The solution to the time-dependent Maxwell equations with charges in a 2D nonsmooth domain

In [3] and [2], we considered the numerical solution to the time-dependent Maxwell equations in the absence of charges in a 2D non-convex domain, using the so-called singular complement method (SCM), for which the computed fields are continuous. In this paper, we present an extension of the SCM, which allows to solve efficiently the time-dependent Maxwell equations with charges, with almost no additional computational cost. Thus, the numerical solution to the Vlasov-Maxwell system of equations can be achieved by coupling the SCM to a particle solver.