Joly–Mercier boundary condition for the finite element solution of 3D Maxwell equations

Solving the time-dependent Maxwell equations in an unbounded domain requires the introduction of artificial absorbing boundary conditions (ABCs) designed to minimize the amplitude of the parasitic waves reflected by the artificial frontier of the domain of computation. The construction of such ABCs needs to perform a rigorous mathematical and numerical analysis, in order to obtain a well-posed problem, from a mathematical point of view, and a stable algorithm, from a numerical point of view. In a previous study, Joly and Mercier (1989) [8] have proposed a new second-order ABC for Maxwell’s equation in dimension 3, well adapted to a variational approach. In this paper, we present how to apply the second-order ABC proposed in [8] in the framework of a finite element method.