Related papers: Enclave Tasking for Discontinuous Galerkin Methods…
An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of transient problems…
This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are…
A well-balanced moving mesh discontinuous Galerkin (DG) method is proposed for the numerical solution of the Ripa model -- a generalization of the shallow water equations that accounts for effects of water temperature variations.…
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [21] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous…
In this paper we investigate the parallelization of dual-primal isogeometric tearing and interconnecting (IETI-DP) type methods for solving large-scale continuous and discontinuous Galerkin systems of equations arising from Isogeometric…
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order…
We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows the consideration of discretizations that do not match on the interfaces. We solve the…
We present a novel high-order accurate nodal discontinuous Galerkin (DG) method for solving nonlinear hyperbolic systems of partial differential equations (PDEs) on fully unstructured three-dimensional polyhedral meshes. A mesh generator is…
We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly…
This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell…
During the last few years discontinuous Galerkin (DG) methods have received increased interest from the geophysical community. In these methods the solution in each grid cell is approximated as a linear combination of basis functions.…
We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational…
We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may…
We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…
A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the…
Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by…
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static,…