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.
Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:ece_etds-1011 |
Date | 01 January 2012 |
Creators | Cheng, Jin |
Publisher | UKnowledge |
Source Sets | University of Kentucky |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations--Electrical and Computer Engineering |
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