Micro-Macro Decomposition Numerical Schemes for Multiscale Simulation of Plasma

等离子体物理学是研究电离气体动力学的学科。由于等离子体通常被称为物质的第四态，是宇宙中最丰富的普通物质形式，因此存在许多重要的应用问题，对等离子体动力学的理解至关重要。这些应用的一些例子包括了解恒星的动力学、太阳风对地球磁层的影响、磁约束聚变装置的动力学以及可用于医学成像应用的激光等离子体装置的动力学。本研究的目的是开发高度精确和高效的计算工具，用于模拟构成感兴趣的等离子体的电子（带负电粒子）和离子（带正电粒子）的动力学。本研究旨在基于新的多尺度方法开发新的计算技术，将基础方程划分为宏观（大尺度现象）和微观（小尺度现象），并以适当的方式将这些尺度耦合起来。这些方法将在利用现代并行计算机体系结构的计算机代码中实现。生成的方法和代码将用于模拟各种应用程序问题，以验证和验证该方法。本研究的主要目的是发展精确和有效的计算方法来求解用于模拟等离子体动力学的非线性微分方程。目的是用一种新的宏微观分解方法求解一类等离子体的多尺度模型。微观-宏观分解背后的思想是从一个足够通用的模型开始，该模型包含宏观和微观现象的耦合动力学，然后将该模型用适当的耦合项写成两个部分，最后对每个部分应用可能不同的数值技术，以优化效率。本研究中使用的具体方案是基于高阶不连续伽辽金有限元方法，采用新颖的时间步进策略来实现计算效率。这项研究将开发新的计算工具来模拟等离子体动力学。特别是，新的微观和宏观分解技术将被设计和实施，允许多种等离子体系统的有效数值解决。将开发新的策略来自适应地打开和关闭微观求解器。作为研究项目的一部分，新的计算方法和软件将在未来被广泛应用于实验室和天体物理等离子体问题。开发的软件将作为DoGPack软件项目的一部分在网络上免费提供。

Plasma physics is the study of the dynamics of ionized gases. Because plasma, often referred to as the fourth state of matter, is the most abundant form of ordinary matter in the universe, there exist many important application problems for which an understanding of the plasma dynamics is critical. Some examples of these applications include understanding the dynamics of stars, the affect of the solar wind on the Earth's magnetosphere, the dynamics of magnetically confined fusion devices, and the dynamics of laser-plasma devices that could be used in medical imaging applications. The objective of this research is to develop highly accurate and efficient computational tools for simulating the dynamics of the electrons (negatively charged particles) and the ions (positively charged particles) that constitute the plasma of interest. This research aims to develop novel computational techniques based on novel multiscale methods that divide the underlying equations into macroscopic (large scale phenomena) and microscopic (small scale phenomena), and couple these scales in some appropriate manner. These methods will be implemented in computer code that will take advantage of modern parallel computer architectures. The resulting methods and codes will be used to simulate various application problems in order to verify and validate the approach.The primary objective of this research is to develop accurate and efficient computational methods for solving nonlinear differential equations used to model plasma dynamics. The goal is to solve a class of multiscale models of plasma using a novel micro-macro decomposition approach. The idea behind the micro-macro decomposition is to start with a general enough model that contains the coupled dynamics of macroscopic and microscopic phenomena, to then write this model into two parts with appropriate coupling terms, and finally to apply potentially different numerical techniques to each part in order to optimize efficiency. The specific schemes that will be used in this research are based on high-order discontinuous Galerkin finite element methods with novel time-stepping strategies to achieve computational efficiency. This research will develop new computational tools for simulating plasma dynamics. In particular, new micro-macro decomposition techniques will be designed and implemented that allow for the efficient numerical solution of multi-species plasma systems. New strategies will be developed to adaptively turn on and off the microscopic solvers. As part of the research project, novel computational methods and software will be produced that in the future could be applied to a wide range of both laboratory and astrophysical plasma problems. The software developed will be made freely available on the web as part of the DoGPack software project.