# 2141418 Numerical Method (NANO)

Course Type/Credits: Elective course/3 credits

Contents

Review of electromagnetics and Maxwell’s equations; finite differencing of partial differential equations; one-dimensional wave equation; the finite-difference time-domain (FDTD) method; numerical stability and dispersion; scattered field formulation; absorbing boundary conditions; method of moments (MoM); finite element method (FEM).

Course Outline

This course examines the principles and applications of numerical techniques for solving practical electromagnetics problems. By the end of this course the student will be able to:

• Understand why numerical methods are needed to solve realistic or practical problems in electromagnetics and why this need will increase.
• Understand the mathematical concepts upon which computational electromagnetics relies.
• Can translate the mathematical description of a solution into a computer program.
• Can choose between the various numerical methods to use the right method for a particular problem.
• Develop a foundation level necessary for successful use of available computational EM tools (programs such as HFSS, Momentum, and others) for research in the area of numerical and applied electromagnetics.

Schedule & Lecture Slides

The following schedule is tentative and subject to changes as the semester goes by.

 Week Topic 1 Review of electromagnetic theory I 2 Review of electromagnetic theory II 3 Overview of analytical and numerical methods 4 Finite-difference time-domain (FDTD) method 5 Absorbing boundary conditions 6 Two- and three-dimensional FDTD methods 7 Midterm examination 8 Applications of FDTD I 9 Perfectly matched layers 10 Stability and numerical dispersion analysis 11 Applications of FDTD method II 12 Advanced topics in FDTD method I 13 Applications of FDTD method III 14 Advanced topics in FDTD method II

• Homework 20%
• Project 50%
• Final Examination 30%

Textbook(s)

• D. B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, Cambridge University Press, 2005.
• A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Artech House, 2005.
• S. M. Musa, Computational Nanotechnology Using Finite Difference Time Domain, CRC Press, 2013.