Development of a parallel Poissonʹs equation solver with adaptive mesh refinement and its application in field emission prediction Original Research Article

A parallel electrostatic Poissonʹs equation solver coupled with parallel adaptive mesh refinement (PAMR) is developed in this paper. The three-dimensional Poissonʹs equation is discretized using the Galerkin finite element method using a tetrahedral mesh. The resulting matrix equation is then solved through the parallel conjugate gradient method using the non-overlapping subdomain-by-subdomain scheme. A PAMR module is coupled with this parallel Poissonʹs equation solver to adaptively refine the mesh where the variation of potentials is large. The parallel performance of the parallel Poissonʹs equation is studied by simulating the potential distribution of a CNT-based triode-type field emitter. Results with ∼100 000 nodes show that a parallel efficiency of 84.2% is achieved in 32 processors of a PC-cluster system. The field emission properties of a single CNT triode- and tetrode-type field emitter in a periodic cell are computed to demonstrate their potential application in field emission prediction.