Actual source code: ex42.c

slepc-3.21.1 2024-04-26
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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.
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:   PetscFunctionBeginUser;
45:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

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

53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
54:                        Build the problem matrices
55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

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

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

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

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

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

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

135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136:                        Check left residual
137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138:   PetscCall(MatCreateVecs(A[0],&v,&r));
139:   PetscCall(VecDuplicate(v,&w));
140:   PetscCall(VecDuplicate(v,&z));
141:   PetscCall(NEPGetConverged(nep,&nconv));
142:   PetscCall(NEPGetTolerances(nep,&tol,NULL));
143:   for (i=0;i<nconv;i++) {
144:     PetscCall(NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL));
145:     PetscCall(NEPGetLeftEigenvector(nep,i,v,NULL));
147:     PetscCall(VecNorm(r,NORM_2,&nrm));
148:     if (nrm>tol*PetscAbsScalar(lambda)) PetscCall(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:   PetscCall(VecSet(v,0.0));
157:   PetscCall(VecSetValue(v,0,-1.0,INSERT_VALUES));
158:   PetscCall(VecSetValue(v,1,3.0,INSERT_VALUES));
159:   PetscCall(VecAssemblyBegin(v));
160:   PetscCall(VecAssemblyEnd(v));
161:   PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
162:   PetscCall(VecNorm(r,NORM_2,&nrm));
163:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
164:   PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
165:   PetscCall(VecNorm(r,NORM_2,&nrm));
166:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));
167:   PetscCall(VecSet(v,1.0));
168:   PetscCall(NEPApplyResolvent(nep,NULL,omega1,v,r));
169:   PetscCall(VecNorm(r,NORM_2,&nrm));
170:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm));
171:   PetscCall(NEPApplyResolvent(nep,NULL,omega2,v,r));
172:   PetscCall(VecNorm(r,NORM_2,&nrm));
173:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm));

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

189: /*TEST

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

195: TEST*/
```