Syllabus:
Finite Difference Method (FDM)
Finite difference approximations, Application: Transmission line capacitance, Application: Waveguide eigenvalue problems
Finite Difference Time Domain Method (FDTD)
One dimensional finite difference time domain method, The Yee algorithm, Numerical dispersion in FDTD , Source implementation in FDTD, Absorbing boundary condition (ABC), Perfectly matched layer(PML), Modeling material dispersion, Modeling Spatial dispersion, Modeling nonlinear media, Modeling high speed electronic circuits, Modeling of antennas
Method of Moments
Commonly used basis and testing functions, Numerical integration, Solution of linear systems of equations, Extraction of circuit parameters from MoM results, Capacitance calculation, Thin wire antennas, TE/TM scattering from conducting and dielectric cylindrical structures
Variational Techniques
Calculus of variations and construction of functional, Rayleigh-Ritz procedure, Method of weighted residuals: Galerkin method, Least square method, Cut-off frequencies in arbitrary shape waveguides, microwave resonators, Characteristic impedance of transmission lines
Finite Element Method (FEM)
Basic steps in FEM analysis, Variational formulation of FEM, One/two dimensional FEM formulations: Galerkin and Ritz approach, Commonly used shape functions Numerical integration, discretization error, FEM applied to waveguide and resonator eigenvalue problems, spurious solutions, (*) Vector FEM: edge based shape functions, Perfectly Matched Layer sorbing boundary condition
References:
· A. Taflove, S.C. Hagness, Computational Electrodynamics: the finite difference time domain method, (3rd Ed.) Artech House, 2005.
· M.N.O. Sadiku, Numerical Techniques in Electromagnetics, 3rd Edition, CRC Press, 2009.
· U.S. Inan, R.A. Marshal, Numerical Electromagnetics: The FDTD Method. Cambridge University Press, 2011.
· W. C. Gibson, The Method of Moments in Electromagnetics, Taylor & Francis, 2008
· R. Luebbers, K. Kunz, The Finite Difference Time Domain Method for Electromagnetics, CRC Press, 1993.
· D.M. Sullivan, Electromagnetic Simulation using the FDTD Method , IEEE Press, 1998.
· M.V.K. Chari, S.J. Salon, Numerical Methods in Electromagnetism, Academic Press, 2000.
· D.B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, Cambridge University Press, 2005.
· C. Christopoulos, The Transmission-Line Modeling Method TLM, The IEEE Series on Electromagnetic Wave Theory.
· J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer-Verlag, 1999.
· R.J. LeVeque, Finite Difference Methods for Partial Differential Equations.
· A. Bonderson, Computational Electromagnetics, Springer.
· J. D. Jackson, Classical Electrodynamics, 3rd ed. New York: Wiley
· L.B. Felsen, Radiation and scattering of waves, IEEE Press.
· J.A. Stratton, Electromagnetic Theory, IEEE Press.