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Volume 2, Issue 3
An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains

Qirong Fang, Jie Shen & Li-Lian Wang

DOI: 10.4208/nmtma.2009.m8014

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 258-274.

Published online: 2009-02

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  • Abstract

An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper. The method is based on the so called transformed field expansion (TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions. Numerical results are presented to show the accuracy and stability of the proposed method.

  • Keywords

Acoustic scattering, high-order methods, boundary perturbations, spectral-Galerkin methods.

  • AMS Subject Headings

78A45, 65N35, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-258, author = {Qirong Fang, Jie Shen and Li-Lian Wang}, title = {An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {3}, pages = {258--274}, abstract = {

An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper. The method is based on the so called transformed field expansion (TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions. Numerical results are presented to show the accuracy and stability of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m8014}, url = {http://global-sci.org/intro/article_detail/nmtma/6025.html} }
TY - JOUR T1 - An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains AU - Qirong Fang, Jie Shen & Li-Lian Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 258 EP - 274 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m8014 UR - https://global-sci.org/intro/article_detail/nmtma/6025.html KW - Acoustic scattering, high-order methods, boundary perturbations, spectral-Galerkin methods. AB -

An efficient and accurate method for solving the two-dimensional Helmholtz equation in domains exterior to elongated obstacles is developed in this paper. The method is based on the so called transformed field expansion (TFE) coupled with a spectral-Galerkin solver for elliptical domain using Mathieu functions. Numerical results are presented to show the accuracy and stability of the proposed method.

Qirong Fang, Jie Shen and Li-Lian Wang. (2009). An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains. Numerical Mathematics: Theory, Methods and Applications. 2 (3). 258-274. doi:10.4208/nmtma.2009.m8014
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