A rational approximation method for solving acoustic nonlinear eigenvalue problems

Mohamed El-Guide, Agnieszka Miȩdlar, Yousef Saad

Research output: Contribution to journalReview articlepeer-review

4 Scopus citations


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
StatePublished - Feb 2020

Bibliographical note

Funding Information:
Work supported by NSF grant 1812927 and 1812695.

Publisher Copyright:
© 2019 Elsevier Ltd


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


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