Actual source code: ex42.c

slepc-3.17.1 2022-04-11
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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*/