Parameterised Electromagnetic Scattering Solutions for a Range of Incident Wave Angles P.D. Ledger ∗1 , J. Peraire † , K. Morgan ∗ , O. Hassan ∗ & N.P. Weatherill ∗ ∗ Civil and Computational Engineering Centre, University of Wales, Swansea, U.K. † Aeronautics and Astronautics, M.I.T. Cambridge, Massachusetts, U.S.A Abstract This paper considers the numerical simulation of 2D electromagnetic wave scattering problems and describes the construction of a reduced–order approximation which enables the rapid prediction of the scattering width distribution for a range of incident wave directions. Associated certainty bounds ensure conﬁdence in the results of the computed approximation. Numerical examples are included to demonstrate the performance of the proposed procedure. 1 Introduction The simulation of electromagnetic wave scattering problems is of importance in many practical application areas where, typically, the interest lies in determining the scattering width distribution for a new design. Computational methods can provide assistance in this area, provided that the simulations allow the full problem parameter space of interest to be rapidly, and accurately, investigated. In general, the parameter space will include changes in the direction of the incident wave, changes in the wave frequency and changes in the geometry and structure of the scatterer. It should also be noted that this requirement for the rapid computation of the scattering width for a range of problem parameters also arises when the solution of inverse problems is considered [1]. The ﬁnite element method is a popular domain based approach for the solution of electromag- netic wave scattering problems, in which an approximation to the scattering width distribution may be obtained by post–processing the computed solution. With this approach, a new compu- tation is necessary to produce the revised scattering width distribution following a change in any of the problem parameters. The implication is that the associated computational costs will be very high for a study involving a large number of parameter changes. In this paper, we present a reduced–order approximation which addresses this problem and can lead to signiﬁcant reduction in the computational costs. Reduced—order approximations operate in two stages. In an initial oﬀ–line stage, full solutions are computed for a set of speciﬁed problem parameters and the results of these computations are stored. In an on–line stage, speciﬁed outputs of interest are computed at low cost for new sets of the problem parameters. In addition, for the outputs to be of practical use, it is important that accuracy can be guaranteed. Reduced–order approximations with these properties have already been successfully applied in the area of computational aerodynamics [2, 3], while sophisticated methods for determining error bounds on the outputs produced by reduced–order approximations have also been developed [4, 5]. We aim to apply a reduced–order approximation in the area of electromagnetic wave scattering. For this initial study, we consider two dimensional wave scattering problems and we have restricted the parameter space investigation to allow only variations in the direction of the incident wave. The selected output of interest is the scattering width distribution and the implementation details describe how it can be eﬀectively computed. To assess the accuracy of the proposed reduced– order approximation, a novel approach for obtaining certainty bounds on the computed output is described. Here certainty is assessed with respect to a full solution computed for the parameter set. 1 Corresponding Author: Civil and Computational Engineering Centre, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, Wales, U.K. Email: P.D.Ledger@swansea.ac.uk 1