Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves

Arbitrary High-order Discontinuous Galerkin Method for Electromagnetic Field Problems

In this paper, we present a time integration scheme applied to the Discontinuous Galerkin finite element method (DG-FEM, [1]) for the computation of electromagnetic fields in the interior of three-dimensional structures. This approach is also known as Arbitrary High-Order Derivative Discontinuous Galerkin (ADER-DG, [2, 3]). By this method, we reach arbitrary high accuracy not only in space but ...

A High-order Discontinuous Galerkin Scheme for Elastic Wave Propagation

In this paper, we introduce a fourth-order leap-frog time scheme combined with a high-order discontinuous Galerkin method for the solution of the elastodynamic equations. The time discretization, obtained via a simple construction based on Taylor developments, provides an accurate scheme for the numerical simulation of seismic wave propagation. Results of the propagation of an eigenmode allow a...

Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation

Abstract. In this paper, we present a local discontinuous Galerkin (LDG) method and two unconditionally energy stable schemes for the phase field crystal (PFC) equation. The semidiscrete energy stability of the LDG method is proved first. The PFC equation is a sixth order nonlinear partial differential equation (PDE), which leads to the severe time step restriction (Δt = O(Δx6)) of explicit tim...

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that pr...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics