Temporal Splitting Methods for Multiscale Problems

多尺度问题的时间分裂方法

• 批准号: 2208498
• 负责人: Yalchin Efendiev
• 金额: $ 30万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-01 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208498&HistoricalAwards=false
• 关键词: Temporal; Splitting; Methods; Multiscale; Problems

In many physical systems of practical interest, phenomena occur in heterogeneous media with properties varying at multiple scales and having disparate values on each scale. Examples include multi-physics processes in filters, membranes, and Earth's subsurface. Standard numerical approaches for simulating these phenomena to obtain accurate predictions require tremendous computational effort. The goal of this project is to develop a unified framework for accurately and efficiently simulating complex multiscale, time dependent physical phenomena that involve flow, transport, and mechanical deformations that arise in porous media. The project will support education by training a new generation of computational mathematicians who work in multidisciplinary research.This project involves the development and analyses of novel temporal splitting methods that are designed to overcome challenges that arise when simulating multiscale, time-dependent physical phenomena. The methods are based on solution decomposition for non-stationary multiscale models and will consider space and time heterogeneities that are highly coupled. The goal is to provide a general framework that combines temporal splitting algorithms and spatial multiscale decompositions with a rigorous theoretical analysis of the new algorithms. The specific objectives of the project are: (i) to study temporal splitting algorithms for simulations of non-stationary multiscale models; (ii) to understand space and time interaction in multiscale models; (iii) to analyze temporal splitting approaches to guide the choice for space decomposition; (iv) to design novel splitting approaches for nonlinear models; and (v) to test and demonstrate proposed approaches for improving predictions of multiscale, time-dependent physical phenomena in engineering and geosciences.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.

在许多实际感兴趣的物理系统中，现象发生在非均匀介质中，其性质在多个尺度上变化，并且在每个尺度上具有不同的值。例子包括过滤器、膜和地球地下的多物理过程。模拟这些现象以获得准确预测的标准数值方法需要大量的计算工作。该项目的目标是开发一个统一的框架，用于准确有效地模拟复杂的多尺度，时间依赖的物理现象，涉及流动，运输和机械变形，出现在多孔介质中。该项目将通过培训从事多学科研究的新一代计算数学家来支持教育，该项目涉及开发和分析新颖的时间分裂方法，旨在克服模拟多尺度、随时间变化的物理现象时出现的挑战。该方法是基于非平稳多尺度模型的解分解，并将考虑高度耦合的空间和时间异质性。我们的目标是提供一个通用的框架，结合时间分裂算法和空间多尺度分解与严格的理论分析的新算法。该项目的具体目标是：（i）研究用于非平稳多尺度模型模拟的时间分裂算法;（ii）理解多尺度模型中空间和时间的相互作用;（iii）分析时间分裂方法以指导空间分解的选择;（iv）设计用于非线性模型的新分裂方法;（iv）设计用于非线性模型的新分裂方法;（iv）设计用于非线性模型的新分裂方法。以及（v）测试和演示用于改进多尺度预测的建议方法，时间--该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值进行评估来支持和更广泛的影响审查标准。

项目成果

Multicontinuum homogenization and its relation to nonlocal multicontinuum theories

多重连续介质均匀化及其与非局部多重连续介质理论的关系

• 发表时间: 2023
• 期刊: Journal of computational physics
• 影响因子: 4.1
• 作者: Efendiev;W.T. Leung
• 通讯作者: W.T. Leung