求解二维非齐次Helmholtz方程的边界元法

基于Laplace方程的基本解讨论了二维非齐次Helmholtz方程的直接边界元解法.通过将Helmholtz方程变形之后加权Laplace方程的基本解和应用Green公式得到相应的直接积分方程,针对积分方程中同时存在域积分项和边界积分项,在应用边界元法分析求解时采用了耦合关于内点和边界点的积分方程求解,最后,通过数值算例验证方法的有效性.

Boundary Element Method for 2D Non-homogeneous Helmholtz Equation

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.