Scientific Computing Seminar

The very nature of the wave equation requires that special finite elements be used in order to avoid spurious solutions. The choice of hybrid Nedelec elements guarantees the desired avoidance of non-physical modes. Another peculiarity of the axisymmetric approach concerns the accurate evaluation of the aforementioned weak form. By exploiting rotational symmetry, some of the quantities to be computed exhibit displeasing characteristics and can hence no longer be computed in a straightforward manner. To this end we developed numerical schemes that allow for an accurate and efficient evaluation of the critical quantities.

A further speciality of our problems concerns the proper consideration of leaky waves. Lossy cavities radiate into their surroundings - an effect which has to be appropriately incorporated, in order for the simulation results to be meaningful. The use of perfectly matched layers, particular layers of absorbing material which can seamlessly be incorporated in our finite element model, provides an attenuation of leaky waves and leads to the desired consideration.