A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain

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...

A Discontinuous Galerkin Method for the Time-Domain Solution of 3D Maxwell's Equations on Non-Conforming Locally Refined Grids

A discontinuous Galerkin method is proposed for the numerical solution of the three-dimensional time-domain Maxwell's equations. A leap frog scheme is used for advancing in time. The scheme resulting can handle highly heterogeneous material, non diffusive and highly adaptable (it has been implemented on tetrahedral or hexahedral grids, including non-conforming). In some cases, some divergence c...

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 ...

High-order/Spectral Methods on Unstructured Grids I. Time-domain Solution of Maxwell’s Equations

We present an ab initio development of a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains. As our main example we present a detailed development and analysis of a scheme suitable for the time-domain solution of Maxwell's equations in a three-dimensional domain. The fully unstructured spatial discretization is made possible by th...

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