A dynamical particle merging and splitting algorithm for Particle-In-Cell simulations

In Particle-In-Cell simulation, macro-particles represent clusters of numerous physical particles. Rational merging or splitting of these macro-particle clusters can significantly improve the efficiency of simulation and reduce unnecessary computational requirements and memory consumption. Here, we propose a dynamical particle merging and splitting algorithm. For macro-particle in different density regions, regional macro-particle clusters are obtained by dividing them with the Minkowski metric function. Dynamic merging and splitting of macro-particles is achieved by dynamically changing the number of macro-particle clusters to reduce the number of macro-particles without substantially distorting the physical description of the system. To test the capability of the algorithm, we also compare its performance under three types of classical plasma cases: two-stream instability (1D), QED cascades (2D), and magnetic shower (3D). The results show a good agreement with expectations.