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.
Bibliographical noteFunding Information:
Work supported by NSF grant 1812927 and 1812695.
© 2019 Elsevier Ltd
- Boundary element method
- Cauchy integral formula
- Nonlinear eigenvalue problem
- Rational approximation