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Advanced Topics in Numerical Analysis

Computational Electromagnetics

CSCI-GA2945.001

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.

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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.

## Reading

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

Homework 1

Homework 2