Symmetric Spline Weighting for Charge and Current Density in Particle Simulation

A general method for computing charge and current density source terms for Maxwellʹs equations from particles weighted to a mesh is described. The method presented here eliminates the need for correction factors often applied in curvilinear coordinates to compensate for errors at the edge of the system, and applied in the interior as well for nonuniform meshes. Generality is achieved by weighting volume elements using a spline symmetric to that by which particle charge and current are weighted to the mesh. The method presented has a number of desirable properties, including conservation of charge, preservation of a uniform distribution, and generality on nonuniform meshes with arbitrary particle–mesh interpolation schemes. The method recovers the exact answer in the limit of mesh sizes approaching zero.