High-Order Locally Implicit Time Integration Strategies in a Discontinuous Galerkin Method for Maxwell's Equations

摘要

The starting point for the present study is a second-order locally implicit time integration method for a nondissipative discontinuous Galerkin (DG) discretisation of Maxwell's equations. The system is split into the explicit and the implicit parts based on the geometry of the mesh: locally refined regions are treated implicitly while the rest of the domain is treated explicitly. When combined with an explicit time integration method one of the main drawbacks of the DG time-domain (DGTD) method is the restriction on the time step when high-order elements are used. If the region of refinement is small relative to the computational domain, the implicit-explicit (IMEX) method allows to overcome this efficiency issue without needing to solve a linear system at each time step for the entire size of the problem. The topic of this study is to propose higher order time integration techniques based on a second-order locally implicit method to fully exploit the attractive features of the IMEX approach combined with a DG discretisation which allows to easily increase the spatial convergence order.