Deng Shaozhong
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.
Comput Phys Commun. 2008 Dec 1;179(11):791-800. doi: 10.1016/j.cpc.2008.07.001.
This paper deals with accurate numerical simulation of two-dimensional time-domain Maxwell's equations in materials with curved dielectric interfaces. The proposed fully second-order scheme is a hybridization between the immersed interface method (IIM), introduced to take into account curved geometries in structured schemes, and the Lax-Wendroff scheme, usually used to improve order of approximations in time for partial differential equations. In particular, the IIM proposed for two-dimensional acoustic wave equations with piecewise constant coefficients [C. Zhang, R.J. LeVeque, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion 25 (1997) 237-263] is extended through a simple least squares procedure to such Maxwell's equations. Numerical results from the simulation of electromagnetic scattering of a plane incident wave by a dielectric circular cylinder appear to indicate that, compared to the original IIM for the acoustic wave equations, the augmented IIM with the proposed least squares fitting greatly improves the long-time stability of the time-domain solution. Semi-discrete finite difference schemes using the IIM for spatial discretization are also discussed and numerically tested in the paper.
本文研究了具有弯曲介质界面的材料中二维时域麦克斯韦方程组的精确数值模拟。所提出的全二阶格式是浸入界面法（IIM）与拉克斯 - 温德罗夫格式的一种混合方法。浸入界面法被引入以在结构化格式中考虑弯曲几何形状，而拉克斯 - 温德罗夫格式通常用于提高偏微分方程时间近似的阶数。特别地，针对具有分段常数系数的二维声波方程所提出的浸入界面法[C. 张，R.J. 勒维克，具有不连续系数的声波方程的浸入界面法，波动 25（1997）237 - 263]通过一个简单的最小二乘法过程扩展到此类麦克斯韦方程组。介质圆柱体对平面入射波电磁散射模拟的数值结果似乎表明，与声波方程的原始浸入界面法相比，采用所提出的最小二乘拟合的增强浸入界面法极大地提高了时域解的长期稳定性。本文还讨论了使用浸入界面法进行空间离散化的半离散有限差分格式并进行了数值测试。
