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Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method. (English) Zbl 1398.65066

Summary: This paper focuses on the development and engineering applications of a new resolvent sampling based Rayleigh-Ritz method (RSRR) for solving large-scale nonlinear eigenvalue problems (NEPs) in finite element analysis. There are three contributions. First, to generate reliable eigenspaces the resolvent sampling scheme is derived from Keldysh’s theorem for holomorphic matrix functions following a more concise and insightful algebraic framework. Second, based on the new derivation a two-stage solution strategy is proposed for solving large-scale NEPs, which can greatly enhance the computational cost and accuracy of the RSRR. The effects of the user-defined parameters are studied, which provides a useful guide for real applications. Finally, the RSRR and the two-stage scheme is applied to solve two NEPs in the FE analysis of viscoelastic damping structures with up to 1 million degrees of freedom. The method is versatile, robust and suitable for parallelization, and can be easily implemented into other packages.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
65F35 Numerical computation of matrix norms, conditioning, scaling
15A18 Eigenvalues, singular values, and eigenvectors
65F10 Iterative numerical methods for linear systems

Software:

NLEVP; FEAST; JDQZ
PDFBibTeX XMLCite
Full Text: DOI

References:

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