线性边值问题的一类新型边界元法

本文由加权残值法导出了边界元法的一类新型积分公式,并提出了相应的内点公式和边界点公式联立求解方法。在这类公式中,不一定要取权函数为控制方程的基本解,在许多问题中。当用常规边界元法而找不到基本解时,可以改用本文的新型积分公式来解决。本文给出了这类积分方程的一般推导方法,就一些具体线性边值问题作了讨论,建立了相应的积分公式和求解方法。这种方法为用边界元法求解名类问题编制系统电算程序提供了方便。

A New Type of Boundary Element Method for Linear Boundary Value Problems

A new type of integration formula for boundary element method(BEM) by means of weighted residuals method is developed together with the corresponding solving method combining boundary point formula with inner point formula.In the integration formula,it is not necessary to take weighted function as the fundamental solution of governing equation.When the fundamental solution is unable to be found in the use of general BEM in some problems,the new type of integration formula can be used.The integration formula is derived,some particular linear boundary problems are discussed,and corresponding formulas and methods are established. This method enabIe compilation of system program to solve various problems by BEM,method for deriving the formula,but also discusses the particular linear boundary problems and gives the corresponding formula together with the method.It is convenient to develop a commonly used computer program for BEM to solve wide area of problems.