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

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

65N99 74J05 74J40.

@Article{JCM-26-728, author = {}, 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 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 KW - Helmholtz equation KW - Inhomogeneous media KW - 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.