椭圆单侧问题的边界元计算方法

单侧问题是一类重要的数学物理问题，它可以转化为互补问题进行求解。由于单侧问题的互补条件位于边界之上，特别适用于边界元法。基于Aitchison提出的关于Laplace算子的开关算法，笔者将之拓广到一般的椭圆型算子，并基于边界元方法应用开关算法，对这一问题给出了简单高效的计算方法，并进行了算法的收敛性分析，最后给出了相应的数值算例。此种算法的优点在于只须在原有的边界元程序巾．做少量的改进．并且迭代效率极高．产生的计算误差很小．结果表明．算法简明高效．

The BEM for Elliptic Unilateral Problems

Unilateral problems is a kind of important partial differential problems. It can be solved by treating it as a complementary problem. As the complementary conditions lie in the boundary of the region,it is suitable for BEM. This paper is based on the switching algorithm,which is first used by J. M. Aitchison for the Signorini Problems of Laplace operator,then extends it to the elliptic operator,and conjunct it with the BEM. At last the detail of the algorithm is given. The new algorithm is easy to be implied effectively and quickly. It only needs the minimal change of the BEM programming. The numerical tests show the algorithm is effective and conventional.