A rational approximation method for solving acoustic nonlinear eigenvalue problems. (February 2020)

• Record Type: Journal Article
• Authors: El-Guide, Mohamed; Miȩdlar, Agnieszka; Saad, Yousef
• Is Part Of: Engineering analysis with boundary elements. Volume 111(2020)
• Page Start: 44
• Page End: 54
• Publication Date: 2020-02
• Subjects: Nonlinear eigenvalue problem -- Boundary element method -- Rational approximation -- Cauchy integral formula; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2019.10.006
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in three-dimensional space. The main idea of the first method is to approximate the resulting boundary element matrix within a contour in the complex plane by a high accuracy rational approximation using the Cauchy integral formula. The second method is based on the Chebyshev interpolation within real intervals. A Rayleigh–Ritz procedure, which is suitable for parallelization is developed for both the Cauchy and the Chebyshev approximation methods when dealing with large-scale practical applications. The performance of the proposed methods is illustrated with a variety of benchmark examples and large-scale industrial applications with degrees of freedom varying from several hundred up to around two million.