针对PEC周围电磁散射的均匀正交网格上基于鬼点的二阶精度有限差分方法
A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around PEC
AI总结：
本文提出一种在均匀正交网格上利用水平集函数和PDE延拓外推鬼点值的二阶精度有限差分法，用于求解含PEC的时域麦克斯韦方程，并通过往返误差校正与补偿在放宽CFL条件的同时保持二阶精度。
摘要：
我们提出了一种有限差分方法，用于在存在阻碍电磁波传播的理想电导体（PEC）的情况下，在时域中求解麦克斯韦方程组。我们的方法是对Zou和Liu[36]现有方法的改进，将局部扰动的贴体网格替换为适用于复杂PEC物体的均匀正交网格。与他们的工作类似，我们通过利用界面的水平集函数和基于偏微分方程的延拓技术来外推鬼点值，这使我们能够避免仔细检查界面的局部几何结构。我们对外推精度提出了一个温和的要求，即鬼点值仅需局部二阶精度即可。尽管如此，由于应用了往返误差校正与补偿，我们的方法最终仍能达到二阶精度，同时这也放宽了CFL条件。我们通过一些数值算例展示了该方法的有效性。
英文摘要：
We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach by Zou and Liu [36], from a locally perturbed body-fitted grid to a uniform orthogonal one for complicated PEC objects. Similar to their work we extrapolate ghost point values by exploiting the level set function of the interface and the PDE-based extension technique, which allows us to circumvent scrutinizing local geometries of the interface. We stipulate a mild requirement on the accuracy of our extrapolation that the ghost values need only be locally second order accurate. Nevertheless the resulting accuracy of our method is second order thanks to the application of back and forth error correction and compensation, which also relaxes CFL conditions. We demonstrate the effectiveness of our approach with some numerical examples.
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