Abstract
AbstractWe present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods, is also high-order accurate in both space and time and can be seen as a generalization of the classical DGTD scheme based on upwind fluxes. We provide numerical results aiming at assessing its numerical convergence properties by considering a model problem and we present some results of the superconvergence property on the Hcurl norm.
Highlights
A appealing solution in this context is given by the concept of hybridizable discontinuous Galerkin (HDG) method
In this paper we outline the formulation of this explicit HDGTD, present numerical results including a preliminary assessment of its superconvergence properties
This work is a first step towards the construction of a hybrid explicit-implicit HDG method for time-domain electromagnetics
Summary
The DGTD method is nowadays a very popular numerical method in the computational electromagnetics community. A lot of works are mostly concerned with time explicit DGTD methods relying on the use of a single global time step computed so as to ensure stability of the simulation. An alternative approach that has been considered in [5, 7, 16] is to use a hybrid explicit-implicit (or locally implicit) time integration strategy Such a strategy relies on a component splitting deduced from a partitioning of the mesh cells in two sets respectively gathering coarse and fine elements. The HDG methods are fully implicit, high-order accurate and most importantly, they reduce the globally coupled unknowns to the approximate trace of the solution on element boundaries, thereby leading to a significant reduction in the degrees of freedom. In view of devising a hybrid explicit-implicit HDG method, a preliminary step is to elaborate on the principles of a fully explicit HDG formulation. This work is a first step towards the construction of a hybrid explicit-implicit HDG method for time-domain electromagnetics
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