Spectral and High Order Methods for Partial Differential Equations S
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this import
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Mathematics, University of Massachusetts Dartmouth. of Applied Mathematics, Brown University. c Universit´ e Pierre et Marie Curie-Paris6 d Dpto. de Matem´ atica Aplicada, Fac. de Matem´ aticas, Uiversidade de Santiago de Compostela b Division
Abstract We study nontrivial applications of the reduced basis method (RBM) for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section (RCS). The method and several extensions are explained with two examples with different characteristics. Parameters that are allowed to vary within the model include frequency, incident angle and measurement angle as well as the geometry of the scatterers. With appropriate applications of the empirical interpolation method (EIM), transformation of the domain, configuration of perfectly matched layer, exponential convergence of the reduced basis solution over the entire parameter domain is achieved. Moreover, we demonstrate that this approach allows for the effective capture of the critical behavior, in this case through shapes that minimize scattering. This further highlights the robustness and quality of the greedy approximation and the reduced basis method approach. Keywords: Reduced Basis Method, Electromagnetic Scattering, Radar Cross Section, Empirical Interpolation Method
1. Introduction In many applications such as computational optimization, control and design, one is required to rapidly yet accurately predict some quantities of interest under the variation of a set of parameters ν ∈ D ⊂ Rp . Here, se (ν) := ℓe (ue (ν); ν) ∈ C is an output of interest with ℓe being a functional and ue is the ∗ Corresponding
author. addresses: [email protected] (Y.Chen) [email protected] (J.Hesthaven) [email protected] (Y.Maday) [email protected] (J.Rodr´ıguez) Xueyu [email protected] (X. Zhu) 1 E-mail
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November 18, 2011
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