Causal--Path Local Time--Stepping in the Discontinuous Galerkin Method for Maxwell's equations

Explicit local time-stepping methods for Maxwell's equations

Explicit local time-stepping methods are derived for the time dependent Maxwell equations in conducting and non-conducting media. By using smaller time steps precisely where smaller elements in the mesh are located, these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators. When combined with a finite element discretization in space with an essentially d...

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

In this paper, we present a non-dissipative spatial high-order discontinuous Galerkin method to solve the Maxwell equations in the time domain. The non-intuitive choice of the space of approximation and the basis functions induce an important gain for mass, stiffness and jump matrices in terms of memory. This spatial approximation, combined with a leapfrog scheme in time, leads also to a fast e...

Multilevel and Local Time-stepping Discontinuous Galerkin Methods for Magma Dynamics

Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column at local chemical equilibrium. DG methods for both advection and elliptic equations provide a robust and efficient solution to the problems of melt migration in the asthenospheric upper mantle. Assembling and solving the elliptic equat...

Local Time-stepping for Explicit Discontinuous Galerkin Schemes

A class of explicit discontinuous Galerkin schemes is described which time approximation is based on a predictor corrector formulation. The approximation at the new time level is obtained in one step with use of the information from the direct neighbors only. This allows to introduce a local time-stepping for unsteady simulations with the property that every grid cell runs with its own optimal ...

Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method