论文标题
分析异质媒体中Maxwell方程的Peaceman-Rachford ADI计划
Analysis of a Peaceman-Rachford ADI scheme for Maxwell equations in heterogeneous media
论文作者
论文摘要
在异质核心上分析了线性时间依赖性麦克斯韦方程的Peaceman-Rachford交流方向（ADI）方案。由于材料参数的不连续性，麦克斯韦方程的解决方案在空间上小于$ h^2 $。对于ADI方案，我们证明了一个严格的时间二散误差，其收敛速率比经典率低的一半订单。我们的陈述仅对初始数据和材料参数提出假设，而不是在解决方案上。为了确定此结果，我们在适当的功能分析框架中详细分析了麦克斯韦方程的规律性。理论发现与数值实验相辅相成，表明该验证的收敛速率确实是可观察到的。
The Peaceman-Rachford alternating direction implicit (ADI) scheme for linear time-dependent Maxwell equations is analyzed on a heterogeneous cuboid. Due to discontinuities of the material parameters, the solution of the Maxwell equations is less than $H^2$-regular in space. For the ADI scheme, we prove a rigorous time-discrete error bound with a convergence rate that is half an order lower than the classical one. Our statement imposes only assumptions on the initial data and the material parameters, but not on the solution. To establish this result, we analyze the regularity of the Maxwell equations in detail in an appropriate functional analytical framework. The theoretical findings are complemented by a numerical experiment indicating that the proven convergence rate is indeed observable and optimal.
