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Graduate Exam Abstract


Elene Chobanyan

Ph.D. Preliminary

January 21, 2014, 9:15-11:45

Mechanical Engineering Conference Room

Volume/Surface Integral Equation Modeling of Antennas and Scatterers Using Diakoptics and Method of Moments


Abstract: The principal objective of this dissertation is to develop, test, and optimize accurate, efficient, and robust computational methodology and tools for modeling of general antennas and scatterers based on solutions of electromagnetic integral equation formulations using the method of moments (MoM) and diakoptics. The approaches and implementations include the volume integral equation (VIE) method and its hybridization with the surface integral equation (SIE) method, in two ways. The first way combines the VIE method for dielectric parts and the SIE method for metallic parts of the structure. The second way performs subdivision of the entire structure into SIE domains of different constant permittivities, while modeling the inhomogeneity within each domain by the VIE method and employing different Green’s functions, with describing the inhomogeneity within each domain in terms of a perturbation with respect to the background permittivity. The first approach is very suitable for analysis of composite wire-plate-dielectric radiation/scattering structures. The second approach provides a particularly efficient solution to problems involving inhomogineities embedded within high-contrast homogeneous dielectric scatterers. The efficiency of computation is enhanced by applying the diakoptic domain decomposition. In the VIE-SIE diakoptic method, the interior diakoptic subsystems containing inhomogeneous dielectric materials are analyzed completely independently applying the VIE-SIE MoM solver, and the solution to the original problem is obtained from linear relations between electric and magnetic surface-current diakoptic coefficients on diakoptic surfaces, written in the form of matrices. The techniques implement Lagrange-type generalized curved parametric hexahedral MoM-VIE volume elements and quadrilateral MoM-SIE and diakoptic patches of arbitrary geometrical-mapping orders, and divergence-conforming hierarchical polynomial vector basis functions of arbitrary current expansion orders. The hexahedra can be filled with inhomogeneous dielectric materials with continuous spatial variations of the permittivity described by Lagrange interpolation polynomials of arbitrary material-representation orders. Numerical computation is further accelerated by MPI parallelization to enable analysis of large electromagnetic problems.

Adviser: Branislav Notaros
Co-Adviser: N/A
Non-ECE Member: Iuliana Oprea, MATH
Member 3: Steven Reising, ECE, V. Chandrasekar, ECE,
Addional Members: Ali Pezeshki, ECE

Publications:
1. E. Chobanyan, M. M. Ili?, and B. M. Notaros, "Double-Higher-Order Large-Domain Volume/SurfaceIntegral Equation Method for Analysis of Composite Wire-Plate-Dielectric Antennas and Scatterers", IEEE Transactions on Antennas and Propagation, vol. 61, No. 12, pp. 6051-6063, December 2013 2. E. Chobanyan, N. J. Sekelji?, A. B. Mani?, B. M. Notaros , and M. M. Ili?, "Atmospheric Particle Scattering Computation Using Higher Order MoM-SIE Method ", 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI), 7-12 July 2013 3. E. Chobanyan, D. I. Ol?an, M. M. Ili?, and B. M. Notaros, "Combining Diakoptic, VIE-MoM, and SIE-MoM Approaches in Analysis of Dielectric Scatterers", 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI), 7-12 July 2013 4. J. Notaros, E. Chobanyan, V. Chandrasekar, and B. M. Notaros, "Accurate and Efficient Full-Wave Electromagnetic Analysis of Scattering from Hailstones," IEEE Antennas and Propagation Society International Symposium, July 7-12, 2013 5. E. Chobanyan, M. M. Ili?, and B. M. Notaros, "Higher Order Volume and Surface Integral Equation Modeling of 3-D Scattering and Radiation Problems", USNC-URSI National Radio Science Meeting, January 9-12, 2013 6. E. Chobanyan, J. Notaros, V. Chandrasekar, and B. M. Notaros, "Accurate Electromagnetic Modeling of Melting Hail", USNC-URSI National Radio Science Meeting, January 9-12, 2013 7. E. Chobanyan, M. M. Ili?, and B. M. Notaros, "Efficient higher order volume-integral-equation modeling of dielectric scatterers", 2012 IEEE Antennas and Propagation Society International Symposium (APSURSI), 8-14 July 2012 8. N. J. Sekelji?, E. Chobanyan, M. M. Ili?, and B. M. Notaros, "Rules for Adoption of Expansion and Integration Orders in Moment-Method Computation of Electromagnetic Scattering and Radiation", USNC-URSI National Radio Science Meeting, January 4-7, 2012


Program of Study:
ECE444
ECE512
ECE641
ECE642
MATH560
MATH652
N/A
N/A