Abstract
Using continuously-differentiable (C1) 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, C1 interpolation of the potential leads to a continuous (C0) electric field, with associated improved fidelity of particle motion.
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