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Center for Nonlinear Studies |
In the relativistic limit, the Vlasov-Maxwell system introduces numerical difficulties as explained in . We develop an efficient solver for the relativistic Vlasov-Maxwell (RVM) system in order to model laser-plasma interactions; and in particular, the acceleration of electrons or ions to relativistic energies. In doing so we expand on the so called Locally Implicit Discontinuous Galerkin method (LIDG) developed in by defining Regionally Implicit Discontinuous Galerkin Methods. These methods are parametrized by the region parameter r. For a given cell, the region parameter determines how many neighboring cells (this collection of cells known as the region) will provide information to the prediction step of the method. We use a Rusanov Riemann solver on the interior of said region and the interior cell values on the boundary of the region. We show that these methods allow a much larger CFL number when compared to the LIDG method, and thus offer a vastly improved efficiency over the LIDG method. Here we introduce the methods applied to the 1D, 2D, and 3D advection equations.
Host: Luis Chacon