Parallel Implementation of a 3-D Electrostatic PIC Method using Unstructured Mesh

Summary form only given. In this report, a parallel three-dimensional electrostatic particle-in-cell (PPIC) method using unstructured tetrahedral mesh is proposed and tested. Poisson\´s equation for electrostatic distribution is formulated using the Galerkin nodal finite element method (FEM), while motion of charged particles are traced using cell-by-cell particle tracking scheme, under the influence of self-consistent electric field. Linear shape function for electrostatic potential is utilized in the FE formulation. Only nonzero entries of the coefficient matrix of the Poisson\´s equation are stored using either compressed sparse row (CSR) scheme for smaller problem or "randomly packed" scheme for larger problem. Resulting sparse matrix equation is then solved by preconditioned conjugate gradient method. Charged-particle motion is traced cell-by-cell using leap-frog integration method and Boris scheme, by taking advantage of the cell-neighboring information that is derived from the element connectivity. Parallel implementation of the current unstructured PIC method is realized on memory-distributed machine utilizing domain decomposition via multi-level graph-partitioning technique. A parallel adaptive mesh refinement (PAMR) module for 3D unstructured tetrahedral mesh can also be coupled to this PPIC for better resolution near locations having large field change. Completed code is then tested on a 24-node PC-cluster system by simulating the field-emission properties of a single carbon nanotube under the application of the external electrical field