S. Ungar:

"Hardy-Raum Infinite Elemente für Resonanzprobleme in zylindrischen Wellenleitern";

Supervisor: L. Nannen, J. Schöberl; Institut für Analysis und Scientific Computing, 2018; final examination: 2018-10-16.

Wave phenomena can be divided into two categories. Scattering problems, where the right side, i.e. a source and a frequency are given. In the case of resonance problems, we look for frequencies, for which the problem is not uniquely solvable. This work deals with the latter. In addition, we consider two types of waves for this work: acoustic and electromagnetic waves. The former are described by the Helmhotz equation, the second by the time-harmonic Maxwell equation. The unrestricted area on which the waves move is of a waveguide type. We subdivide this into a restricted inner and an unrestricted outer space into which the wave radiates or leaks. The interior is processed using the Finite Element Method. For the unrestricted outer space, special Inifinte Elements are required, which depend on a parameter and the number of outer degrees of freedom. These special Infinite Elements are the main subject of this work. In the numerical examples at the end of the work, we show exponential falling behavior of the error in the direction of emission with respect to the number of degrees of freedom. We also show how the resonances behave, depending on the parameter.

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