具有对角线各向异性的三维介质中麦克斯韦方程组的完美匹配层的惊人不稳定性结果

Pub Date : 2021-04-20 DOI:10.5802/CRMATH.165

É. Bécache, S. Fliss, M. Kachanovska, M. Kazakova

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引用次数: 1

摘要

用对角线介质张量模拟三维无界各向异性均匀介质中电磁波的时域传播，给出了笛卡尔完美匹配层(pml)的分析。与三维标量波动方程或二维麦克斯韦方程相反，一些对角线各向异性导致反向波的存在，从而导致pml的不稳定性。数值实验证实了上述结果。

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On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy

The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.

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