Mitigation of the self-force effect in unstructured PIC codes using generalized moving least squares. (15th July 2019) - Trask, Nathaniel; Bochev, Pavel; Perego, Mauro
Abstract: Electrostatic particle-in-cell (PIC) methods use point clouds to represent a collection of charged particles and a mesh to compute the electric field generated by these particles. Such methods involve a data transfer of charge from the point cloud to the mesh and another transfer of the electric field from the mesh to the point cloud. The approximation errors introduced during these data transfers manifest as an artificial self-force acting on particles, causing a loss of momentum conservation. There exist PIC schemes on uniform Cartesian grids that provably avoid this effect. However, these schemes rely on a translation invariance property of a discrete Green's function and cannot be extended to arbitrary unstructured grids. We present a new meshless data transfer approach that uses generalized moving least squares (GMLS) to reconstruct the electric field at particles from local mesh data on non-uniform meshes. The approach enriches the GMLS approximation space with singular functions to recover the singularity introduced at particles. This reduces the strength of the self-force by several orders of magnitude. We present results reconstructing both from linear finite elements and from Raviart–Thomas elements, demonstrating that the approach is generally applicable to PIC codes having degrees of freedom of arbitrary type.