NJIT Applied Mathematics Colloquium
Friday, February 3, 2012, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology
Efficient, accurate and rapidly-convergent algorithms for evaluation of the interaction
between electromagnetic fields and complex structures
Catalin Turc
Case Western Reserve University
We present a computational methodology based on boundary integral
equations that can deliver (1) 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), and (2) Efficient simulations of wave propagation in
penetrable periodic structures with a particular emphasis on resonant
problems relevant to the design of photonic crystals and Negative Index
Materials (NIM). 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; (c) Use of equivalent sources, FFT-based
acceleration algorithms; and (d) Acceleration of the convergence of
periodic Green's functions based on smooth windowing functions.
Joint work with A. Anand (IIT Kanpur, India), O. Bruno (ACM
Caltech), J. Chaubell (JPL Caltech), S. Shipman (LSU), and S. Venakides
(Duke).
|