Actual source code: test9.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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;

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

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

 52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 53:                        Build the problem matrices
 54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 56:   /* initialize matrices */
 57:   for (i=0;i<NMAT;i++) {
 58:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 59:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
 60:     MatSetFromOptions(A[i]);
 61:     MatSetUp(A[i]);
 62:   }
 63:   MatGetOwnershipRange(A[0],&Istart,&Iend);

 65:   /* A0 */
 66:   for (i=Istart;i<Iend;i++) {
 67:     MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES);
 68:     if (i>0) { MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES); }
 69:     if (i<n-1) { MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES); }
 70:   }

 72:   /* A1 */
 73:   for (i=Istart;i<Iend;i++) {
 74:     MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES);
 75:     if (i>0) { MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES); }
 76:     if (i<n-1) { MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES); }
 77:   }

 79:   /* A2 */
 80:   if (Istart<=n-1 && n-1<Iend) {
 81:     MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES); 
 82:   }

 84:   /* assemble matrices */
 85:   for (i=0;i<NMAT;i++) {
 86:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
 87:   }
 88:   for (i=0;i<NMAT;i++) {
 89:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
 90:   }

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:                        Create the problem functions
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

108:   /* f3=lambda/(lambda-sigma)=1+sigma/(lambda-sigma) */
109:   FNCreate(PETSC_COMM_WORLD,&g);
110:   FNSetType(g,FNRATIONAL);
111:   numer[0] = sigma;
112:   denom[0] = 1.0; denom[1] = -sigma;
113:   FNRationalSetNumerator(g,1,numer);
114:   FNRationalSetDenominator(g,2,denom);
115:   FNCreate(PETSC_COMM_WORLD,&f[2]);
116:   FNSetType(f[2],FNCOMBINE);
117:   FNCombineSetChildren(f[2],FN_COMBINE_ADD,f[0],g);

119:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120:                 Create the eigensolver and solve the problem
121:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

123:   NEPCreate(PETSC_COMM_WORLD,&nep);
124:   NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
125:   NEPSetProblemType(nep,NEP_RATIONAL);
126:   NEPSetFromOptions(nep);
127:   NEPSolve(nep);

129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130:                     Display solution and clean up
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

133:   /* show detailed info unless -terse option is given by user */
134:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
135:   if (terse) {
136:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
137:   } else {
138:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
139:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
140:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
141:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
142:   }
143:   NEPDestroy(&nep);
144:   for (i=0;i<NMAT;i++) {
145:     MatDestroy(&A[i]);
146:     FNDestroy(&f[i]);
147:   }
148:   FNDestroy(&g);
149:   SlepcFinalize();
150:   return ierr;
151: }

153: /*TEST

155:    test:
156:       suffix: 1
157:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
158:       requires: !single

160: TEST*/