Date Available
12-5-2012
Year of Publication
2012
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Engineering
Department/School/Program
Electrical Engineering
Advisor
Dr. Robert J. Adams
Abstract
This dissertation develops surface integral equations using constraint-based Helmholtz decompositions for electromagnetic modeling. This new approach is applied to the electric field integral equation (EFIE), and it incorporates a Helmholtz decomposition (HD) of the current. For this reason, the new formulation is referred to as the EFIE-hd. The HD of the current is accomplished herein via appropriate surface integral constraints, and leads to a stable linear system. This strategy provides accurate solutions for the electric and magnetic fields at both high and low frequencies, it allows for the use of a locally corrected Nyström (LCN) discretization method for the resulting formulation, it is compatible with the local global solution framework, and it can be used with non-conformal meshes.
To address large-scale and complex electromagnetic problems, an overlapped localizing local-global (OL-LOGOS) factorization is used to factorize the system matrix obtained from an LCN discretization of the augmented EFIE (AEFIE). The OL-LOGOS algorithm provides good asymptotic performance and error control when used with the AEFIE. This application is used to demonstrate the importance of using a well-conditioned formulation to obtain efficient performance from the factorization algorithm.
Recommended Citation
Cheng, Jin, "Formulation and Solution of Electromagnetic Integral Equations Using Constraint-Based Helmholtz Decompositions" (2012). Theses and Dissertations--Electrical and Computer Engineering. 11.
https://uknowledge.uky.edu/ece_etds/11
