Collaborative Research: Lab-Data-Enabled Modeling, Numerical Methods, and Validation for a Three-Dimensional Interface Inverse Problem for Plasma-Material Interactions

等离子体-材料相互作用在许多科学和工程应用中起着至关重要的作用，包括纳米颗粒合成，燃烧中的烟尘形成和空间科学。这个合作项目将推动计算等离子体科学和工程的发展，以及与等离子体-材料相互作用相关的应用。它还将为下一代研究人员在现代和未来的超级计算平台上进行亿亿次计算的时代做好准备。该项目为本科生和研究生提供了数据建模，数值方法和代码包开发，数学分析和工程应用方面的宝贵培训机会。他们将获得计算数学和数据科学的坚实基础，宝贵的研究经验，以及与数学家和工程师的广泛合作经验。从这项合作工作开始，研究人员计划将提出的模型，方法和代码包传播给更多的工程师和科学家，以解决他们的问题，在专业会议和座谈会上介绍工作，并在相关工作的会议上组织特别会议。在模拟含材料等离子体的PIC（Particle-In-Cell）方法中，电势由介电系数不连续、通量跳跃不均匀的二阶椭圆界面问题控制。浸没有限元（Immersed Finite Element，IFE）方法是一类在结构网格上求解界面问题的高精度、高效率的数值方法。然而，在涉及导体的模拟中，人们通常只知道导体表面上的总电荷量，而不是表面电荷密度，这是求解二阶椭圆界面方程所必需的。因此，本计画将从一个反界面问题的模型出发，以实验室的实验数据为基础，辨识表面电荷密度。根据实验数据的可用性，对代价泛函中数据的不同数学考虑将导致各种伴随问题。然后，有效的迭代算法的基础上IFEs将开发解决反问题。改进IFE求解器的关键技术包括新的三线性IFE基函数、部分惩罚方案、真实的界面形状和基于后验误差估计的自适应网格细化。将数值计算结果与相应的实验室实验结果进行了比较。最后，开发的模型和方法将被纳入PIC模拟充电的月球着陆器/漫游车/栖息地和灰尘太阳风等离子体条件下的月球探测。这一奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

Plasma-material interactions play a crucial role in many science and engineering applications, including nanoparticle synthesis, soot formation in combustion, and space science. This collaborative project will advance the state of the art of computational plasma science and engineering, and applications related to plasma-material interactions. It will also prepare the next generation of researchers for the era of exascale computing on modern and future supercomputing platforms. This project provides undergraduate and graduate students valuable training opportunities in data-enabled modeling, development of numerical methods and code packages, mathematical analysis, and engineering applications. They will gain a solid foundation in computational math and data science, valuable research experience, and extensive collaboration experience with mathematicians and engineers. Starting from this collaborative work, the investigators plan to disseminate the proposed model, methods, and code packages to more engineers and scientists for solving their problems, present the work in professional conferences and colloquia, and organize special sessions in conferences for related works. In the Particle-In-Cell (PIC) method for plasma simulation involving materials, the electric potential is governed by the second-order elliptic interface problem with discontinuous dielectric coefficients and non-homogeneous flux jumps. Immersed finite element (IFE) methods are a class of accurate and efficient numerical methods for solving interface problems on structured meshes, which are desirable in PIC method because of the efficient particle-mesh interactions. However, in simulations involving conductors, one usually only knows the total electric charge quantity on the conductor surface, not the surface charge density, which is necessary for solving the second-order elliptic interface equation. Therefore, this project will start from the modeling for an inverse interface problem to identify the surface charge density based on the lab experiment data. According to the lab data availability, different mathematical considerations of the data in the cost functionals will lead to various adjoint problems. Then efficient iterative algorithms based on IFEs will be developed to solve the inverse problem. The key techniques to improve the IFE solver include new trilinear IFE basis functions, a partially penalized scheme, realistic interface shapes, and adaptive mesh refinement based on a posteriori error estimates. The numerical results will be compared with the corresponding lab experiment results. Finally, the developed model and method will be incorporated into PIC simulations of the charging of lunar landers/rovers/habitats and dusts under solar wind plasma conditions for lunar exploration.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.