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# Numerical Analysis and Finite Elements for Electromagnetics and Wave Propagation

Lecture (4 SWS) with Tutorial (2 SWS) in summer term 2012 at TU Berlin

Dates
Time
Room
Lecturer
Lectures
Wed, 4.00 pm - 5.30 pm
MA 651
Dr. Kersten Schmidt
Wed, 5.45 pm - 7.15 pm
MA 651
Dr. Kersten Schmidt
Exercises
Thu, 4.15 pm - 5.45 pm
MA 545
Dr. Anastasia Thöns-Zueva

Next exercise class: Thu, June 21st, 4.15 pm in Unix-Pool

## Content Alternating Magnetic Field The lecture deals with problems in electromagnetics described by Maxwell's equations, including regimes of low frequency, that are electrostatics and quasi-electrostatics, and of high frequency, that is electromagnetic wave propagation or optics. For a numerical description of the elliptic partial differential equations (PDEs) behind, we use finite elements and the variational framework they are based on. It is the aim that the participants are able to implement own finite element code(s) in Matlab/Octave in 2D and understand why the modelling by finite elements leads to accurate approximations of electrostatic potentials electromagnetics fields.

Topics:

• Overview over electromagnetic phenomena and models
• Elliptic PDEs from electrostatics and the eddy-current model in 2D
• Variational formulation of elliptic PDEs
• Finite element method (FEM)
• Numerical analysis, error analysis
• Wave propagation in frequency domain: Helmholtz equation
• Analysis of the Helmholtz equation (Fredholm theory)
• Wave propagation towards infinity, non-reflecting boundary conditions
• Error analysis for higher order FEM for the Helmholtz equation
• Eddy current model in 3D, variational formulation in H(curl, Ω)
• Finite elements for Maxwell's equations (Nédélec elements)

## References

• D. Brass, "Finite Elemente", Springer-Verlag, 2007.
• P. Solin, "Partial Differential Equations and the Finite Element Method", John Wiley & Sons, 2006.
• P.G. Ciarlet, "The finite element method for elliptic problems", North-Holland, 1978.
• A. Alonso Rodriquez, A. Valli, "Eddy Current Approximation of Maxwell Equations", Springer-Verlag, 2010.

## Audience

Students at bachelor, master level or diploma students in mathematics (incl. Techno-, Wirtschaftsmathematik and Scientific Computing), as well as doctoral students (incl. BMS). Students in physics and engineering disciplines with interest in a theoretical base of FEM are welcome.

## Requirements

Analysis I-II, Linear Algebra, (Introduction into) Numerical Mathematics.

Helpful: Basic knowledge of differential equations.

## Auxiliary Functions

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TU Berlin
Institute of Mathematics
sec. MA 6-4
Strasse des 17. Juni 136
D-10623 Berlin

## How to find us

Maths Building (MA)
6th floor
rooms 363, 365 and 379