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Boundary Element Method for 2D Non-homogeneous Helmholtz Equation

Jianping Liu

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Abstract

A direct boundary element method based on the basic solution of the Laplace equation for solving two-dimensional non-homogeneous Helmholtz equation is described in this paper.The fundamental solution of the Laplace equation and Green formula was used after the distortion of the Helmholtz equation to obtain the direct integral equation.Aiming at the concurrence of the region integral subentry and the boundary integral subentry in the integral eqution,coupling of the integral equations about the points in the region and those on the boundary were used when the boundary element method was applied to solve the problem.Finally,validity of the method is discussed by an example.

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What this paper is about

A direct boundary element method based on the basic solution of the Laplace equation for solving two-dimensional non-homogeneous Helmholtz equation is described in this paper.The fundamental solution of the Laplace equation and Green formula was used after the distortion of the Helmholtz equation to obtain the direct integral equation.Aiming at the concurrence of the region integral subentry and the boundary integral subentry in the integral eqution,coupling of the integral equations about the points in the region and those on the boundary were used when the boundary element method was applied to solve the problem.Finally,validity of the method is discussed by an example.

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Available abstract

A direct boundary element method based on the basic solution of the Laplace equation for solving two-dimensional non-homogeneous Helmholtz equation is described in this paper.The fundamental solution of the Laplace equation and Green formula was used after the distortion of the Helmholtz equation to obtain the direct integral equation.Aiming at the concurrence of the region integral subentry and the boundary integral subentry in the integral eqution,coupling of the integral equations about the points in the region and those on the boundary were used when the boundary element method was applied to solve the problem.Finally,validity of the method is discussed by an example.

Key concepts: Helmholtz equation, Boundary element method, Mathematical analysis, Integral equation, Electric-field integral equation, Laplace's equation, Mathematics, Method of fundamental solutions

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