Bruno, Oscar and Elling, Tim and Paffenroth, Randy and Turc, Catalin (2009) Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations. Journal of Computational Physics, 228 (17). pp. 6169-6183. ISSN 0021-9991 http://resolver.caltech.edu/CaltechAUTHORS:20090826-112852554
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We present a new class of integral equations for the solution of problems of scattering of electromagnetic fields by perfectly conducting bodies. Like the classical Combined Field Integral Equation (CFIE), our formulation results from a representation of the scattered field as a combination of magnetic- and electric-dipole distributions on the surface of the scatterer. In contrast with the classical equations, however, the electric-dipole operator we use contains a regularizing operator; we call the resulting equations Regularized Combined Field Integral Equations (CFIE-R). Unlike the CFIE, the CFIE-R are Fredholm equations which, we show, are uniquely solvable; our selection of coupling parameters, further, yields CFIE-R operators with excellent spectral distributions—with closely clustered eigenvalues—so that small numbers of iterations suffice to solve the corresponding equations by means of Krylov subspace iterative solvers such as GMRES. The regularizing operators are constructed on the basis of the single layer operator, and can thus be incorporated easily within any existing surface integral equation implementation for the solution of the classical CFIE. We present one such methodology: a high-order Nyström approach based on use of partitions of unity and trapezoidal-rule integration. A variety of numerical results demonstrate very significant gains in computational costs that can result from the new formulations, for a given accuracy, over those arising from previous approaches.
|Additional Information:||Copyright © 2009 Elsevier. Received 21 October 2008; revised 23 April 2009; accepted 11 May 2009. Available online 20 May 2009. We gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.|
|Subject Keywords:||Electromagnetic scattering; Combined Field Integral Equations; Pseudodifferential operators; Regularizing operator|
|Official Citation:||Oscar Bruno, Tim Elling, Randy Paffenroth, Catalin Turc, Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations, Journal of Computational Physics, Volume 228, Issue 17, 20 September 2009, Pages 6169-6183, ISSN 0021-9991, DOI: 10.1016/j.jcp.2009.05.020. (http://www.sciencedirect.com/science/article/B6WHY-4WBC1Y4-1/2/07667a7c6269b12e5943c4b40a202d57)|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||George Porter|
|Deposited On:||11 Sep 2009 19:01|
|Last Modified:||26 Dec 2012 11:15|
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