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Volume 30, Issue 4
Tailored Finite Cell Method for Solving Helmholtz Equation in Layered Heterogeneous Medium

Zhongyi Huang & Xu Yang

DOI: 10.4208/jcm.1111-m3679

J. Comp. Math., 30 (2012), pp. 381-391.

Published online: 2012-08

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  • Abstract

In this paper, we propose a tailored finite cell method for the computation of two-dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number (high frequency). The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.

  • Keywords

Tailored finite cell method, Helmholtz equation, Heterogeneous media, Sommerfeld condition.

  • AMS Subject Headings

65N35, 35L10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-381, author = {Zhongyi Huang and Xu Yang}, title = {Tailored Finite Cell Method for Solving Helmholtz Equation in Layered Heterogeneous Medium}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {4}, pages = {381--391}, abstract = {

In this paper, we propose a tailored finite cell method for the computation of two-dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number (high frequency). The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1111-m3679}, url = {http://global-sci.org/intro/article_detail/jcm/8437.html} }
TY - JOUR T1 - Tailored Finite Cell Method for Solving Helmholtz Equation in Layered Heterogeneous Medium AU - Zhongyi Huang & Xu Yang JO - Journal of Computational Mathematics VL - 4 SP - 381 EP - 391 PY - 2012 DA - 2012/08 SN - 30 DO - http://doi.org/10.4208/jcm.1111-m3679 UR - https://global-sci.org/intro/article_detail/jcm/8437.html KW - Tailored finite cell method, Helmholtz equation, Heterogeneous media, Sommerfeld condition. AB -

In this paper, we propose a tailored finite cell method for the computation of two-dimensional Helmholtz equation in layered heterogeneous medium. The idea underlying the method is to construct a numerical scheme based on a local approximation of the solution to Helmholtz equation. This provides a computational tool of achieving high accuracy with coarse mesh even for large wave number (high frequency). The stability analysis and error estimates of this method are also proved. We present several numerical results to show its efficiency and accuracy.

Zhongyi Huang and Xu Yang. (2012). Tailored Finite Cell Method for Solving Helmholtz Equation in Layered Heterogeneous Medium. Journal of Computational Mathematics. 30 (4). 381-391. doi:10.4208/jcm.1111-m3679
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