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了解对此至关重要。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、磁约束聚变设备的动力学以及可用于医学成像应用的激光-等离子体设备的动力学。这项研究的目的是开发高精度和高效的计算工具来模拟构成感兴趣的等离子体的电子(带负电的粒子)和离子(带正电的粒子)的动力学。这项研究旨在开发基于新的多尺度方法的新的计算技术，该方法将基本方程分为宏观(大尺度现象)和微观(小尺度现象)，并以某种适当的方式耦合这些尺度。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。所得到的方法和程序将被用来模拟各种应用问题，以验证和验证该方法。本研究的主要目标是开发准确和高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组。目标是使用一种新的微观-宏观分解方法来求解一类多尺度等离子体模型。微观-宏观分解背后的思想是从一个足够普遍的模型开始，该模型包含宏观和微观现象的耦合动力学，然后将该模型写成具有适当耦合项的两个部分，最后对每个部分应用可能不同的数值技术，以优化效率。本研究中将使用的具体格式是基于高阶间断Galerkin有限元方法，并采用新颖的时间推进策略来提高计算效率。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，将设计和实施新的微观-宏观分解技术，以便对多物种等离子体系统进行有效的数值求解。将开发新的策略，以自适应地打开和关闭微观解算器。作为研究项目的一部分，将产生新的计算方法和软件，在未来可以应用于广泛的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.