The reduced basis method for the electric field integral equation

Authors:
M. Fares;J. S. Hesthaven;Y. Maday;B. Stamm
Affiliations:
2 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France;Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912, USA;Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boíte courrier 18, 75252 Paris Cedex 05, France;Department of Mathematics, University of California, Berkeley, CA 94720, USA
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.