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.

在许多实践意义的物理系统中，现象发生在多个尺度上的异质介质中，并且在每个量表上具有不同的值。示例包括过滤器，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巨大的计算工作。该项目的目的是开发一个统一的框架，以准确有效地模拟复杂的多尺度，依赖时间的物理现象，该现象涉及多孔介质中出现的流动，运输和机械变形。该项目将通过培训在多学科研究中工作的新一代计算数学家来支持教育。该项目涉及对新型时间分裂方法的开发和分析，这些方法旨在克服模拟多阶段，时间依赖的物理现象时出现的挑战。这些方法基于非平稳多尺度模型的溶液分解，将考虑高度耦合的空间和时间异质性。目的是提供一个一般框架，将时间分裂算法和空间多尺度分解与新算法的严格理论分析相结合。该项目的具体目标是：（i）研究非平稳多尺度模型模拟的时间分裂算法； （ii）了解多尺度模型中的空间和时间互动； （iii）分析时间分裂方法，以指导空间分解的选择； （iv）为非线性模型设计新颖的分裂方法； （v）测试和展示提出的方法，用于改善工程和地球科学中多尺度，时间依赖的物理现象的预测。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评估标准通过评估来获得支持的。

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