发展方程的完美匹配边界层模型

THE PERFECTLY MATCHED LAYER MODEL FOR EVOLUTION EQUATION

在有界区域上使用数值方法模拟无界区域上的偏微分方程时,要求在有界区域边界上添加人工边界条件。构造的人工边界条件必须能消除边界上不必要的反射,完美匹配边界层是非常有效的人工吸收边界条件之一。本研究采用复值坐标拉伸的方法,在不分离变量的前提下对发展方程推导出了完美匹配边界层模型。通过平面波分析可知,波在初始求解区域边界上无反射,且在有界的完美匹配边界层上振幅是指数衰减的。

For the numerical simulation of infinite domain partial differential equation in finite domain,it requires adding artificial boundary conditions to the model.This artificial boundary conditions can eliminate the unwanted reflections.Perfectly matched boundary layer is one of the most effective artificial absorbing boundary conditions.In this paper,the perfectly matched layer model for the evolution equation is constructed by using complex-value coordinate stretching methods,without coordinate separation.Through plane wave analysis,reflection doesn’t happen in the original boundary.The amplitude of the plane wave is exponential decay in the perfectly matched layer.