Developing Energy-Conserving Deterministic Solvers for Kinetic Electromagnetic Plasma Simulations

在这个提议中，研究人员计划开发和分析一类能量守恒的确定性求解器的动力学电磁等离子体模拟。所提出的方法有几个特点，克服了许多传统的求解器的困难：它保存的总粒子数和系统的能量;它有一个系统的方式，将显式或隐式的时间步长取决于刚度的方程;它是专为实现非结构化网格在物理空间中的复杂几何形状。为了实现这一目标，研究课题包括一系列分析和计算主题。研究者提出为耦合Vlasov-Maxwell系统设计一种新的能量守恒分裂，使得分裂后的方程仍然保持能量守恒，并且可以在降维的情况下进行计算.研究者计划建立一个通用的框架，将各种类型的节能时间和空间离散化。将探讨通过使用各种局部基、局部时间步进和混合求解器来进一步提高计算效率的方法。将讨论如何执行电荷连续性和正性的问题。分析方面，如数值色散关系，稳定性和误差估计将被考虑。拟议的活动之间的算法开发，分析和应用。所得到的数值方案可以应用于广泛的等离子体模拟。 理论研究将为此类数值方法的设计提供依据和指导。拟议活动的更广泛影响将是其跨学科外联和教育部分。拟议的研究是多学科的性质。研究人员积极与物理，电气工程部门的教职员工互动和咨询。将为学生和博士后提供培训机会。计算数学课程开发将被纳入。

In this proposal, the investigator plans to develop and analyze a class of energy-conserving deterministic solvers for kinetic electromagnetic plasma simulations. The proposed methods have several features that overcome the difficulties of many traditional solvers: it conserves the total particle number and energy of the system; it has a systematic way to incorporate explicit or implicit time stepping depending on the stiffness of the equations; and it is designed for implementations on unstructured grids for complex geometries in the physical space. To achieve the objective, the research topics include a range of analytical and computational subjects. The investigator proposes to design a new energy-conserving splitting for the coupled Vlasov-Maxwell system, so that the splitted equations still maintain energy conservation and can be computed in reduced dimensions. The investigator plans to set up a general framework to incorporate various type of energy-conserving temporal and spatial discretizations. Methods to further improve computational efficiency by using various local basis, local time stepping and hybrid solvers will be explored. Issues on how to enforce charge continuity and positivity will be addressed. Analytical aspects such as the numerical dispersion relation, stability and error estimates will be considered.The proposed activity lies between algorithm development, analysis and applications. The resulting numerical schemes can be applied to a wide range of plasma simulations. The theoretical studies will provide foundation and guidance to the design of such numerical methods. The broader impacts of the proposed activity will be its interdisciplinary outreach and educational components. The proposed research is multidisciplinary in its nature. The investigator actively interacts and consults with faculty members in physics, electrical engineering departments. Training opportunities for students and postdocs will be provided. Computational math curriculum development will be incorporated.