Numerical Methods in Electrical Engineering SS 2012
| Lecture: | Dr. Clemens Pechstein | Thursday, 13.45 – 16.00 | T 212 starting by March 8 |
| Tuesday, 13. March, 13.45 | S2 059 (exception) | ||
| Tutorial: | DI Monika Wolfmayr | Wednesday, 10.15 – 11.00 | S2 0346 start: March 14 |
Most problems in electrical engineering can be described using Maxwell's equations or special cases thereof. This includes low-frequent applications (electric motors, transformers, etc.) as well as high-frequent applications (antennas, mobile phones, etc.).
In this lecture, I will discuss in detail the governing equations and the necessary variational framework. Herefor, we need suitable Sobolev spaces beyond H1 (called H(curl) and H(div)), and we will treat these in detail. Even more importantly, the right discretization must be chosen; standard H1-conforming finite elements, e.g. continuous P1 elements, will fail in general. Hence, we will discuss the correct finite element spaces, such as the H(curl)-conforming Nédélec elements. Finally, we will see how to solve the discretized systems of equations.
The lecture itself is blocked to lessons of 120 minutes per week (with a little break in between) and will be finished by end of May.
Contents:
- Maxwell's equations
- Variational framework
- Discretization
- Solvers
Additional material (PDF):
- Maxwell's equations (overview)
- Trace operators
- Regimes of Maxwell's equations
- Existence and uniqueness theorems
- Helmholtz decomposition
- Finite element basics
- Abstract error estimates
- Additive Schwarz preconditioning
Related literature:
- P. Monk. Finite Element Methods for Maxwell's Equations, Oxford University Press, New York, 2003
- M. Kaltenbacher. Numerical Simulation of Mechatronic Sensors and Actuators, Springer-Verlag, Berlin, 2004
- N. Ida and J.P.A. Bastos, Electromagnetics and Calculation of Fields, Springer-Verlag, New York, 1997 (2nd edition)
- J. Schöberl, Lecture notes Numerical Methods for Maxwell Equations (PDF), SS 2009
Lecture Exam:
oral, you can arrange an exam with me from October 2012 on (contact me before)
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