Improved C1 shape functions for simplex meshes

Using continuously-differentiable (C-1) interpolation methods previously developed for computer visualization and other applications, a new class of shape functions is constructed and applied to electrostatic (ES) Particle-In-Cell (PIC) simulations on simplex (triangle or tetrahedral) meshes. The resulting shape functions are non-negative and partition unity, and lead to a reduction of shot noise and aliasing associated with particle interpolation to and from the mesh. For an energy-conserving implementation as chosen, C-1 interpolation of the potential leads to a continuous (C-0) electric field, with associated improved fidelity of particle motion. (C) 2020 Published by Elsevier Inc.

Automated summary

A new class of shape functions constructed using continuously-differentiable interpolation methods improves the accuracy and stability of particle motion in electrostatic Particle-In-Cell simulations on simplex meshes.