Date: 2022-03-31T15:29:35+00:00

Actual source code: ex42.c
slepc-3.17.0 2022-03-31
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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[] = "Illustrates computation of left eigenvectors and resolvent.\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];         /* functions to define the nonlinear operator */
     37:   NEP            nep;             /* nonlinear eigensolver context */
     38:   RG             rg;
     39:   Vec            v,r,z,w;
     40:   PetscInt       n=100,Istart,Iend,i,nconv;
     41:   PetscReal      kappa=1.0,m=1.0,nrm,tol;
     42:   PetscScalar    lambda,sigma,numer[2],denom[2],omega1,omega2;

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

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

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

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

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

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

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

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

    114:   NEPCreate(PETSC_COMM_WORLD,&nep);
    115:   NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
    116:   NEPSetProblemType(nep,NEP_RATIONAL);
    117:   NEPSetDimensions(nep,8,PETSC_DEFAULT,PETSC_DEFAULT);

    119:   /* set two-sided NLEIGS solver */
    120:   NEPSetType(nep,NEPNLEIGS);
    121:   NEPNLEIGSSetFullBasis(nep,PETSC_TRUE);
    122:   NEPSetTwoSided(nep,PETSC_TRUE);
    123:   NEPGetRG(nep,&rg);
    124:   RGSetType(rg,RGINTERVAL);
    125: #if defined(PETSC_USE_COMPLEX)
    126:   RGIntervalSetEndpoints(rg,4.0,700.0,-0.001,0.001);
    127: #else
    128:   RGIntervalSetEndpoints(rg,4.0,700.0,0,0);
    129: #endif
    130:   NEPSetTarget(nep,5.0);

    132:   NEPSetFromOptions(nep);
    133:   NEPSolve(nep);

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:                        Check left residual
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    138:   MatCreateVecs(A[0],&v,&r);
    139:   VecDuplicate(v,&w);
    140:   VecDuplicate(v,&z);
    141:   NEPGetConverged(nep,&nconv);
    142:   NEPGetTolerances(nep,&tol,NULL);
    143:   for (i=0;i<nconv;i++) {
    144:     NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL);
    145:     NEPGetLeftEigenvector(nep,i,v,NULL);
    146:     NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL);
    147:     VecNorm(r,NORM_2,&nrm);
    148:     if (nrm>tol*PetscAbsScalar(lambda)) PetscPrintf(PETSC_COMM_WORLD,"Left residual i=%" PetscInt_FMT " is above tolerance --> %g\n",i,(double)(nrm/PetscAbsScalar(lambda)));
    149:   }

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:                       Operate with resolvent
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   omega1 = 20.0;
    155:   omega2 = 150.0;
    156:   VecSet(v,0.0);
    157:   VecSetValue(v,0,-1.0,INSERT_VALUES);
    158:   VecSetValue(v,1,3.0,INSERT_VALUES);
    159:   VecAssemblyBegin(v);
    160:   VecAssemblyEnd(v);
    161:   NEPApplyResolvent(nep,NULL,omega1,v,r);
    162:   VecNorm(r,NORM_2,&nrm);
    163:   PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
    164:   NEPApplyResolvent(nep,NULL,omega2,v,r);
    165:   VecNorm(r,NORM_2,&nrm);
    166:   PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);
    167:   VecSet(v,1.0);
    168:   NEPApplyResolvent(nep,NULL,omega1,v,r);
    169:   VecNorm(r,NORM_2,&nrm);
    170:   PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
    171:   NEPApplyResolvent(nep,NULL,omega2,v,r);
    172:   VecNorm(r,NORM_2,&nrm);
    173:   PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);

    175:   /* clean up */
    176:   NEPDestroy(&nep);
    177:   for (i=0;i<NMAT;i++) {
    178:     MatDestroy(&A[i]);
    179:     FNDestroy(&f[i]);
    180:   }
    181:   VecDestroy(&v);
    182:   VecDestroy(&r);
    183:   VecDestroy(&w);
    184:   VecDestroy(&z);
    185:   SlepcFinalize();
    186:   return 0;
    187: }

    189: /*TEST

    191:    test:
    192:       suffix: 1
    193:       requires: !single

    195: TEST*/