This text reviews the state of the art of the Discontinuous Galerkin (DG) method applied to
the solution of the Maxwell's equations in Time Domain (TD). The work is divided into two …

Locally refined meshes severely impede the efficiency of explicit Runge--Kutta (RK)
methods for the simulation of time-dependent wave phenomena. By taking smaller time …

This paper presents a numerical scheme of arbitrary order of accuracy in both space and
time, based on the arbitrary high-order derivatives methodology, for transient acoustic …

In this paper we consider the full discretization of linear Maxwell's equations on spatial grids
which are locally refined. For such problems, explicit time integration schemes become …

Local time-stepping methods permit to overcome the severe stability constraint on explicit
methods caused by local mesh refinement without sacrificing explicitness. Diaz and Grote …

Local mesh refinement severely impedes the efficiency of explicit time-stepping methods for
numerical wave propagation. Local time-stepping (LTS) methods overcome the bottleneck …

This book presents the notes from the seminar on wave phenomena given in 2019 at the
Mathematical Research Center in Oberwolfach. The research on wave-type problems is a …

We present a time-implicit hybridizable discontinuous Galerkin (HDG) method for
numerically solving the system of three-dimensional (3D) time-domain Maxwell equations …

We propose a new implicit–explicit scheme to address the challenge of modeling wave
propagation within thin structures using the time‐domain finite element method. Compared …

Based on an implicit time scheme, this paper presents a new implicit hybridizable
discontinuous Galerkin time-domain (imHDGTD) method for solving the 3-D electromagnetic …