Time- and frequency-domain hybridizable discontinuous Galerkin solvers for the calculation of the Cherenkov radiation

Abstract

This work proposes novel hybridizable discontinuous Galerkin (HDG) methods, both in the time and in the frequency domain, to accurately compute the Cherenkov radiation emitted by a charged particle travelling in a uniform medium at superluminal speed. The adopted formulations enrich existing HDG approaches for the solution of Maxwell’s equations by including perfectly matched layers (PMLs) to effectively absorb the outgoing waves and Floquet-periodic boundary conditions to connect the boundaries of the computational domain in the direction of the moving charge. A wave propagation problem with smooth solution is used to show the optimal convergence of the HDG variables and the superconvergence of the postprocessed electric field and a second example examines the role of the PML parameters on the absorption of the electromagnetic field. A series of numerical experiments both in 3D and 2D-axisymmetric components show the capability of the proposed methods to faithfully reproduce Cherenkovian effects in different conditions and their high accuracy is confirmed by comparing the numerical results with the Frank–Tamm formula.