Unconditionally stable and parallel Discontinuous Galerkin solver

Abstract

We describe a parallel and quasi-explicit Discontinuous Galerkin (DG) kinetic scheme for solving systems of balance laws. The solver is unconditionally stable (i.e., the CFL number can be arbitrary) and has the complexity of an explicit scheme. It can be applied to any hyperbolic system of balance laws, see [2,21]. In this work, we assess the performance of the scheme in the particular cases of the three-dimensional wave equation and of Maxwell's equations. We measure the benefit of the unconditional stability by performing experiments with very large CFL numbers. In addition, the parallel possibilities of the method are investigated.