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

协作研究：等离子体-材料相互作用的三维界面反问题的实验室数据建模、数值方法和验证

• 批准号: 2110833
• 负责人: Xu Zhang
• 金额: $ 21.28万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110833&HistoricalAwards=false
• 关键词: Collaborative; Research; Lab; Data; Enabled

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.

血浆物质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，燃烧中的烟灰形成和太空科学。该协作项目将推动计算等离子科学和工程的艺术状况，以及与等离子体材料相互作用有关的应用。它还将为现代和未来超级计算平台上的Exascale计算时代的下一代研究人员做好准备。该项目为支持数据建模，数值方法和代码套件的开发，数学分析和工程应用程序提供了宝贵的培训机会。他们将在计算数学和数据科学，宝贵的研究经验以及与数学家和工程师的广泛合作经验方面获得坚实的基础。从这项合作工作开始，研究人员计划向更多的工程师和科学家传播提出的模型，方法和代码包，以解决他们的问题，在专业会议和官方中介绍工作，并在相关工作会议上组织特殊会议。在涉及材料的血浆模拟的粒子中（PIC）方法中，电势受不连续的介电系数和非均匀通量跳跃的二阶椭圆界面问题控制。沉浸式有限元（IFE）方法是一类精确，有效的数值方法，用于解决结构化网格上的界面问题，由于有效的粒子 - 网格相互作用，因此在PIC方法中是可取的。但是，在涉及导体的模拟中，通常只知道导体表面上的总电荷数量，而不是表面电荷密度，这对于求解二阶椭圆界面方程是必不可少的。因此，该项目将从逆接口问题的建模开始，以根据实验室实验数据识别表面电荷密度。根据实验室数据的可用性，成本功能中数据的不同数学考虑将导致各种伴随问题。然后将开发基于IFE的有效迭代算法来解决反问题。改进IFE求解器的关键技术包括基于后验错误估计值的新的三联IFE基函数，部分惩罚的方案，现实的接口形状和自适应网格细化。数值结果将与相应的实验实验结果进行比较。最后，开发的模型和方法将被纳入对月球探索的太阳风等离子体条件下的月球登陆器/流浪者/栖息地和尘埃的PIC模拟中。该奖项反映了NSF的法定任务，并被视为值得通过基金会的知识绩效和更广泛影响的评估来通过评估来获得支持的审查审查标准。

项目成果

Weak scaling of the parallel immersed-finite-element particle-in-cell (PIFE-PIC) framework with lunar plasma charging simulations

• DOI: 10.1007/s40571-022-00470-0
• 发表时间: 2022-03
• 期刊: Computational Particle Mechanics
• 影响因子: 3.3
• 作者: D. Lund;Xiaoming He;Xu Zhang;D. Han

Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods

• DOI: 10.1016/j.camwa.2023.07.014
• 发表时间: 2023-08-03
• 期刊: COMPUTERS & MATHEMATICS WITH APPLICATIONS
• 影响因子: 2.9
• 作者: Chen，Yuan;Hou，Songming;Zhang，Xu
• 通讯作者: Zhang，Xu

An immersed Crouzeix-Raviart finite element method for Navier-Stokes equations with moving interfaces

具有移动界面的纳维-斯托克斯方程的浸入式 Crouzeix-Raviart 有限元法

• 发表时间: 2022
• 期刊: International journal of numerical analysis and modeling
• 影响因子: 1.1
• 作者: Wang, Jin;Zhang, Xu;Zhuang, Qiao
• 通讯作者: Zhuang, Qiao

Solving Navier–Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes

• DOI: 10.1007/s10915-023-02414-z
• 发表时间: 2023-12
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Yuan Chen;Xu Zhang

Error analysis of Petrov-Galerkin immersed finite element methods

• DOI: 10.1016/j.cma.2022.115744
• 发表时间: 2023-02
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Cuiyu He;Shun Zhang;Xu Zhang