Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method

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• 作者：Jinyou Xiao ; Hang Zhou ; Chuanzeng Zhang ; Chao Xu
• 关键词：Finite element methods ; Viscoelastic material structures ; Nonlinear eigenvalue problems ; Rayleigh ; Ritz projection
• 刊名：Computational Mechanics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：59
• 期：2
• 页码：317-334
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics; Computational Science and Engineering; Classical and Continuum Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0924
• 卷排序：59

文摘

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.