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Introduction into Maxwell's Equations (Winter Semester 2012/13)

Lecture: Monday 11:30-13:00 1C-03
Wednesday 11:30-13:00 1C-03
Problem class: Friday 11:30-13:00 Z 2
Lecturer, Problem classes Prof. Dr. Andreas Kirsch
Office hours: by apointment
Room 0.011 Kollegiengebäude Mathematik (20.30)
Email: Andreas.Kirsch@kit.edu
Problem classes M.Sc. Oleksandr Bondarenko
Office hours: Dienstags von 15 bis 16 Uhr oder nach Absprache
Room 1.049 Kollegiengebäude Mathematik (20.30)
Email: bondarenko@kit.edu

Electromagnetic wave propagation is modeled by a system of two partial differential equations for the electric and magnetic fields E and H, the Maxwell system. This will be the starting point of our lecture. We will consider time-harmonic fields (i.e. periodic in time) solely and study two model problems in detail: First, we investigate a scattering problem and treat this special boundary value problem in an unbounded domain by a boundary integral equation method. Second, we study a cavity problem; that is, a boundary value problems in a bounded domain, and treat this by a variational method. For this part we will make use of Sobolev spaces, which will be introduced at the beginning of this section.


Vordiplom or Bachelor in Mathematics, Physics or in Engineering

Basic knowledge of functional analysis is needed, in particular the notions of normed spaces, Hilbert spaces including their most important examples, linear and bounded or compact operators, the representations theorem of Riesz in Hilbert spaces. Further facts on functional analysis will be derived during the course.

Literature: (e.g.)

D. Colton, R. Kress: Inverse Acoustic and Electromagnetic Scattering Theory. 2nd edition. Springer Verlag, 1998.

Monk: Finite Element Methods for Maxwell's Equations. Oxford University Press 2003.


Part 1

Part 2

Part 3