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 …

An enriched finite element method is presented to solve various wave propagation
problems. The proposed method is an extension of the procedure introduced by Kohno …

This work presents a new high performance open‐source numerical code, namely SPectral
Elements in Elastodynamics with Discontinuous Galerkin, to approach seismic wave …

A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution
partial differential equations. It is based on approximations of generalized Lax pairs …

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient
acoustic wave equations in arbitrary space dimensions, extending the one-dimensional …

In this study we investigate a stabilized space-time formulation for linear and non-linear
elastodynamics. We use Isogeometric Analysis (IGA) in order to benefit from its numerical …

We present the first a priori error analysis of the hybridizable discontinuous Galerkin
methods for the acoustic equation in the time-continuous case. We show that the velocity …

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling
wave propagation in coupled poroelastic–elastic media. The upwind numerical flux is …

We devise the first symplectic Hamiltonian hybridizable discontinuous Galerkin (HDG)
methods for the acoustic wave equation. We discretize in space by using a Hamiltonian …

Hamilton's principle is the variational principle for dynamical systems, and it has been widely
used in mathematical physics and engineering. However, it has a critical weakness, termed …