2016•Unpublished venueRequires access

A tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous medium

Houde Han, Zhongyi Huang

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 L2-norm.

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Key concepts: Helmholtz equation, Piecewise, Mathematics, Mathematical analysis, Point (geometry), Finite set, Wave equation, Exact solutions in general relativity