双层位势问题新的基本解法公式

A New Method of Fundamental Solution Formulation to Double Layer Potential Problems

基于单层位势和叠加原理的传统的基本解法,在求解某些有限域问题时,虚边界位置的选择会受到一定的限制,在求解某些无限域问题时可能会无解。为此提出了基于双层位势和叠加原理的改进的基本解法,避免了传统基本解法的不足。该方法适合求解任何边值问题,其特点是有限域问题和无限域问题的基本解法公式具有不同的形式。

The conventional method of fundamental solution（ MFS）,based on the single layer potential and the superposition principle,has many shortcomings,for instance,for special interior problems its fictitious boundary location may be limited and for certain exterior problems it may fail.In this paper,a new method of fundamental solution formulation,which is built on the double layer potential and the superposition principle,is developed. The method avoids some disadvantages of the traditional method of fundamental solution and thus is suitable for solving any boundary value problems.