While the fundamental equations governing the axion-photon interaction are widely recognized, their comprehensive calculations become imperative when applied to intricate experimental setups. In this work, we utilize COMSOL Multiphysics, a commercially available software that employs the finite element method, to numerically solve the partial differential equations underlying axion electrodynamics. We simulate diverse experimental schemes, including axion haloscope and axion-photon regeneration. We show that the numerical simulations are in excellent agreement with the analytical calculations, confirming that they are reliable for describing axion electrodynamics.