有势场逆问题的边界元法

本文给出了位势方程逆问题的一种最小二乘边界元解法。控制方程为Ｌａｐｌａｃｅ方程，但一部分边界上未给出任何边值，而只在某些内点上给出了势函值。这一问题在数学上属不适定问题，但在一定条件下存在唯一解。本文同时给出了一种估计解的可靠性的方法。数值试验表明，这类逆问题采用边界元法是非常有效的。

A BEM SCHEME FOR INVERSE POTENTIAL PROBLEM

In this paper, a BEM scheme for Laplace inverse problem is presented. Wherein, on a part of boundary there is no boundary value given at all, but the potential values at some internal points are given instead. It is well known that this kind of problem is not well posed mathematically, but its solution still exists conditionally. In this paper, an error estimation or reliability analysis of the BEM scheme is introduced together with the BEM formulation. The numerical results show that this BEM inverse scheme is really efficient for such cases.