Actual source code: ex42.c
slepc-3.18.3 2023-03-24
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;
45: SlepcInitialize(&argc,&argv,(char*)0,help);
47: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
48: PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);
49: PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL);
50: sigma = kappa/m;
51: 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: MatCreate(PETSC_COMM_WORLD,&A[i]);
60: MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
61: MatSetFromOptions(A[i]);
62: MatSetUp(A[i]);
63: }
64: MatGetOwnershipRange(A[0],&Istart,&Iend);
66: /* A0 */
67: for (i=Istart;i<Iend;i++) {
68: MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES);
69: if (i>0) MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES);
70: if (i<n-1) MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES);
71: }
73: /* A1 */
74: for (i=Istart;i<Iend;i++) {
75: MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES);
76: if (i>0) MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES);
77: if (i<n-1) MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES);
78: }
80: /* A2 */
81: if (Istart<=n-1 && n-1<Iend) MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);
83: /* assemble matrices */
84: for (i=0;i<NMAT;i++) MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
85: for (i=0;i<NMAT;i++) MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Create the problem functions
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
91: /* f1=1 */
92: FNCreate(PETSC_COMM_WORLD,&f[0]);
93: FNSetType(f[0],FNRATIONAL);
94: numer[0] = 1.0;
95: FNRationalSetNumerator(f[0],1,numer);
97: /* f2=-lambda */
98: FNCreate(PETSC_COMM_WORLD,&f[1]);
99: FNSetType(f[1],FNRATIONAL);
100: numer[0] = -1.0; numer[1] = 0.0;
101: FNRationalSetNumerator(f[1],2,numer);
103: /* f3=lambda/(lambda-sigma) */
104: FNCreate(PETSC_COMM_WORLD,&f[2]);
105: FNSetType(f[2],FNRATIONAL);
106: numer[0] = 1.0; numer[1] = 0.0;
107: denom[0] = 1.0; denom[1] = -sigma;
108: FNRationalSetNumerator(f[2],2,numer);
109: FNRationalSetDenominator(f[2],2,denom);
111: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112: Create the eigensolver and solve the problem
113: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115: NEPCreate(PETSC_COMM_WORLD,&nep);
116: NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
117: NEPSetProblemType(nep,NEP_RATIONAL);
118: NEPSetDimensions(nep,8,PETSC_DEFAULT,PETSC_DEFAULT);
120: /* set two-sided NLEIGS solver */
121: NEPSetType(nep,NEPNLEIGS);
122: NEPNLEIGSSetFullBasis(nep,PETSC_TRUE);
123: NEPSetTwoSided(nep,PETSC_TRUE);
124: NEPGetRG(nep,&rg);
125: RGSetType(rg,RGINTERVAL);
126: #if defined(PETSC_USE_COMPLEX)
127: RGIntervalSetEndpoints(rg,4.0,700.0,-0.001,0.001);
128: #else
129: RGIntervalSetEndpoints(rg,4.0,700.0,0,0);
130: #endif
131: NEPSetTarget(nep,5.0);
133: NEPSetFromOptions(nep);
134: NEPSolve(nep);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Check left residual
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: MatCreateVecs(A[0],&v,&r);
140: VecDuplicate(v,&w);
141: VecDuplicate(v,&z);
142: NEPGetConverged(nep,&nconv);
143: NEPGetTolerances(nep,&tol,NULL);
144: for (i=0;i<nconv;i++) {
145: NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL);
146: NEPGetLeftEigenvector(nep,i,v,NULL);
147: NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL);
148: VecNorm(r,NORM_2,&nrm);
149: if (nrm>tol*PetscAbsScalar(lambda)) PetscPrintf(PETSC_COMM_WORLD,"Left residual i=%" PetscInt_FMT " is above tolerance --> %g\n",i,(double)(nrm/PetscAbsScalar(lambda)));
150: }
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Operate with resolvent
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: omega1 = 20.0;
156: omega2 = 150.0;
157: VecSet(v,0.0);
158: VecSetValue(v,0,-1.0,INSERT_VALUES);
159: VecSetValue(v,1,3.0,INSERT_VALUES);
160: VecAssemblyBegin(v);
161: VecAssemblyEnd(v);
162: NEPApplyResolvent(nep,NULL,omega1,v,r);
163: VecNorm(r,NORM_2,&nrm);
164: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
165: NEPApplyResolvent(nep,NULL,omega2,v,r);
166: VecNorm(r,NORM_2,&nrm);
167: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);
168: VecSet(v,1.0);
169: NEPApplyResolvent(nep,NULL,omega1,v,r);
170: VecNorm(r,NORM_2,&nrm);
171: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
172: NEPApplyResolvent(nep,NULL,omega2,v,r);
173: VecNorm(r,NORM_2,&nrm);
174: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);
176: /* clean up */
177: NEPDestroy(&nep);
178: for (i=0;i<NMAT;i++) {
179: MatDestroy(&A[i]);
180: FNDestroy(&f[i]);
181: }
182: VecDestroy(&v);
183: VecDestroy(&r);
184: VecDestroy(&w);
185: VecDestroy(&z);
186: SlepcFinalize();
187: return 0;
188: }
190: /*TEST
192: test:
193: suffix: 1
194: requires: !single
196: TEST*/