论文标题
电磁学的局部多个痕迹公式：平滑几何形状的稳定性和预处理
Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries
论文作者
论文摘要
我们考虑了单位球的时间谐波电磁传输问题。吸引了矢量球形谐波分析，我们证明了电磁学的局部多重痕量配方（MTF）的第一个稳定性结果，最初是由Hiptmair和Hiptmair和Jerez-Hanckes引入的[adv。 comp。数学。 37（2012），37-91]对于声学案例，铺平了向通用分段均匀散射器扩展的道路。此外，我们研究了本地MTF方案的预处理技术，并研究了诱导运营商的积累点。特别是，我们提出了一种新型的二阶逆近似值。数值实验验证了我们的主张并确认了预处理策略的相关性。
We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple trace formulation (MTF) for electromagnetics, originally introduced by Hiptmair and Jerez-Hanckes [Adv. Comp. Math. 37 (2012), 37-91] for the acoustic case, paving the way towards an extension to general piecewise homogeneous scatterers. Moreover, we investigate preconditioning techniques for the local MTF scheme and study the accumulation points of induced operators. In particular, we propose a novel second-order inverse approximation of the operator. Numerical experiments validate our claims and confirm the relevance of the preconditioning strategies.
