边界元法中区域积分的降维计算方法

REDUCING DIMENSIONS OF DOMAIN INTEGRATION IN BOUNDARY ELEMENT METHOD

§1.引言 边界元方法是在经典的积分方程法和有限元离散化技术的基础上发展起来的求解偏微分方程的数值计算方法.由于它在几何上的广泛适应性,输入数据的简单性以及在数值上的确定性,这种方法已广泛地应用于不同学科领域及各种工程技术问题的数值计算,其基本的思想是利用Green公式和微分方程的基本解尽可能地把区域上的积分转化为边界上的积分.

The main advantage of Boundary Element Method (BEM) is reducing the dimensions by one in performing calculation. When inhomogeneous term appears in the governing equation of the problem, the domain integral is inevitable excepting some special cases. The common way to perform the domain integral involves subdividing the domain into a series of subdornains over which a numerical integration formula or an analytical quadrature can be applied. This paper presents an alternative way to transform the domain integral over subdornains into equivalent boundary integrals on the boundary of each subdomain, so that all the integrals are performed on the boundary case. It makes the whole calculation of BEM reduced by one dimension really.