Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic

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

High-Order Numerical Methods for Maxwell's Equations on Unstructured Meshes

For more than fifteen years, spectral finite elements (i.e. finite element methods on hexahedral meshes with mass-lumping) showed their efficiency to model the propagation of acoustic and elastic waves in the time domain, in particular in terms of accuracy. Moreover, their mixed formulation [1] dramatically increases their efficiency in terms of storage and computational time. This approach, wh...

HP a-priori error estimates for a non-dissipative spectral discontinuous Galerkin method to solve the Maxwell equations in the time domain

In this paper, we present the hp-convergence analysis of a nondissipative high-order discontinuous Galerkin method on unstructured hexahedral meshes using a mass-lumping technique to solve the time-dependent Maxwell equations. In particular, we underline the spectral convergence of the method (in the sense that when the solutions and the data are very smooth, the discretization is of unlimited ...

Algebraic Multigrid Preconditioning of High-Order Spectral Elements for Elliptic Problems on a Simplicial Mesh

Algebraic multigrid is investigated as a solver for linear systems that arise from high-order spectral element discretizations. An algorithm is introduced that utilizes the efficiency of low-order finite elements to precondition the high-order method in a multilevel setting. In particular, the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral ...

Parallel Implementation of the Discontinuous Galerkin Method

This paper describes a parallel implementation of the discontinuous Galerkin method. The discontinuous Galerkin is a spatially compact method that retains its accuracy and robustness on non-smooth unstructured grids and is well suited for time dependent simulations. Several parallelization approaches are studied and evaluated. The most natural and symmetric of the approaches has been implemente...