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Dipl.-Math. Lizzy Blank | |
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Discontinuous Galerkin Methods for nonlinear Maxwell's equations Office hour for students: Room: 8.14 (Physikhochhaus) IWRMM (20.52) Tel.: 0721-608 46949 Email: Lizzy.Blank@math.uni-karlsruhe.de |
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Research interest:
"The Discontinuous Galerkin Method applied to Nonlinear Maxwell's Equations".
The DG method is applied to Maxwell's equations with a nonlinearity (later maybe also
). It turns out that the numerical flux, which is a main ingredient of the DG method, is a solution of the corresponding Riemann problem. If possible, an analytical solution of the Riemann problem shall be found. If this is possible we expect it to be complex, which is not advantageous for implementation. Therefore, another question is to find a "good" approximation to the analytical flux.
As an introduction to the topic the DG method is applied to so-called Body of Revolution Maxwell's equations in 3D; due to rotational symmetry, Maxwell's equations reduce to a 2D problem.
The project is supervised by Prof. Dörfler and Prof. Busch (Photonics Group of the Institute of Solid State Physics).
Work and Publications:
E. Blank, T. Dohnal, Families of Surface Gap Solitons and their Stability via the Numerical Evans Function Method, SIADS, 2011 (accepted).
E. Blank, In-/Stability of Surface Gap Solitons, Diploma Thesis, 2009.
You find more information about research and members of the Photonics Group (TFP) here: http://www.tfp.kit.edu/108.php