Actual source code: ex42.c
slepc-3.21.0 2024-03-30
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: 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));
146: PetscCall(NEPApplyAdjoint(nep,lambda,v,w,r,NULL,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*/