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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.

多尺度多物理场过程的数学建模和数值模拟是非常重要的，但具有很高的挑战性，因为各种过程发生在不同的尺度和耦合在一起。在处理复杂的大规模系统（例如，海洋和沿海建模中出现的系统）时，这些问题更为关键。该项目的目标是提高多尺度多物理场系统的局部时间步进算法的效率和保真度，并应用于大规模地球物理流的多分辨率模拟。所开发的算法将有效地捕获空间和时间上的广泛尺度，以在很长一段时间内对这些系统进行准确和鲁棒的模拟。研究计划与该项目的教育活动紧密结合，其中包括（i）在奥本大学暑期科学研究所开发计算数学课程模块，这是一项针对高中生的教育充实计划，旨在让年轻学生尽早接触应用数学，并激励他们从事科学、技术、工程和数学（STEM）方面的职业;及（ii）为本科生及研究生提供跨学科的应用数学教育及研究训练，包括女性及少数族裔学生。在技术上，首席研究员将根据非重叠区域分解，发展准确及有效的混合局部时间步进算法：一方面，局部时间步长的显式格式被用来模拟小时间尺度下的过程，而不受全局CFL条件对时间步长的严格限制。另一方面，本地化的指数时间积分器，使大的时间步长发生在低速的过程中，并通过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。主要研究目标有三：（i）发展和分析求解刚性非线性方程的非重叠局部指数时间差分方法;（ii）研究求解各种非均匀问题的混合局部时间步算法;以及（iii）这些算法在模拟海洋的三维原始方程中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。