Project Details
Description
Turc
DMS-1008076
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.
Status | Finished |
---|---|
Effective start/end date | 7/1/10 → 10/31/12 |
Funding
- National Science Foundation: $80,212.00