Abstract
New types of current conserving particle-mesh algorithms for solving the coupled relativistic Vlasov-Maxwell set of equations are presented. They are derived using finite elements in both space and time. These new numerical schemes offer considerable advantages over the currently used finite difference PIC methods. They are charge and energy conserving, have good dispersive properties and are computationally fast. Their finite element derivations allow them to be applied to complex geometries more readily than their finite difference PIC counterparts. The local nature of their discrete equations is ideally suited to massively parallel computer architectures. In this paper, an outline of the general derivation is given. One and two dimensional cases are treated in some detail, and the extension to three dimensions is discussed. Procedures for lumping and noise reduction (using a transverse current adjustment - TCA), both of which result in substantial speedups, are outlined. The name “virtual particle” arises from an interpretation of the current assignment scheme.
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