Toward real-time electromagnetics design: Fast, accurate, and robust integral equation-based solvers
Abstract
The goal of my project Toward real-time electromagnetics design: Fast, accurate, and robust integral equation-basedsolvers is to develop novel methods - and improve on existing methods - for several problems in computationalelectromagnetics. These methods will enable the rapid, robust, and high-order accurate solution of the partialdifferential equations (PDEs) known as Maxwell~s equations, which govern electromagnetic wave propagation.The fast PDE solvers that I intend to develop as part of this project will largely be based on integral equationformulations of Maxwell~s equations. When carefully formulated, integral equations have many advantages over standard methods: matrix-conditioning which is indicative of the physical problem, compatibility with complexgeometries and highly-adaptive discretizations, and efficient computation in unbounded domains, just to name a few.In particular, the fast integral equation-based solvers I plan to build will address physical phenomena such aselectromagnetic scattering from dielectric materials and perfectly conducting bodies (and heterogeneous objectscomprised of both classes of materials), inverse imaging problems, and electrical component design. These fastsolvers will require the design and implementation of several classes of analysis-based fast algorithms. Specifically, the fast solvers I plan to develop will be constructed from a hybrid of fast multipole methods, butterfly algorithms, and fast direct solvers. Furthermore, the solvers will be compatible with geometries and discretizations that can begenerated with modern computer-aided design (CAD) and engineering (CAE) packages. They will rely on modernadvances in the theory of numerical quadrature for the weakly-singular integrals of potential theory, and be high-order accurate (in the sense of obtaining several digits of accuracy, not necessarily high-order convergent in the classical sense). These qualities will make this class of fast solvers for computational electromagnetic problems ideally suited for the inner-loop of a design cycle, bringing design by simulation that much closer to a reality.Not only are the choices of computational algorithms and methods I have made for this project ones that are suited tothe demands of engineering design, they are also aligned with foreseeable developments in high-performancecomputing, namely many-core computing. Algorithms of this type have been shown to have near optimal scaling insuch environments, and should continue to do so in the future.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 05, 2017
- Source ID
- N000141712451
Entities
People
- Michael O Neil
Organizations
- New York University
- Office of Naval Research
- United States Navy