Graduate Exam Abstract

Eve Klopf

Ph.D. Preliminary

May 12, 2011, 10:30am


Optimal Higher Order Modeling Methodology Based on Finite Element Method and Method of Moments for Electromagnetics

Abstract: Traditional computational electromagnetic (CEM) tools are low-order (also referred to as small-domain or subdomain) techniques, according to which the electromagnetic structure is modeled by volume and/or surface geometrical elements that are electrically very small and with planar sides, and the fields and/or currents within the elements are approximated by low-order basis functions. This results in very large requirements in computational resources. An alternative that can greatly reduce the number of unknowns for a given problem and enhance the accuracy and efficiency of the CEM analysis is the higher order (also known as the large-domain or entire-domain) computational approach, which utilizes higher order basis functions defined in large geometrical elements. However, the principal advantage of higher order techniques, their flexibility in terms of the size and shape of elements and spans of approximation functions, is also their greatest shortcoming in terms of dilemmas, uncertainties, and so many open, equally attractive, options and decisions to be made on how to actually use them. Consequently, characterization of modeling parameter interactions towards the development of a tool to automatically select optimal simulation values is of the greatest interest in facilitating the use of higher order methods. This work will demonstrate this in the context of higher order techniques based on using generalized curved parametric hexahedral and quadrilateral elements to model the geometry of the structure in conjunction with curl and divergence-conforming hierarchical polynomial vector basis functions to model fields and currents, in the framework of the method of moments (MoM), the finite element method (FEM) and a hybrid CEM technique. Parameters that can be varied and will be systematically studied toward determining optimal choices are geometrical orders of elements, approximation orders of field/current basis and testing functions, and orders of the corresponding Gauss-Legendre integration formulas, all of which can, theoretically, be arbitrary. Generally, field/current polynomial approximation orders for a given level of result accuracy are directly proportional to the corresponding electrical dimensions of elements, but often not in a linear fashion. In addition, being able to specify the level of desired accuracy -- or, equivalently, the acceptable uncertainty -- of the results being computed is extremely important, so this work will also investigate tradeoffs between accuracy and efficiency, i.e., the cost of getting the results. Through very extensive numerical experiments and theoretical studies, as precise as possible quantitative “recipes” for the adoption of higher order and large-domain parameters will be developed. The purpose of this work is to establish and validate general guidelines and instructions in order for the higher order CEM modeling methodology to be an easily used analysis and design tool, with a minimum of expert interaction required to produce valuable results in practical applications. The goal is to develop an optimal higher order modeling methodology based on the finite element method and method of moments for electromagnetics.

Adviser: Dr. Branislav Notaros
Co-Adviser: N/A
Non-ECE Member: Dr. Iuliana Oprea, Mathematics
Member 3: Dr. V. Chandrasekar, Electrical & Computer Engineering
Addional Members: Dr. S. C. Reising, Electrical & Computer Engineering

Klopf, E. M., N. J. Sekeljic, M. M. Ilic, B. M. Notaros, "Investigations of Optimal Geometrical and Field/Current Modeling Parameters for Higher Order FEM, MOM, and Hybrid CEM Techniques," Paper B5-1, 2011 USNC-URSI National Radio Science Meeting, Boulder, January 2011. Klopf, E. M., F. Iturbide-Sanchez and S. C. Reising, "Design and Performance of a Miniaturized Cloud Liquid Water Radiometer to Augment a Miniaturized Water Vapor Profiling Radiometer," Paper F3-3, 2005 URSI National Radio Science Meeting, Boulder, January 2005.

Program of Study:
ECE 641
ECE 642
ECE 695
MATH 561
MATH 652
MATH 676
ECE 799