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首页> 外文期刊>International journal of computer mathematics >Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods
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Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

机译：径向积分边界积分和积分微分方程方法数值求解二维变系数亥姆霍兹方程

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摘要

This paper presents new formulations of the boundary-domain integral equation (BDIE) and the boundary-domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods.
机译：本文为二维变系数亥姆霍兹方程的数值解提供了边界域积分方程（BDIE）和边界域积分微分方程（BDIDE）方法的新公式。当材料参数是可变的（具有恒定或可变的波数）时，采用参数将Helmholtz方程简化为BDIE或BDIDE。但是，当材料参数恒定（波数可变）时，在公式中使用Laplace方程的标准基本解。然后，采用径向积分方法将BDIE和BDIDE方法中产生的域积分转换为等效边界积分。由此产生的公式导致没有边界积分的纯边界积分和积分微分方程。给出了几个简单问题的数值示例，并提供了精确的解决方案，以证明所提出方法的效率。

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