Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

  • Authors:

  • Oscar Bruno;Tim Elling;Randy Paffenroth;Catalin Turc

  • Affiliations:

  • California Institute of Technology, Applied and Computational Mathematics, MC 217-50, 1200 East California Blvd., CA 91125, United States;California Institute of Technology, Applied and Computational Mathematics, MC 217-50, 1200 East California Blvd., CA 91125, United States;Numerica Corporation, 4850 Hahns Peak Drive, Suite 200 Loveland, CO 80538, United States;Case Western Reserve University, Department of Mathematics, 10900 Euclid Ave., Yost Hall 216, Cleveland, OH 44106, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

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 Nystrom 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.