CAREER: Efficient and Accurate Local Time-Stepping Algorithms for Multiscale Multiphysics Systems

职业：多尺度多物理系统的高效、准确的局部时间步进算法

基本信息

批准号：
2041884
负责人：
Thi Thao Phuong Hoang
金额：
$ 43.91万
依托单位：
Auburn University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2026-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2041884&HistoricalAwards=false
关键词：
CAREER Efficient Accurate Local Time

项目摘要

Mathematical modeling and numerical simulations of multiscale multiphysics processes are of great importance, yet highly challenging as various processes occur at different scales and are coupled together. The issues are more crucial when dealing with complex large-scale systems (for example, those arising in ocean and coastal modeling). The goal of this project is to advance the efficiency and fidelity of local time-stepping algorithms for multiscale multiphysics systems with application to multi-resolution simulations of large-scale geophysical flows. The developed algorithms will efficiently capture the wide range of scales in both space and time to produce accurate and robust simulations of these systems over a long period of time. The research plan is closely integrated with the educational activities of the project which include (i) developing curricular modules in computational mathematics at the Auburn University Summer Science Institute, an educational enrichment program for high school students, to provide young students early exposure to applied mathematics and inspire them to pursue a career in Science, Technology, Engineering and Mathematics (STEM); and (ii) providing interdisciplinary applied mathematics education and research training for both undergraduate and graduate students, including women and underrepresented minorities.Technically, the Principal Investigator will develop accurate and effective hybrid local time-stepping algorithms based on nonoverlapping domain decomposition: on the one hand, explicit schemes with local time steps are used to model processes at small time scales without suffering a severe restriction on the time step size dictated by the global CFL condition. On the other hand, localized exponential time integrators are employed to enable large time step sizes for processes occurring at slow speeds, and to accelerate the computation of matrix exponentials and their products by performing these calculations locally and in parallel. Three main research objectives will be pursued: (i) development and analysis of nonoverlapping localized exponential time differencing methods for stiff nonlinear equations; (ii) study of hybrid local time-stepping algorithms for various heterogeneous problems; and (iii) application of these algorithms to the three-dimensional primitive equations for modeling ocean/atmosphere circulations.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.

多尺度多物理过程的数学建模和数值模拟非常重要，但是随着各种过程发生在不同的尺度上并耦合在一起，高度挑战。处理复杂的大型系统（例如，在海洋和沿海建模中出现的问题）时，这些问题更为重要。该项目的目的是提高多尺度多物理系统的局部时间步变算法的效率和保真度，并将其应用于大规模地球物理流的多分辨率模拟。开发的算法将有效地捕获空间和时间中的广泛尺度，以在很长一段时间内对这些系统进行准确而健壮的模拟。该研究计划与该项目的教育活动紧密融合，包括（i）在奥本大学夏季科学学院开发计算数学的课程模块，这是一项针对高中生的教育丰富计划，为年轻学生提供早期接触应用数学并激发他们从事科学，技术，工程技术，工程和数学（词干）的职业; （ii）为本科生和研究生提供跨学科的数学教育和研究培训，包括妇女和代表性不足的少数群体。在技术上，首席研究者将开发准确有效的本地时间稳定算法的准确和有效的混合算法，该算法基于非宽恕域分解的范围，以典型的范围进行典范的范围，以典型的态度进行操作。在时间步长上由全球CFL条件决定。另一方面，采用局部指数时间集成器来启用以缓慢速度发生的过程的大长时间尺寸，并通过在本地和并行执行这些计算来加速矩阵指数及其产品的计算。将实现三个主要的研究目标：（i）对僵硬的非线性方程的非重叠局部指数时间差异方法的开发和分析；（ii）研究各种异质问题的混合局部时间步变算法；（iii）将这些算法应用于建模海洋/气氛循环的三维原始方程。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智力优点和更广泛的影响审查标准的评估来获得支持的。