The two main objectives of the course are the following:
1. To teach the students how to define, analyze and numerically solve electromagnetic field problems.
2. To provide them a general survey of the more commonly used computation schemes, with emphasis on some of the most popular methods, such as: Finite Difference Method (FDM), Finite Element Method (FEM), Boundary Element Method (BEM), Method of Moments (MOM) and Finite Difference Time Domain (FDTD).
Course Content (Syllabus)
Variational principles and techniques:
- Introduction to the basic concepts of variational calculus.
- Formulation of Maxwell's equations via Hamilton's principle.
- The non-homogeneous Helmholtz equation as a variational calculus problem.
Weighted residual methods:
- The concept of the weighted residual in error estimation for the analytical and computational treatment of field problems.
- Point-Matching, Rayleigh-Ritz, Galerkin, Least Squares and Sub-domain Collocation techniques as special cases of the weighted residual methodology.
- Numerical methods for complex field prtoblems.
Introduction to computational techniques:
- The Finite Difference Method: domain discretization, difference equations, error estimation, iterative techniques, Gauss-Seidel and SOR methods, Crank-Nicolson and Dufort-Frankel schemes.
- The Finite Element Method: discretization, local and global numbering, basis functions, stiffness and mass matrix, system solution, post-processing and visualization of results.
- The Moment and Boundary Element Method: basis and weighting functions, categories of integral equations, Green's functions.
- The Finite-Difference Time-Domain Method: difference equations, Yee's algorithm, stability, dispersion, open-boundary problems, absorbing boundary conditions, PML technique.
Additional bibliography for study
1. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press, 1993.
2. M. N. O. Sadiku, Numerical Techniques in Electromagnetics, CRC Press, 2010.
3. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, Cambridge University Press, 1996.
4. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edition, Artech House, 2005.