  The axion is a hypothetical particle motivated to address the strong CP
problem, and is one of the appealing dark matter candidates. Numerous
experimental searches for dark matter axions have been proposed relying on
their coupling with photons. The classical equations of motion for the
axion-photon coupling are well known but need to be fully computed for complex
experimental setups. The partial differential equations of axion
electrodynamics can be numerically solved using finite element methods. In this
work, we simulate axion electrodynamics using COMSOL Multiphyics, a
commercially available simulation software, for various experimental schemes,
including the dish antenna haloscope, cavity haloscope, dielectric haloscope,
and axion-photon regeneration. We show that the numerical results are in good
agreement with the analytical solutions.
