椭圆及热传导界面问题浸入界面方法的研究

Immersed Interface Method for Elliptic Interface and Heat Conduction Problem

摘要: 界面问题的研究具有重要的应用背景。本文从简单的模型出发，改进了浸入界面方法的构造格式.着重讨论界面及附加区域的求解。选取一维椭圆和热传导界面模型问题，采用改进的浸入界面方法求解。最后通过数值算例，利用MATLAB编程验证了格式的有效性和可行性。并且可以进一步推广应用到更复杂的界面问题模型。

Abstract: The study of interface problems has important application background. In this paper immersed interface method is improved, and especially the difficulty about the interface and the area near the interface is discussed. We use this method for solving the one-dimensional elliptic and heat equation. At last based on MATLAB, we give some numerical experiments in order to show the correctness and efficiency of the scheme. The modified immersed interface method can be used for more complicated interface problems.