Development of a 3D finite element particle-in-cell code with adaptive meshing

Summary form only given. Calabazas Creek Research, Inc., in association with U.C. Berkeley, is developing a fully relativistic, 3D, one-specie, particle-in-cell simulation code with adaptive finite element meshing. This initial version will simulate particles in quasistatic fields, which are solved by the standard finite element method. In quasistatic PIC analysis, all particles are synchronized in time, and the fields are resolved at every time step. In later versions, the vector finite element with adaptive meshing technology will be used to solve the complete Maxwell´s equations for the electro-magnetic fields as they evolve in time in a fully explicit approximation. Currently, most PIC codes use finite difference techniques with fixed, orthogonal, structured elements. Finite element meshes, compared to finite difference meshes, allows more accurate modeling of non-orthogonal boundaries, eliminating the short wavelength noise introduced by orthogonal mesh stair step representations. Adaptive meshing, compared to fixed mesh models, may reduce the number of elements by 2-3 orders of magnitude while maintaining or improving accuracy, particularly when small features translate spatially. Similar improvements in PIC modeling could result in dramatic reduction in computation size and execution times, while allowing improved design and analysis. In this paper, we will discuss feasibility issues such as accuracy, stability and charge allocation related to tracking particles in a 3D, quasistatic, electric field and adaptive finite element mesh. We will demonstrate that finite element adaptive meshing can be implemented for PIC analysis, and will provide an indication of computational resources needed and the accuracy that can be achieved for this model.