Some Aspects of Non-Split Vlasov Simulation Methods

This note summarizes some of the work done on Vlasov simulation methods during the two-week visit of E. Sonnendrucker to LBNL in July-August, 2002. It describes a variety of algorithms which might be employed in solving the coupled Vlasov-Poisson system on a grid in phase space. In particular, it emphasizes a class of methods which do not employ the sort of operator splitting commonly used in Vlasov methods, whereby the distribution function information is alternately updated along planes of constant x and constant v. Instead, the distribution function information on the phase space nodes is given by either (a) multi-dimensional interpolation of the gridded f at an earlier time onto a set of phase space locations which are obtained by tracking the nodes back to that earlier time (''backward semi-Lagrangian''), or (b) weighted deposition or averaging of f values from orbits onto nodes (''forward semi-Lagrangian'' or ''fully Lagrangian'').