A domain decomposition parallelization scheme for the Poisson equation in particle-in-cell simulation

A novel domain decomposition parallelization scheme for solving the Poisson equation in explicit electrostatic particle-in-cell (PIC) plasma simulation is proposed in this paper. Using the Schwarz method, the original problem is transformed into a mapping process on a series of subsets of unknowns, thereby reducing the original problem to a problem with much fewer unknowns. The solver using this scheme will have explicit parallelism brought by domain decomposition and near theoretical scalability benefiting from low communication cost. A two-dimensional Poisson solver code is developed and a series of tests are implemented to verify its correctness and performance. This scheme can provide effective performance improvement for electrostatic PIC simulations.