A rational approximation method for solving acoustic nonlinear eigenvalue problems

Mohamed El-Guide, Agnieszka Miȩdlar, Yousef Saad

Research output: Contribution to journalReview article

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.

Original languageEnglish (US)
Pages (from-to)44-54
Number of pages11
JournalEngineering Analysis with Boundary Elements
Volume111
DOIs
StatePublished - Feb 2020

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Chebyshev approximation
Nonlinear Eigenvalue Problem
Rational Approximation
Boundary element method
Approximation Methods
Industrial applications
Interpolation
Acoustics
Boundary Elements
Cauchy's integral formula
Real Interpolation
Chebyshev Approximation
Chebyshev's Method
Eigenfrequency
Industrial Application
Chebyshev
Parallelization
Argand diagram
Cauchy
Eigenvalue Problem

Keywords

  • Boundary element method
  • Cauchy integral formula
  • Nonlinear eigenvalue problem
  • Rational approximation

Cite this

A rational approximation method for solving acoustic nonlinear eigenvalue problems. / El-Guide, Mohamed; Miȩdlar, Agnieszka; Saad, Yousef.

In: Engineering Analysis with Boundary Elements, Vol. 111, 02.2020, p. 44-54.

Research output: Contribution to journalReview article

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