Multiple time and length scales pose significant computational challenges for many complex physical systems. The proposed research will forge together two innovative approaches to the spatial and temporal refinement of Poisson-based particle-in-cell (PIC) systems: 1) structured adaptive mesh refinement (AMR), and 2) explicit discrete-event simulation (DES). This work will result in a fully asynchronous AMR-Poisson PIC code with multi-resolution capabilities far exceeding those of any codes in existence today. Although the proposed technique is quite general, the focus of this proposal is to develop a multi-scale electrostatic PIC code and apply it to two problems of current interest to laboratory plasma physics: ion beam and virtual cathode dynamics. In this work we abandon time-stepping methodology in favor of a novel event-driven simulation method, which has never been applied to potential-based systems. In DES, a global time step is replaced by a physically meaningful information unit. In effect, this technique introduces an individual self-adaptive temporal mesh for every computational entity. This enables fully asynchronous time integration of the system state and eliminates unnecessary computation in inactive regions. This enables large CPU speed-ups for systems with a high degree of numerical stiffness. DES also adaptively adjusts local time increments in accordance with local physical frequencies. This increases computational accuracy in stiff parts of the computation domain. In addition, DES codes run successfully in regimes where standard codes are explosively unstable.
The specific objectives of this proposal are: (1) Enable independent resolution of multiple time and length scales by combining spatial refinement (stretched and AMR mesh) with asynchronous computation (DES). Develop a multi-resolution electrostatic PIC code uniquely capable of addressing multi-scale problems and possessing superior stability and accuracy properties. (2) Apply the multi-resolution code to study two multi-scale problems of great interest to the plasma physics community: a) ion beam injection, b) virtual cathode formation.
Poisson-based PIC simulations are used in many diverse areas of science (e.g., plasma physics, astrophysics, fluid dynamics, semiconductor physics, biology, to name a few). This new multi-resolution approach will have a broad impact on all these fields. The project includes a plan to develop an object oriented API for developing parallel, multi-dimensional AMR-DES-PIC applications. This will provide 1) object-oriented algorithms and data structures that could be readily reused by all computational physicists, 2) a flexible framework for collaborative activities whereby various physical and chemical processes can be added to the code in a plug-and-play fashion. This work will also provide new summer internship opportunities for undergraduate students as part of the ongoing collaboration with UCSD and Georgia Institute of Technology.
