Numerical solution of nonlinear diffraction problems
type: Item
instance of: scholarly article
title: Numerical solution of nonlinear diffraction problems
zbMATH Open document ID: 1092.78012
author: Gang Bao
author: Ying Li
author: Haijun Wu
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: The paper develops an adaptive finite element method for solving nonlinear diffraction problems for periodic gratings. Under some assumptions on the nonlinear optical material the problem is equivalent to the usual TM polarization problem for periodic gratings coupled with the TE polarization problem with a right hand side depending on the magnetic field. The authors give the variational formulation of the problem and analyze its PML extension, which is the basis of the FE solution. They define a local error estimator and prove a posteriori error estimates.
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 5015175
zbMATH Keywords: nonlinear gratings
zbMATH Keywords: second harmonic generation
zbMATH Keywords: adaptive finite element method
zbMATH Keywords: PML
reviewed by: Gunther Schmidt
MaRDI profile type: Publication
full work available at URL: j.cam.2005.01.045
OpenAlex ID: W2074716586
cites work: A Nonlinear Grating Problem in Diffractive Optics
cites work: Mathematical modeling in optical science. Proceedings of a minisymposium on optics at SIAM's annual meeting, Stanford Univ., Palo Alto, CA, USA, 1997
cites work: Optimal design of nonlinear diffraction gratings.
cites work: An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
cites work: Diffraction in periodic structures and optimal design of binary gratings. Part I: direct problems and gradient formulas
cites work: Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
DOI: 10.1016/J.CAM.2005.01.045
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description: scientific article; zbMATH DE number 5015175