The objective of this course is to provide hands-on experience with contemporary numerical approaches in electromagnetics (EM) to student researchers for applications in RF-microwave circuits, high-speed interconnects, MEMS, antenna analysis and design and bio-medical imaging.

Module 1: Review of basic EM principles

• Maxwell’s equations
• Applications of Computational Electromagnetics
• Electrostatics and Magnetostatics
• Wave equation and propagation
• Scalar and vector potentials
• Surface equivalence principle
• Greens Function
• Boundary conditions
• Linear algebra for computational EM

Module 2: Method of Moments (MoM)

• 2D vs 2.5D vs. 3D Formulations
• Electrostatic Formulation: Capacitance matrix extraction
• Magnetostatic Formulation: Inductance matrix extraction
• Electric Field Integral Equation (EFIE): S-parameter extraction
• Partial Element Equivalent Circuit (PEEC) Method
• Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE)
• PMCHWT Formulation: Dielectric modeling
• Parallelization techniques

Module 3: Finite Difference Time Domain (FDTD) Method

• Basics of FDTD: Finite Differences
• FDTD Solution of Maxwell Equations in simple cases
• Scattered field vs total field formulation
• Implementation issues
• Outer Radiation Boundary Conditions
• Yee cell, Yee algorithm for 3D Formulation of FDTD
• Perfectly Matched Layer ABC
• Frequency Domain Results from Time Domain Output of FDTD
• Computational issues: Stair casing errors, numerical dispersion
• Frequency Dependent Materials

References

1. A. Taflove and SC Hagness Computational Electrodynamics: The Finite Difference Time Domain Method, 3rd Ed., Artech House
2. Andrew F. Peterson, Scott L. Ray, Raj Mittra: Computational Methods for Electromagnetics, 1st Ed., IEEE Press Series on Electromagnetic Wave Theory
3. Walton C. Gibson: The Method of Moments in Electromagnetics, 1st Ed., Chapman and Hall
4. Roger F. Harrington: Field Computation by Moment Methods, 1993, Wiley-IEEE Press