Graduate Exam Abstract
April 2, 2014, 10:00 AM - 12:00 PM
Dean''s Conference Room, Engr. B 214
Transient Analysis of Closed- and Open-Region Electromagnetic Problems Using Higher Order Finite Element Method and Method of Moments in the Time Domain
Abstract: The principal objective of this dissertation is to develop computational electromagnetic (CEM) methodology and tools for modeling of closed (waveguide and cavity based) and open (radiation and scattering) electromagnetic structures in the time domain (TD), employing two CEM approaches. The first method is a novel higher order and large-domain Galerkin finite element method (FEM) for transient analysis of multiport microwave waveguide devices with arbitrary metallic and dielectric discontinuities. It is based on geometrical modeling using Lagrange interpolation generalized hexahedral elements, spatial field expansion in terms of hierarchical curl-conforming polynomial vector basis functions, time-stepping with an implicit unconditionally stable finite difference scheme using the Newmark-beta method, and mesh truncation introducing the waveguide port boundary condition. The second method is a novel higher order and large-domain Galerkin method of moments (MoM) in conjunction with the surface integral equation (SIE) formulation for transient analysis of antennas and scatterers of arbitrary shapes and metallic/dielectric material compositions. It is based on using Lagrange generalized curved parametric quadrilateral patches and hierarchical divergence-conforming polynomial vector basis functions for spatial current distributions, approximation of time variations by orthogonal temporal basis functions derived from Laguerre polynomials, and iterative solution of the final system of spatially and temporally discretized SIE equations in a marching-on-degree fashion. The first and the second phase of the research are based on development and implementation each of the methods. Finally, the third phase includes modeling, testing and cross-validation with alternative frequency and TD numerical techniques as well as with measurements. The ultimate goal of the dissertation is to provide accurate, stable, and efficient transient solution to large-domain 3-D EM applications using both methodologies, TDFEM and MoM-TDSIE.
Adviser: Prof. Branislav Notaros
Non-ECE Member: Prof. Jennifer Mueller, MATH
Member 3: Prof. Steven Reising, ECE, and Prof. V. Chandrasekar, ECE
Addional Members: Prof. Milan Ilic, affiliate faculty, ECE
1. N. J., Sekeljic, M. M. Ilic, and B. M. Notaros, "Higher Order Time-Domain Finite Element Method for Microwave Device Modeling with Generalized Hexahedral Elements," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 4, April 2013, pp. 1425-1434.
2. E. M. Klopf, N. J. Sekeljic, M. M. Ilic, and B. M. Notaros, "Optimal Modeling Parameters for Higher Order MoM-SIE and FEM-MoM Electromagnetic Simulations", IEEE Transactions on Antennas and Propagation, vol.60, no.6, pp.2790-2801, June 2012.
3. N. J. Sekeljic, M. M. Ilic, and B. M. Notaros, "p-Refined Large-Domain 3-D Curvilinear FEM Solutions of Arbitrarily Loaded and Shaped Waveguide Sections and Bends in the Time Domain," Proc. 2014 USNC-URSI National Radio Science Meeting, January 8-11, 2014, Boulder, Colorado.
4. N. J. Sekeljic, A. Manic, M. M. Ilic, and B. M. Notaros, "Transient Analysis of 3D Waveguides Using Double- Higher-Order Time-Domain Finite Element Method," Proceedings of 2013 IEEE Antennas and Propagation Society International Symposium, July 7-12, 2013, Orlando, Florida.
5. E. Chobanyan, N. J. Sekeljic, A. B. Manic, M. M. Ilic, and B. M. Notaros, "Atmospheric Particle Scattering Computation Using Higher Order MoM-SIE Method," Proceedings of 2013 IEEE Antennas and Propagation Society International Symposium, July 7-12, 2013, Orlando, Florida.
6. N. J. Sekeljic, S. B. Manic, M. M. Ilic, and B. M. Notaros, "Direct and Indirect Time-Domain FEM Higher Order Solutions to 3-D Closed-Region Problems," Proc. 2013 USNC-URSI National Radio Science Meeting, January 9-12, 2013, Boulder, Colorado.
7. N. J. Sekeljic, S. V. Savic, M. M. Ilic, and B. M. Notaros, "Rules for Adoption of Expansion and Integration Orders in FEM Analysis Using Higher Order Hierarchical Bases on Generalized Hexahedral Elements," invited paper, Special Session "Adaptive FEM, Higher Order Bases, and Advanced FEM Formulations," 11th International Workshop on Finite Elements for Microwave Engineering - FEM2012, June 4-6, 2012, Estes Park, Colorado.
8. B. M. Notaros, M. M. Ilic, S. V. Savic, N. J. Sekeljic, and A. Z. Ilic, "Accurate and Efficient Curvilinear Geometrical Modeling Using Interpolation Parametric Elements in Higher Order CEM Techniques," invited paper, Special Session "Higher Order Numerical Methods", Proceedings of the 28th International Review of Progress in Applied Computational Electromagnetics - ACES 2012, April 10-14, 2012, Columbus, Ohio, pp. 602-607.
9. N. J. Sekeljic, E. Chobanyan, M. M. Ilic, and B. M. Notaros, "Rules for Adoption of Expansion and Integration Orders in Moment-Method Computation of Electromagnetic Scattering and Radiation," Proc. 2012 USNC-URSI National Radio Science Meeting, January 4-7, 2012, Boulder, Colorado.
10. E. M. Klopf, N. J. Sekeljic, M. M. Ilic, and B. M. Notaros, "Investigations of Optimal Geometrical and Field/Current Modeling Parameters for Higher Order FEM, MoM, and Hybrid CEM Techniques," Proc. 2011 USNC-URSI National Radio Science Meeting, January 5-8, 2011, Boulder, Colorado.
Program of Study: