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 …

The numerical modeling of mechanical waves is currently a fundamental tool for the study
and investigation of their propagation in media with heterogeneous physical properties …

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 …

A spacetime domain can be progressively meshed by tent shaped objects. Numerical
methods for solving hyperbolic systems using such tent meshes to advance in time have …

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

In this paper, we discuss a time domain finite element method for the approximate solution of
Maxwell's equations. A weak formulation is derived for the electric and magnetic fields with …

In this paper we develop explicit local time-stepping (LTS) schemes with second and third
order accuracy for the shallow water equations. The system is discretized in space by a C …

In this article, an efficient transient analysis method with arbitrary high-order accuracy for
nonlinear field-circuit cosimulation problems is proposed. The proposed method combines a …

It is well known that graphene demonstrates spatial dispersion properties, ie, its conductivity
is nonlocal and a function of spectral wavenumber (momentum operator). In this paper, to …