Advanced Topics in Numerical Analysis
Computational Electromagnetics
Spring 2012
Professor Leslie Greengard

Tuesday 9:30-11:20
Warren Weaver Hall, Room 512

Prerequisites: complex analysis, partial differential equations, numerical analysis, basic functional analysis
The field of computational electromagnetics is devoted to the solution of Maxwell's equations, with application (for example)
to antenna and chip design, electromagnetic compatibility, wave scattering, and optics. We will review the basic theory,
followed by an overview of finite difference, finite element, and integral equation methods. The course will emphasize scattering
theory from an integral equation perspective.

Recommended Text : Theory and Computation of Electromagnetic Fields,
Jian-Ming Jin, Wiley-IEEE Press, 2010.
Supplementary Text : Theory of Electromagnetic Wave Propagation,
Charles H. Papas, Dover, 1988.
Supplementary Text : Partial Differential Equations of Mathematical
Physics and Integral Equations,
Ronald B. Guenther and John W. Lee, Dover, 1996.

Grading: this course will be graded as a seminar course.


Lectures 1-4 :
Basic Electromagnetic Theory: Jin, Chapters 1-3
Papas, Chapters 1-3
Lectures 5-7 :
Integral Equations, Quadratures, Fast Multipole Methods :
Guenther & Lee, Chapters 7-8,
A Short Course on Fast Multipole Methods
Remarks on the implementation of the wideband FMM for the Helmholtz equation in two dimensions
Lectures 8-10 :
Electromagnetic Scattering in 3D; The Lorenz/Debye/Mie formalism;
the Electric Field Integral Equation, the Magnetic Field Integral Equation,
the Combined Field Integral Equation :
Jin, Chapters 6,7,10,
Papas, Chapter 4


Homework 1
Homework 2