An a priori error estimate for the finite element modelling of electromagnetic waves interacting with a periodic diffraction grating

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Lord, Natacha and Mulholland, Anthony (2013) An a priori error estimate for the finite element modelling of electromagnetic waves interacting with a periodic diffraction grating. Mathematical Methods in the Applied Sciences, 36 (10). 1187–1205. ISSN 0170-4214 (https://doi.org/10.1002/mma.2671)

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Abstract

An a priori error estimate using a so called α,β- periodic transformation to study electromagnetic waves in a periodic diffraction grating is derived. It has been reported for single scattering that there is an instability in numerical methods for high wavenumbers. To address this problem, the analytical solution of the scattering problem when the domain is scatterer free and an unknown function called the α,β-quasi periodic solution are used to transform the associated Helmholtz problem. The well-posedness of the resulting continuous problem is analysed before approximating its solution using a finite element discretization. To guarantee the uniqueness of this approximate solution, an a priori error estimate is derived. Finally, numerical results are presented that suggest that the α,β-quasi periodic method converges at a far lower number of degrees of freedom than the α,0-quasi periodic method reported previously; especially for high wavenumbers. This is particularly true when the incident wave only undergoes a small perturbation because of the presence of the scatterer.

ORCID iDs

Lord, Natacha and Mulholland, Anthony ORCID logoORCID: https://orcid.org/0000-0002-3626-4556;
  • Item type:Article
    ID code:41263
    Dates:
    Date
    Event
    15 July 2013
    Published
    13 September 2012
    Published Online
    Notes:change of date
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:26 Sep 2012 15:22
    Last modified:15 Dec 2024 01:17
    URI:https://strathprints.strath.ac.uk/id/eprint/41263
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