Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Automatic mesh generator with specified boundary
Computer Methods in Applied Mechanics and Engineering
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Stability of explicit-implicit hybrid time-stepping schemes for Maxwell's equations
Journal of Computational Physics
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Some unconditionally stable time stepping methods for the 3D Maxwell's equations
Journal of Computational and Applied Mathematics
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media
Journal of Scientific Computing
High-order RKDG Methods for Computational Electromagnetics
Journal of Scientific Computing
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Journal of Computational Physics
Journal of Computational Physics
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
Interior penalty DG methods for Maxwell's equations in dispersive media
Journal of Computational Physics
High-order explicit local time-stepping methods for damped wave equations
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Journal of Computational Physics
Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
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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 heterogeneous media that characterize realistic propagation problems. Such DGTD methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step. A more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part, resulting in an hybrid explicit-implicit (or locally implicit) time integration strategy. In this paper, we report on our recent efforts towards the development of such a hybrid explicit-implicit DGTD method for solving the time domain Maxwell equations on unstructured simplicial meshes. Numerical experiments for 3D propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes.