Courant Institute, NYU
COMPUTATIONAL ELECTROMAGNETICS (MATH 2011, CSCI 2945)
Fall 2022
Instructor
Mike O'Neil (oneil@cims.nyu.edu)

Office hours
By appointment

Description
Electromagnetic wave propagation is governed by Maxwell's equations, a PDE system that couples time varying changes in electromagnetic waves with spatial changes. Solving these equations computationally is quite challenging, as there are many different regimes to consider: time-domain problems, high-frequency problems, complex geometry, etc. This course were give an overview of the PDE and integral equation theory for Maxwell's equations, and then tackle various numerical methods for solving these problems.

Lecture
Thursday 1:25pm - 3:15pm, CIWW 1302
Materials
The following textbooks are recommended for reference material throughout the course:

- Papas, Theory of Electromagnetic Wave Propagation, 1988
- Friedrichs, Mathematical Methods of Electromagnetic Theory, 2014
- Jackson, Classical Electrodynamics
- Jin, Theory and Computation of Electromagnetic Fields, 2015

Grading
The overall course grade will be determined based on a final project.

Announcements
None.
Schedule
Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.
Date Topics Materials
Sep 1 Maxwell's Equations, potentials Papas: 1.1-1.4
Sep 8 Green's functions, electrostatics Papas: 2.1-2.2
Sep 15 Discretization, adaptive quadrature Greengard, et. al., 2021
Sep 22 Laplace FMM in 3D Greengard & Rokhlin, 1988
Epton & Dembart, 1995
Sep 29 FMM accelerations, plane waves Greengard & Rokhlin, 1997
Oct 6 Helmholtz FMM, planewaves
Maxwell FMM via Helmholtz
Greengard, Huang, Rokhlin, & Wandzura, 1998
Oct 13 Code benchmarking/validation, Lorenz-Debye-Mie solution,
spurious resonances, adjoint problems
Jin: 7.1-7.4
Colton: Ch. 5
Oct 20 Combined field equations,
low-frequency breakdown
Colton & Kress, Sec 4.6
Epstein, et. al., 2013
Oct 27 Project discussions
Nov 3 Non-reflecting boundary conditions Jin: 8.5-8.6, 9.6
Alpert, Greengard, Hagstrom, 2000
Alpert, Greengard, Hagstrom, 2002
Nov 10 Layered media scattering O'Neil, Greengard, & Pataki, 2014
O'Neil, 2014
Nov 17 Geometric optics and diffraction Popov, 2002
Engquist and Runborg, 2003
Nov 24 NO CLASS: THANKSGIVING
Dec 1 Volume scattering
High frequency FMM
Dec 8 Project Presentations