An Adaptive Finite Element Method with a Modified Perfectly Matched Layer Formulation for Diffraction Gratings
Jie Chen 1, Desheng Wang 1*, Haijun Wu 21 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371.
2 Department of Mathematics, Nanjing University, Jiangsu 210093, China.
Received 26 April 2008; Accepted (in revised version) 29 August 2008
Available online 15 December 2008
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.AMS subject classifications: 65N30, 78A45, 35Q60
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Key words: Diffraction grating, adaptive finite element method, PML, a posteriori error estimates.
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