Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method

Locally implicit discontinuous Galerkin method for time domain electromagnetics

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneou...

Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

In this paper, we develop a high order semi-implicit time discretization method for highly nonlinear PDEs, which consist of the surface diffusion and Willmore flow of graphs, the Cahn-Hilliard equation and the Allen-Cahn/Cahn-Hilliard system. These PDEs are high order in spatial derivatives, which motivates us to develop implicit or semi-implicit time marching methods to relax the severe time s...

Horizontally Explicit and Vertically Implicit (HEVI) Time Discretization Scheme for a Discontinuous Galerkin Nonhydrostatic Model

A two-dimensional nonhydrostatic (NH) atmospheric model based on the compressible Euler system has been developed in the (x, z) Cartesian domain. The spatial discretization is based on a nodal discontinuous Galerkin (DG) method with exact integration. The orography is handled by the terrain-following heightbased coordinate system. The time integration uses the horizontally explicit and vertical...

Discontinuous Galerkin Time-Domain method for nanophotonics

The numerical study of electromagnetic wave propagation in nanophotonic devices requires among others the integration of various types of dispersion models, such as the Drude one, in numerical methodologies. Appropriate approaches have been extensively developed in the context of the Finite Differences Time-Domain (FDTD) method, such as in [1] for example. For the discontinuous Galerkin time-do...

A-stable discontinuous Galerkin-Petrov time discretization of higher order