LEAPS-MPS: Hybridizable discontinuous Galerkin methods for non-linear integro-differential boundary value problems in magnetic plasma confinement

LEAPS-MPS：磁等离子体约束中非线性积分微分边值问题的混合不连续伽辽金方法

• 批准号: 2137305
• 负责人: Tonatiuh Sanchez-Vizuet
• 金额: $ 25万
• 依托单位: University of Arizona
• 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: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2137305&HistoricalAwards=false
• 关键词: LEAPS; MPS; Hybridizable; discontinuous; Galerkin; LEAPS; MPS; Hybridizable; discontinuous; Galerkin

The goal of this project is to develop computational methods for the solution of a family of non-linear and integro-differential equations that arise from the study of magnetic equilibrium in axisymmetric fusion reactors. The tools and techniques developed as part of the project will contribute to the theoretical understanding of the behavior of magnetic confinement fusion. In addition, it will provide a tool to the plasma physics community for the efficient simulation of some of the processes taking place in a reactor. Thus, the project has the potential to contribute to the development of clean energy sources. As part of the broader goal of increasing the participation of ethnic minorities in Science, Technology, Engineering and Mathematics, the project will organize a colloquium addressed to undergraduate and beginning graduate students at the University of Arizona. The colloquium will feature mathematicians from underrepresented communities who are successful practitioners of mathematics in a variety of settings (academia, national laboratories, industrial research and development, and government agencies). Speakers will present a broad and accessible view of their research and will interact with the students, share advice and personal experiences related to the mathematical profession and their own educational career. This will serve the dual purpose of (1) challenging the perceived "traditional image" of a professional mathematician by showcasing the contributions of individuals with diverse cultural and ethnical backgrounds, and (2) providing students with several non-standard role models and a more diverse image of the mathematical profession. The scientific component of the project has two main goals: (1) devise and analyze hybridizable discontinuous Galerkin (HDG) discretizations for a broad class of non-linear elliptic integro-differential equations, and (2) apply the results obtained from the previous point into a freely available software implementation that can be used directly by the computational plasma physics community. The mathematical interest in the problems considered extends well beyond the field of plasma physics and will motivate the expansion of the theory of the HDG method into areas where it had not been applied before. From the point of view of applications, the project will develop a set of freely available computational tools and software that will directly influence the magnetic fusion community and can be beneficial to other areas of applied science and engineering.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.

该项目的目的是开发用于求解非线性和全差异方程的溶液的计算方法，该方程是由轴对称融合反应器中磁平衡研究产生的。作为项目的一部分开发的工具和技术将有助于对磁性限制的行为的理论理解。此外，它将为等离子物理界提供一个工具，以有效地模拟反应堆中发生的某些过程。因此，该项目有可能为清洁能源的发展做出贡献。作为增加少数民族参与科学，技术，工程和数学的更广泛目标的一部分，该项目将组织一个针对亚利桑那大学的本科生和初学者的讲话。该座谈会将由来自代表性不足的社区的数学家展示，他们在各种环境（学术界，国家实验室，工业研究与发展以及政府机构）中是数学成功的从业者。演讲者将展示其研究的广泛且可访问的观点，并将与学生互动，分享与数学专业和他们自己的教育事业有关的建议和个人经验。这将达到（1）通过展示具有多种文化和种族背景的个人的贡献，以及（2）为学生提供多种非标准榜样以及数学职业的更多样化的形象，来挑战专业数学家感知的“传统形象”的双重目的。该项目的科学组成部分具有两个主要目标：（1）设计和分析可杂交的不连续的Galerkin（HDG）离散化，用于一类广泛的非线性椭圆形信息方程式，（2）将从上一点点可用的软件实施中获得的结果应用于计算据计算的据计算据称的据计算的帕斯玛（Comporational Tocuction palistalitiation Communition），将其应用于上一点点可用的软件实施。对所考虑问题的数学兴趣远远超出了血浆物理学领域，并将激发HDG方法理论的扩展到以前未应用的领域。从应用程序的角度来看，该项目将开发一组免费的计算工具和软件，这些工具和软件将直接影响磁性融合社区，并可能对应用科学和工程的其他领域有益。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查审查的评估来通过评估来获得支持的。