Actual source code: ex42.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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);if (ierr) return ierr;
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=%D 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) {
82: MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);
83: }
85: /* assemble matrices */
86: for (i=0;i<NMAT;i++) {
87: MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
88: }
89: for (i=0;i<NMAT;i++) {
90: MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
91: }
93: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: Create the problem functions
95: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: /* f1=1 */
98: FNCreate(PETSC_COMM_WORLD,&f[0]);
99: FNSetType(f[0],FNRATIONAL);
100: numer[0] = 1.0;
101: FNRationalSetNumerator(f[0],1,numer);
103: /* f2=-lambda */
104: FNCreate(PETSC_COMM_WORLD,&f[1]);
105: FNSetType(f[1],FNRATIONAL);
106: numer[0] = -1.0; numer[1] = 0.0;
107: FNRationalSetNumerator(f[1],2,numer);
109: /* f3=lambda/(lambda-sigma) */
110: FNCreate(PETSC_COMM_WORLD,&f[2]);
111: FNSetType(f[2],FNRATIONAL);
112: numer[0] = 1.0; numer[1] = 0.0;
113: denom[0] = 1.0; denom[1] = -sigma;
114: FNRationalSetNumerator(f[2],2,numer);
115: FNRationalSetDenominator(f[2],2,denom);
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Create the eigensolver and solve the problem
119: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: NEPCreate(PETSC_COMM_WORLD,&nep);
122: NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
123: NEPSetProblemType(nep,NEP_RATIONAL);
124: NEPSetDimensions(nep,8,PETSC_DEFAULT,PETSC_DEFAULT);
126: /* set two-sided NLEIGS solver */
127: NEPSetType(nep,NEPNLEIGS);
128: NEPNLEIGSSetFullBasis(nep,PETSC_TRUE);
129: NEPSetTwoSided(nep,PETSC_TRUE);
130: NEPGetRG(nep,&rg);
131: RGSetType(rg,RGINTERVAL);
132: #if defined(PETSC_USE_COMPLEX)
133: RGIntervalSetEndpoints(rg,4.0,700.0,-0.001,0.001);
134: #else
135: RGIntervalSetEndpoints(rg,4.0,700.0,0,0);
136: #endif
137: NEPSetTarget(nep,5.0);
139: NEPSetFromOptions(nep);
140: NEPSolve(nep);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Check left residual
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: MatCreateVecs(A[0],&v,&r);
146: VecDuplicate(v,&w);
147: VecDuplicate(v,&z);
148: NEPGetConverged(nep,&nconv);
149: NEPGetTolerances(nep,&tol,NULL);
150: for (i=0;i<nconv;i++) {
151: NEPGetEigenpair(nep,i,&lambda,NULL,NULL,NULL);
152: NEPGetLeftEigenvector(nep,i,v,NULL);
153: NEPApplyAdjoint(nep,lambda,v,w,r,NULL,NULL);
154: VecNorm(r,NORM_2,&nrm);
155: if (nrm>tol*PetscAbsScalar(lambda)) {
156: PetscPrintf(PETSC_COMM_WORLD,"Left residual i=%D is above tolerance --> %g\n",i,nrm/PetscAbsScalar(lambda));
157: }
158: }
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Operate with resolvent
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: omega1 = 20.0;
164: omega2 = 150.0;
165: VecSet(v,0.0);
166: VecSetValue(v,0,-1.0,INSERT_VALUES);
167: VecSetValue(v,1,3.0,INSERT_VALUES);
168: VecAssemblyBegin(v);
169: VecAssemblyEnd(v);
170: NEPApplyResolvent(nep,NULL,omega1,v,r);
171: VecNorm(r,NORM_2,&nrm);
172: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
173: NEPApplyResolvent(nep,NULL,omega2,v,r);
174: VecNorm(r,NORM_2,&nrm);
175: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);
176: VecSet(v,1.0);
177: NEPApplyResolvent(nep,NULL,omega1,v,r);
178: VecNorm(r,NORM_2,&nrm);
179: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega1),(double)nrm);
180: NEPApplyResolvent(nep,NULL,omega2,v,r);
181: VecNorm(r,NORM_2,&nrm);
182: PetscPrintf(PETSC_COMM_WORLD,"resolvent, omega=%g: norm of computed vector=%g\n",(double)PetscRealPart(omega2),(double)nrm);
184: /* clean up */
185: NEPDestroy(&nep);
186: for (i=0;i<NMAT;i++) {
187: MatDestroy(&A[i]);
188: FNDestroy(&f[i]);
189: }
190: VecDestroy(&v);
191: VecDestroy(&r);
192: VecDestroy(&w);
193: VecDestroy(&z);
194: SlepcFinalize();
195: return ierr;
196: }
198: /*TEST
200: test:
201: suffix: 1
202: requires: !single
204: TEST*/