Collaborative Research: An Asynchronous Exterior Calculus Framework for Charge-Conservative Electromagnetic Particle-in-Cell Simulations of Space-Charge Effects on Irregular Grids

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The objective of this research is to develop new electromagnetic particle-in-cell discretizations for irregular grids that will neither require linear solvers nor be bounded by global stability constraints on the time step. The approach is based on (1) the use of an exterior calculus framework and tools from algebraic topology to represent discrete spatial derivatives and particle gather/scatter operations on irregular meshes in a consistent fashion and (2) the coupling of the proposed spatial discretization with an explicit asynchronous technique for time integration. Intellectual Merit The intellectual merit is to provide a transformative approach for the modeling of multiscale phenomena combining partial differential equations and particles on irregular meshes. Current linear solver technology sets an upper limit on the size of problems solvable on such meshes, and solvers with disparate time scales require enormous resources in terms of computing time when using traditional time-stepping algorithms. This research program will enable accurate solution of problems presently beyond reach. Broader ImpactThe results of this research will benefit the analysis and design of new microwave, terahertz, and optical devices with complex geometries; the simulation of transport in porous media and electromagnetic fields in complex geological formations for energy prospection or monitoring of environmental contaminants; and the simulation of plasma flows, to name a few applications. This research project will support one graduate student at the Ohio State University and two senior researchers. Results of this research will be integrated into several courses at OSU and the software will be publicly disseminated.