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

这项研究的目的是为不规则网格开发新的电磁粒子单元离散化，它既不需要线性求解器，也不受时间步长的全局稳定性约束的限制。该方法基于（1）使用外部微积分框架和代数拓扑工具来以一致的方式表示不规则网格上的离散空间导数和粒子聚集/分散操作，以及（2）将所提出的空间离散化与用于时间积分的显式异步技术相结合。 智力优点 智力优点是为结合偏微分方程和不规则网格上的粒子的多尺度现象建模提供一种变革性方法。当前的线性求解器技术对此类网格上可求解问题的大小设置了上限，并且在使用传统时间步进算法时，具有不同时间尺度的求解器在计算时间方面需要大量资源。该研究计划将能够准确解决目前无法解决的问题。更广泛的影响这项研究的结果将有利于新型微波、太赫兹和具有复杂几何形状的光学器件的分析和设计；模拟多孔介质中的输运和复杂地质构造中的电磁场，用于能源勘探或环境污染物监测；以及等离子体流的模拟等应用。该研究项目将支持俄亥俄州立大学的一名研究生和两名高级研究人员。这项研究的结果将被纳入俄勒冈州立大学的几门课程中，并且该软件将被公开传播。

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.