An implicit maxwell solver

Abstract

In this work, we present progress towards the develop of a Lagrangian method which can be implemented as a semi-implicit or a fully implicit scheme for the Vlasov Maxwell system aimed at bridging the time scale gap between electron plasma oscillations and the speed of light. At the heart of the proposed method is the development of an implicit Maxwell solver that recovers the Darwin limit of electromagnetics as c →∞. The proposed implicit Maxwell solver differs from others in that the method will first discretize the time operator and then invert the resulting semi-discreet wave operator using a free space Greens function. We refer to the approach of first discretizing in time as the Method of Lines Transpose (MOLT), but this work departs from other MOLt methods in that we work directly with high order time derivatives. A major advantage of the new method over purely using the Darwin limit is that the new method can incorporate dielectric layers, which is not possible if the strict Darwin limit is used.