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
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.
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 |