Author ORCID Identifier

https://orcid.org/0000-0003-3103-3510

Year of Publication

2021

Degree Name

Master of Science in Electrical Engineering (MSEE)

Document Type

Master's Thesis

College

Engineering

Department/School/Program

Electrical and Computer Engineering

First Advisor

Dr. Robert J. Adams

Second Advisor

Dr. John C. Young

Abstract

Electrical and computer engineers rely on electromagnetic field (EM) theory to formulate and design systems that utilize information or energy obtained from a signal. Over time these systems have been increased in scale and complexity and adapted to handle a wider array of problems. This has motivated substantial developments in computational sciences including the area of computational electromagnetics (CEM).The focus of CEM is the simulation of electromagnetic fields. At the University of Kentucky, the CEM group has developed several modeling tools that are based on the application of approximation theory to integral equations. This allows the physical problem to be represented as a linear system of equations. Often times, these simulations prove difficult to implement due to issues related to hardware limitations, problem scale, complicated geometries, etc. To deal with large problems that might otherwise exceed the capacity of a computing platform, several sparse sampling methods have been developed. These methods enable the construction of controllably accurate, data-sparse representations of large, dense matrices using only a sparse set of samples of the underlying matrix. One such method is the Adaptive Cross Approximation (ACA) - which is a type of Pseudoskeleton (PSK) method. However, recently it has been observed that the ACA fails to provide adequate error control for certain types of structured, low-rank matrices. In this presentation, we develop modified versions of the ACA and investigate their application to matrices for which the original ACA fails.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2021.312

Funding Information

The support of this research is provided by the Office of Naval Research under grant N00014-16-1-3066 in 2019-2021.

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