论文标题
来自非线性边界条件的电磁散射的数值分析
Numerical analysis for electromagnetic scattering from nonlinear boundary conditions
论文作者
论文摘要
这项工作从与波浪相互作用的障碍物中研究了时间依赖性电磁散射，这些障碍是由非线性边界条件完全确定的。特别是，这项工作中研究的边界条件强制了沿边界的电场和磁场之间的功率定律类型关系。基于经典边界运算符的时间依赖性跳跃条件，我们得出了一个非线性的时间依赖性边界积分方程系统，该系统决定了散射电场和磁场的切向痕迹。这些字段随后可以通过评估时间依赖性表示公式在外部域中的任意点进行计算。 完全离散的方案是通过在时间和raviart的runge基于kutta的卷积正交中离散边界积分方程的非线性系统 - 空间中的thomas边界元素。在确切解决方案足够规律性的假设下，证明了具有明确指定的收敛速率的误差边界。误差分析是通过基于时间滴定传输问题和使用新的离散部分集成不平等的新技术进行的。数值实验说明了提出的方法的使用并提供了经验收敛速率。
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power law type relation between the electric and magnetic field along the boundary. Based on time-dependent jump conditions of classical boundary operators, we derive a nonlinear system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. These fields can subsequently be computed at arbitrary points in the exterior domain by evaluating a time-dependent representation formula. Fully discrete schemes are obtained by discretising the nonlinear system of boundary integral equations with Runge--Kutta based convolution quadrature in time and Raviart--Thomas boundary elements in space. Error bounds with explicitly stated convergence rates are proven, under the assumption of sufficient regularity of the exact solution. The error analysis is conducted through novel techniques based on time-discrete transmission problems and the use of a new discrete partial integration inequality. Numerical experiments illustrate the use of the proposed method and provide empirical convergence rates.
