Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

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

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

Full text not available in this repository. (Request a copy from the Strathclyde author)

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.