Efficient, accurate and rapidly-convergent algorithms for evaluation of the interaction between electromagnetic fields and complex structures

Catalin Turc

Mathematics, Case Western Reserve University

We present a computational methodology based on boundary integral equations that can deliver fast, high-order numerical solutions of three-dimensional scattering problems in domains that exhibit a wide range of material properties (e.g. perfectly conducting materials, dielectric materials, dielectrics with metallic coatings) as well as a variety of geometrical features (e.g. closed and open surfaces, edges and corners). Our approach uses a combination of the following main elements (a) Pseudodifferential-calculus-based design of well-conditioned integral equation formulations leading to small numbers of Krylov-subspace iterations for a wide range of electromagnetic scattering and transmission problems; (b) High-order resolution of the singularities of the solutions of the boundary integral equations in non-smooth domains; and (c) Use of equivalent sources, FFT-based acceleration algorithms. Joint work with A. Anand (IIT Kanpur, India), O. Bruno (ACM Caltech), and J. Chaubell (JPL Caltech).

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