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Volume 26, Issue 5
A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium

Houde Han & Zhongyi Huang

J. Comp. Math., 26 (2008), pp. 728-739.

Published online: 2008-10

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  • Abstract

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number $k$ in $L^2$-norm.

  • Keywords

Tailored finite point method, Helmholtz equation, Inhomogeneous media, High frequency wave.

  • AMS Subject Headings

65N99, 74J05, 74J40.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-728, author = {Houde Han and Zhongyi Huang}, title = {A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {728--739}, abstract = {

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number $k$ in $L^2$-norm.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8655.html} }
TY - JOUR T1 - A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium AU - Houde Han & Zhongyi Huang JO - Journal of Computational Mathematics VL - 5 SP - 728 EP - 739 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8655.html KW - Tailored finite point method, Helmholtz equation, Inhomogeneous media, High frequency wave. AB -

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number $k$ in $L^2$-norm.

Houde Han and Zhongyi Huang. (2008). A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium. Journal of Computational Mathematics. 26 (5). 728-739. doi:
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