Volume 6, Issue 2
An Adaptive Finite Element Method with a Modified Perfectly Matched Layer Formulation for Diffraction Gratings

Jie Chen, Desheng Wang & Haijun Wu

DOI:

Commun. Comput. Phys., 6 (2009), pp. 290-318.

Published online: 2009-06

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  • Abstract

For numerical simulation of one-dimensional diffraction gratings both in TE and TM polarization, an enhanced adaptive finite element method is proposed in this paper. A modified perfectly matched layer (PML) formulation is proposed for the truncation of the unbounded domain, which results in a homogeneous Dirichlet boundary condition and the corresponding error estimate is greatly simplified. The a posteriori error estimates for the adaptive finite element method are provided. Moreover, a lower bound is obtained to demonstrate that the error estimates obtained are sharp.

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