Fast high-order CAD-compatible Nystrom methods for frequency-domain electromagnetics
Abstract
The goal of my proposed project Fast high-order CAD-compatible Nystr~m methods for frequency domainelectromagnetics is to develop the necessary high-order numerical methods and fast algorithms for solving boundary value integral equations arising in electromagnetic wave scattering from arbitrary geometries. The resulting numerical methods will be compatible with geometry descriptions generated from common Computer Aided Drawing (CAD) andEngineering (CAE) software, namely curvilinear triangular patches, and rely on high-order quadrature methods for singular integrals. Furthermore, the asymptotic complexity required to solve the corresponding dense N ~ N linear systems will scale as O.N / or O.N logN/. Over the past three decades, there has been amyriad of advances in fast algorithms, singular quadrature, and integral equation theory relevant to the computational solution of partial differential equations, namely Maxwell~s equations,which govern the propagation of electromagnetic radiation. These advances have culminated in the ability to perform large-scale computations, but high-order accurate applications to solving integral equations has mostly been restricted to trivial geometries defined by analytic formulas, or large analytically defined patches. These geometrical descriptions are very limiting, given the advances that have been made in three-dimensional modeling software and fabrication. The integral equation methods that I intend on developing will be based on advancing methods in three main areas: (1)the development of efficient tools to manipulate curvilinear triangular discretizations of surfaces (namely function interpolation and integration), (2) the extension of the method of Quadrature by Expansion (QBX) to weakly-singular, oscillatory surface integrals along curvilinear triangles, and (3) the construction of QBX-compatible fast multipole methods for Maxwell~s equations in three dimensions. The combination of these three results will enable the computational efficient and accurate solution to many of the standard integral equations used in electromagnetic scattering theory. In the long-term, this class of algorithms can be embedded inside optimization methods in order to perform design-by-simulation calculations which are currently intractable.This project is most relevant to ONR~s Science and Technology Organization, Code 31: Command, Control,Communications, Computers, Intelligence, Surveillance and Reconnaissance. In particular, the work is most directly related to the effort of Division 311: the Applied and Computational Analysis Program.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 04, 2017
- Source ID
- N000141712059
Entities
People
- Michael O Neil
Organizations
- New York University
- Office of Naval Research
- United States Navy