A rational approximation method for solving acoustic nonlinear eigenvalue problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866914953661775872 |
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| author | El-Guide, Mohamed Miedlar, Agnieszka Saad, Yousef |
| author_facet | El-Guide, Mohamed Miedlar, Agnieszka Saad, Yousef |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1906_03938 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A rational approximation method for solving acoustic nonlinear eigenvalue problems El-Guide, Mohamed Miedlar, Agnieszka Saad, Yousef Numerical Analysis 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. |
| title | A rational approximation method for solving acoustic nonlinear eigenvalue problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1906.03938 |