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Chang, S.-L.; Chien, C.-S.

A multigrid-Lanczos algorithm for the numerical solutions of nonlinear eigenvalue problems. (English) Zbl 1062.65117

Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 5, 1217-1228 (2003).
Summary: We study numerical methods for solving nonlinear elliptic eigenvalue problems which contain folds and bifurcation points. First we present some convergence theory for the minimal residual algorithm, a variant of the Lanczos method. A multigrid-Lanczos method is then proposed for tracking solution branches of associated discrete problems and detecting singular points along solution branches. The proposed algorithm has the advantage of being robust and can be easily implemented. It can be regarded as a generalization and an improvement of the continuation-Lanczos algorithm. Our numerical results show the efficiency of this algorithm.

Cited in 9 Documents

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35B32 Bifurcations in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations

Keywords:

Multigrid method; Lanczos method; continuation method; nonlinear elliptic eigenvalue problems; bifurcation; minimal residual algorithm; convergence; singular points; numerical results

Software:

HOMPACK
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References:

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