Developing Energy-Conserving Deterministic Solvers for Kinetic Electromagnetic Plasma Simulations

在这项提案中，研究人员计划开发和分析一类用于动力学电磁等离子体模拟的节能确定性求解器。所提出的方法有几个特点克服了许多传统求解器的困难：它守恒了系统的总粒子数和总能量；它有一种系统的方法来结合显式或隐式的时间步长，取决于方程的刚度；它是为在物理空间中复杂几何的非结构网格上实现而设计的。为了实现这一目标，研究课题包括一系列的分析和计算主题。研究人员建议为耦合的Vlasov-Maxwell系统设计一种新的能量守恒分裂，使得分裂的方程仍然保持能量守恒，并且可以降维计算。研究人员计划建立一个通用框架，将各种类型的节能时间和空间离散纳入其中。将探索利用各种局部基、局部时间步长和混合求解器来进一步提高计算效率的方法。关于如何加强电荷连续性和正性的问题将得到解决。将考虑数值色散关系、稳定性和误差估计等分析方面的问题。拟议的活动介于算法开发、分析和应用之间。所得到的数值格式可广泛应用于等离子体模拟。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。拟议的研究本质上是多学科的。调查员积极与物理、电气工程系的教职员工进行互动和咨询。将为学生和博士后提供培训机会。计算数学课程开发将纳入其中。

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.