PERFECTLY MATCHED LAYERS FOR DIFFRACTION GRATINGS IN INHOMOGENEOUS MEDIA. STABILITY AND ERROR ESTIMATES

被引：4

作者：

Kalvin, Victor ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math Informat Technol, FI-40014 Jyvaskyla, Finland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 01期

基金：

芬兰科学院;

关键词：

perfectly matched layer; absorbing layers; complex scaling; resonances; surface waves; limiting absorption principle; dilation analytic; gradient-index medium; refractive index; diffraction gratings; SCATTERING; WAVES;

D O I：

10.1137/08073442X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the scattering of acoustic or electromagnetic waves at diffraction gratings in inhomogeneous media. The refractive index stabilizes to 1 as the distance to the grating increases. Outgoing solutions are characterized by means of the limiting absorption principle. We prove the unique solvability of the problem with perfectly matched layer of finite length. Further, we show that solutions of the latter problem approximate outgoing solutions of the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity. Contribution of eigenvalues and resonances to the error of approximation is clarified.

引用

页码：309 / 330

页数：22