Simulation studies for the MADMAX axion direct detection experiment

We present a general approach to solve the Maxwell-axion equations for arbitrary geometries and materials. The approach is based on the finite element method (FEM) and applied to experimental setups related to the new MADMAX (MAgnetized Disc and Mirror Axion eXperiment) project. Analytical methods are used to verify the FEM simulations. MADMAX is a dielectric haloscope which will utilize axion-photon conversion at many dielectric interfaces and probe axions in the mass range $m_a=40-400\mu \text{eV}$.