Special Research Colloquium — Monday, October 13, 2008

"High-Order Unstructured Particle-in-Cell Simulation"

Andreas Kloeckner
Division of Applied Mathematics
Brown University



We present first experiences with the implementation of a high-order unstructured Particle-in-Cell (PIC) solver for the Vlasov-Maxwell problem. In this method, a Discontinuous Galerkin (DG) field solver is coupled to a particle approximation of the density function describing the motion of charge carriers in a domain. While the DG Maxwell solver should be considered a mature, stable part of this system, it is considerably less clear how the coupling of the particles to the field is to be achieved. The coupling consists of two directions: the reconstruction of a current density to drive the Maxwell solver, and the calculation of the Lorentz force to drive the particles. The focus of this talk is to motivate and present various algorithms for both of these stages. We describe implementation issues and discuss initial numerical evidence of the advantages and disadvantages of each approach. Special emphasis is given to the validation of numerical results, and we are striving to establish a standard set of examples by which the performance of a PIC method can be judged. We present a small initial set of such examples, as well as a few criteria to be used for evaluation. In concluding, we describe the real-world application that we are targeting and show practical uses of our methods.



Room: 126 Clements Hall
Coffee: 3:15 pm – 3:30 pm
Colloquium: 3:30 pm – 4:30 pm