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Lecture SS 23 Advanced Topics in Numerical Analysis

Finite Element Methods for Helmholtz and Maxwell equations

Prof. Barbara Verfürth
Tuesdays 8-10 and Wednesdays 8-10 in room 2.035 in FHA7 (INS building)

The first lecture will be on April 4, starting at 8.30.

This lecture deals with (time-harmonic) electromagnetic wave propagation problems as they ouccur in may applications such as microwaves, optical fibers, lasers, etc. Maxwell equations are the governing equations, but in certained situations the Helmholtz equation can be studied as simplified model. After an introduction into the modelling of electromgnetic waves, we will focus on their numerical simulation which comes with a couple of challenges. First, solutions are typically very oscillatory in space - at least when the freuqnecy of the wave is high. This requires then a tight resolution of the mesh and we will derive the corresponding conditions. Second, Maxwell equations include the curl as the main differential operator. This calls for new function spaces and finite elements (in comparison to the Poisson problem). We will introduce the necessary spaces and study their properties. In the end, we will be able to conduct a numerical analysis of electromagnetic wave propgation problems governed by Maxwell equations.

Further information and course material will be provided in the eCampus course.