa>, stiffness of elastic spring.\n"
 27:   "  -mass <m>, mass of the attached load.\n\n";

 29: #include <slepcnep.h>

 31: #define NMAT 3

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

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

 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=%" 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:     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) MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);

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

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:                        Create the problem functions
 87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

101:   /* f3=lambda/(lambda-sigma)=1+sigma/(lambda-sigma) */
102:   FNCreate(PETSC_COMM_WORLD,&g);
103:   FNSetType(g,FNRATIONAL);
104:   numer[0] = sigma;
105:   denom[0] = 1.0; denom[1] = -sigma;
106:   FNRationalSetNumerator(g,1,numer);
107:   FNRationalSetDenominator(g,2,denom);
108:   FNCreate(PETSC_COMM_WORLD,&f[2]);
109:   FNSetType(f[2],FNCOMBINE);
110:   FNCombineSetChildren(f[2],FN_COMBINE_ADD,f[0],g);

112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113:                 Create the eigensolver and solve the problem
114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123:                     Display solution and clean up
124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

145: /*TEST

147:    test:
148:       suffix: 1
149:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
150:       filter: sed -e "s/[+-]0\.0*i//g"
151:       requires: !single

153: TEST*/