Fast, High-Order, Well-Conditioned Algorithms for the Solution of Three-Dimensional Acoustic and Electromagnetic Scattering Problems

We present a novel computational methodology based on Nyström discretizations to produce fast and very accurate solutions of acoustic and electromagnetic problems in small numbers of Krylov-subspace iterative solvers. At the heart of our approach are integral equation formulations that exhibit excellent spectral properties. In the case of scattering from perfectly conducting structures, and just as the classical Combined Field Integral Equation (CFIE), our well-conditioned equations result from representations of the scattered fields as a combination of surface magneticand electric-dipole distributions that involve use of certain types of regularizing operators. We call the resulting equations Regularized Combined Field Integral Equations (CFIE-R). A variety of numerical results demonstrate that, for a given accuracy, the new equations can give rise to significant reductions in computational costs over those resulting from previous approaches, especially in the high-frequency regime.