arXiv subjects

Mohamed El-Guide

Publications and source records attributed to Mohamed El-Guide.

2 recordsLinked to original sources

arXiv2019

A rational approximation method for solving acoustic nonlinear eigenvalue problems

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.

math.NA↗

arXiv2019

A rational approximation method for the nonlinear eigenvalue problem

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a form of linearization. Eigenpairs of the expanded form of this linearization are not extracted directly. Instead, its structure is exploited to develop a scheme that allows to extract all eigenvalues in a certain region of the complex plane by solving an eigenvalue problem of much smaller dimension. Because of its simple implementation and the ability to work efficiently in large dimensions, the presented method is appealing when solving challenging engineering problems. A few theoretical results are established to explain why the new approach works and numerical experiments are presented to validate the proposed algorithm.

math.NA↗