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## Numerics of Partial Differential Equations II - Modelling of Electrodynamic

Lecture (4 SWS) with Tutorial (2 SWS) in summer term 2016 at TU Berlin

Time | Room | Lecturer | |
---|---|---|---|

Lectures | Wed, 10.15 - 11.45 | MA 542 | Dr. Kersten Schmidt |

**15. Juni will not take place, replacement lecture on June 30th 4pm-5:30pm in room MA 376**

**20. Juli will not take place, replacement lecture on July 14th 4pm-5:30pm in room MA 376**

**Replacement lecture on Thursday, May 26th, 16.00 - 17.30 in room MA 376.**

## Content

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.

**Topics:**

- Overview over electromagnetic phenomena and models
- Finite Element Method (FEM) for equations of Electrostatic/Magnetostatic in 3D
- Eddy current model in 3D, variational formulation in H(curl, Ω)
- Finite Element Method (FEM) for Maxwell equations (Nédélec-Element)
- Analysis of the Helmholtz equation (Fredholm theory) for time harmonic wave propagation
- Analysis of time harmonic Maxwell equations in H(curl, Ω)
- Exact sequence of finite elements (DeRahm-diagram)
- Numerical analysis of finite element method for time harmonic Maxwell equations

## Literature

- P. Monk, "Finite Element Methods for Maxwell's Equations", Clarendon Press, 2003.
- A. Alonso Rodriguez, A. Valli, "Eddy Current Approximation of Maxwell Equations", Springer, 2014.