时域有限差分法中的吸收边界条件与角点处理

The Corner Point Processing and Absorbing Boundary Conditions in Finite-Difference Time-Domain

吸收边界条件是时域有限差分法 (FDTD)中的一个重要部分 ,而吸收边界条件中角点的处理又对吸收边界条件本身影响甚大 ,角点处理的不恰当 ,可能导致完全不合逻辑的结果。传统二维二阶近似吸收边界条件中对角点的处理则比较复杂 ,且不易向三维情况推广。针对这种情况 ,文中基于单向行波吸收理论 ,讨论了一种简单易处理的角点处理方法 ,并设计了一数值试验方法进行了验证 ,计算结果表明这种方法满足对吸收边界条件所提出的各项要求并具有较高的计算精度。同时 ,这种角点处理法也极易向三维情况推广。

ABC(Absorbing Boundary Conditions) is an important component part in FDTD(Finite-Difference Time-Domain) method,the processing of corner point affect ABC itself,that is,the inadequate processing of them may cause unnaturally results.The processing of corner points in traditional second-order absorbing boundary condition for 2D case is complex,and it is difficult to extend to 3D case.For these reasons,a simpler method about the corner points based on unidirectional out traveling wave absorbing theorem is discussed in this paper,and validated by a numerical method proposed by authors.The results show that this method satisfies the demands for ABC and is more efficient and more precise.Meanwhile,it is easy to extent to 3D case.