A Tailored Finite Point Method for the Helmholtz Equation with High Wave Numbers in Heterogeneous Medium
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8655
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 5 : pp. 728–739
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Tailored finite point method Helmholtz equation Inhomogeneous media High frequency wave.