Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 8
ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, Z. Bittnar
Chapter 5
Finite Element Methods for Electromagnetic Scattering K. Morgan+, P.D. Ledger+, J. Peraire*, O. Hassan+ and N.P. Weatherill+
+Civil & Computational Engineering, University of Wales, Swansea, Wales K. Morgan, P.D. Ledger, J. Peraire, O. Hassan, N.P. Weatherill, "Finite Element Methods for Electromagnetic Scattering", in B.H.V. Topping, Z. Bittnar, (Editors), "Engineering Computational Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 5, pp 105120, 2002. doi:10.4203/csets.8.5
Keywords: electromagnetic scattering, arbitrary order edge elements, output error bounds, goal orientated.
Summary
This paper will describe an arbitrary order edge element approach
for the solution of 2D electromagnetic problems. The chosen
application area is the simulation of the scattering of
electromagnetic waves. The numerical solution is obtained, in the
frequency domain, on hybrid meshes of triangles and quadrilaterals
using the Galerkin method [1] and the shape functions
defined by Ainsworth and Coyle are employed [2]. At the
truncated far field boundary, the outgoing scattered wave
condition is applied by the use of a perfectly matched
layer [3,1].
An aposteriori error estimation procedure is developed that enables the bounding of computational outputs of direct engineering interest. This procedure is an extension of a method that has been presented recently for the Helmholtz equation [4]. In the simulation of electromagnetic wave scattering, the prediction of the distribution of the scattering width is of prime importance and it is demonstrated how bounds may be placed on this quantity at selected viewing angles [5]. Reducedorder models for computational simulations may be constructed by employing full finite element solutions for a small set of the problem parameters. These models can then be applied to enable the rapid prediction of computational outputs for different values of the parameters [6,7]. Initially, a reducedorder model will be developed to enable error bounds to be produced for the complete scattering width distribution [8]. Then, using data from a limited number of finite element computations involving selected wave incidence angles, the approach is also applied to enable the efficient prediction of the scattering width distribution for different angles of incidence. The numerical performance of the procedures that are described will be illustrated by analysing problems involving the scattering of plane electromagnetic waves by cylindrical and aerofoil shaped objects. References
purchase the fulltext of this chapter (price £20)
go to the previous chapter 
