Bruno, Oscar P. and Hyde, E. McKay (2005) Higher-Order Fourier Approximation in Scattering by Two-Dimensional, Inhomogeneous Media. SIAM Journal on Numerical Analysis, 42 (6). pp. 2298-2319. ISSN 0036-1429. http://resolver.caltech.edu/CaltechAUTHORS:BRUsiamjna05
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This paper provides a theoretical analysis of a higher-order, FFT-based integral equation method introduced recently [IEEE Trans. Antennas and Propagation, 48 (2000), pp. 1862-1864] for the evaluation of transverse electric-polarized electromagnetic scattering from a bounded, penetrable inhomogeneity in two-dimensional 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 higher-order 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.
|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 F49620-98-1-0368. 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 F49620-96-1-0008, F49620-99-1-0010, and F49620-02-1-0049; the NSF through the NYI award DMS-9596152 and through contracts DMS-9523292, DMS-9816802, and DMS-0104531; 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 VTK-based 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, Lippmann-Schwinger integral equation, transverse electric scattering, TM scattering, fast Fourier transform|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||18 Jun 2005|
|Last Modified:||26 Dec 2012 08:40|
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