Bruno, Oscar P. and Hyde, E. McKay (2005) HigherOrder Fourier Approximation in Scattering by TwoDimensional, Inhomogeneous Media. SIAM Journal on Numerical Analysis, 42 (6). pp. 22982319. ISSN 00361429. http://resolver.caltech.edu/CaltechAUTHORS:BRUsiamjna05

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Abstract
This paper provides a theoretical analysis of a higherorder, FFTbased integral equation method introduced recently [IEEE Trans. Antennas and Propagation, 48 (2000), pp. 18621864] for the evaluation of transverse electricpolarized electromagnetic scattering from a bounded, penetrable inhomogeneity in twodimensional space. Roughly speaking, this method is based on Fourier smoothing of the integral operator and the refractive index n(x). Here we prove that the solution of the resulting integral equation approximates the solution of the exact integral equation with higherorder accuracy, even when n(x) is a discontinuous function  as suggested by the numerical experiments contained in the paper mentioned above. In detail, we relate the convergence rates of the computed interior and exterior fields to the regularity of the scatterer, and we demonstrate, with a few numerical examples, that the predicted convergence rates are achieved in practice.
Item Type:  Article 

Additional Information:  © 2005 Society for Industrial and Applied Mathematics. Received by the editors April 7, 2003; accepted for publication (in revised form) March 25, 2004; published electronically March 31, 2005. This effort was sponsored in part by the Air Force Office of Scientific Research (AFOSR), Air Force Materials Command, USAF, under the AASERT award F496209810368. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. The research of [Oscar P. Bruno] was supported by AFOSR grants F496209610008, F496209910010, and F496200210049; the NSF through the NYI award DMS9596152 and through contracts DMS9523292, DMS9816802, and DMS0104531; and the Powell Research Foundation. The research of [E. McKay Hyde] was supported by a DOE Computational Science Graduate Fellowship, an Achievement Rewards for College Scientists (ARCS) Fellowship, and an NSF Mathematical Sciences Postdoctoral Research Fellowship. Color visualizations were generated with the VTKbased visualization tool Vizamrai, developed by Steven Smith at the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. The authors also gratefully acknowledge the constructive suggestions of an anonymous referee. 
Subject Keywords:  Helmholtz equation, LippmannSchwinger integral equation, transverse electric scattering, TM scattering, fast Fourier transform 
Record Number:  CaltechAUTHORS:BRUsiamjna05 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:BRUsiamjna05 
Alternative URL:  http://dx.doi.org/10.1137/S0036142903425811 
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  432 
Collection:  CaltechAUTHORS 
Deposited By:  Archive Administrator 
Deposited On:  18 Jun 2005 
Last Modified:  26 Dec 2012 08:40 
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