Efficient, accurate and rapidly convergent algorithms for solutions of wave propagation problems in configurations complex material and geometrical features

Project: Research project

Project Details




The investigator develops efficient, accurate and rapidly

convergent algorithms for evaluation of the interaction between

electromagnetic fields and complex structures. Specifically, the

investigator and his collaborators develop a family of algorithms

that focus mainly on (1) Fast, high-order numerical solutions for

wave-propagation problems in domains that contain geometric

singularities, and (2) Scattering problems from penetrable

electromagnetic periodic structures, with a particular emphasis

on resonant problems relevant to the design of photonic crystals

and Negative Index Materials (NIM). The investigator

concentrates on development and implementation of a massively

parallel computational framework based on integral equation

formulations capable of producing fast and high-order solutions

of wave scattering problems of realistic complexity. The

approach consists of the following main elements: (a) High-order

resolution of the singularities of the solutions of the boundary

integral equations in non-smooth domains; (b)

Pseudodifferential-calculus-based design and analysis of

well-conditioned integral equation formulations leading to small

numbers of Krylov-subspace iterations for a wide range of

electromagnetic transmission problems; and (c) Use of equivalent

sources, FFT-based acceleration algorithms, and implementations

that take advantage of the newly available Graphic Processing

Units (GPUs) computational platforms to dramatically enhance

computational times and capabilities.

The algorithms that are developed as part of this project

are of fundamental significance to diverse applications such as

electromagnetic interference and compatibility (electronic

circuits), dielectric/magnetic coated conductors, and composite

meta-materials (photonic crystals and Negative Index Materials).

The simulation of electromagnetic wave propagation in complex

structures gives rise to a host of significant computational

challenges that result from non-coercive formulations,

oscillatory solutions, geometric singularities, resonances, and

ill-conditioning in the high-frequency regime. The recent

efforts of the investigator and his collaborators resulted in the

development of a highly efficient computational methodology that

resolved several of these difficulties and whose extension

enables the fulfillment of an ambitious plan: to simulate with

high fidelity realistic scattering environments with a high

dynamic range.

Effective start/end date7/1/1010/31/12


  • National Science Foundation: $80,212.00


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