论文标题
麦克斯韦方程的自适应有限元DTN方法
An Adaptive Finite Element DtN Method for Maxwell's Equations
论文作者
论文摘要
本文与三维中有界且难以穿透的障碍物的时间谐波电磁波散射的数值解决方案有关。电磁波传播是由障碍物外部域中麦克斯韦方程的边界值问题建模的。基于由无限序列定义的Dirichlet到Neumann（DTN）运算符，引入了确切的透明边界条件，并将散射问题等效地减少到有界域。基于后验误差估计的一种自适应有限元DTN方法是为了解决离散的变分问题而开发的，其中DTN运算符被截断为有限的许多术语。 A后验误差估计值考虑了有限元近似误差和DTN操作员的截断误差。后者证明相对于截断参数呈指数衰减。提出了数值实验，以说明该方法的有效性。
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value problem of Maxwell's equations in the exterior domain of the obstacle. Based on the Dirichlet-to-Neumann (DtN) operator, which is defined by an infinite series, an exact transparent boundary condition is introduced and the scattering problem is reduced equivalently into a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is developed to solve the discrete variational problem, where the DtN operator is truncated into a sum of finitely many terms. The a posteriori error estimate takes into account both the finite element approximation error and the truncation error of the DtN operator. The latter is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.
