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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

Link to university calendar

Dates
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

Alternating Magnetic Field
Lupe

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.

Exams

At the end of the semester, an oral exam is offered.

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, Basic knowledge of differential equations.

Helpful: Numerical method for Partial Differential Equations, Numerical Mathematics II for Engineers

Zusatzinformationen / Extras

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