RII Track-4:NSF: Construction of New Additive and Semi-Implicit General Linear Methods

RII Track-4：NSF：新的加法和半隐式一般线性方法的构造

• 批准号: 2327484
• 负责人: Tommaso Buvoli
• 金额: $ 21.22万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327484&HistoricalAwards=false
• 关键词: RII; Track; NSF; Construction; New

The modeling of complex dynamical phenomena is critical to many fields of science and engineering. In particular, numerical simulations provide us with a greater understanding of natural processes and play an essential role in the design and optimization of engineering systems. In many cases, these simulations require the solution of time-dependent partial differential equations. Solving such equations is challenging due to the presence of wide-ranging spatial and temporal scales. There is therefore a continuing need for carefully designed time integration algorithms that allow modelers to simulate complex physical systems more efficiently and accurately.This EPSCoR RII Track-4 award provides a fellowship to an Assistant Professor at Tulane University and support for a graduate student. It will strengthen a collaboration between Tulane University and Los Alamos National Laboratory by enabling multiple visits to collaborate and interact with leading mathematicians and scientists. The project will develop new implicit general linear methods for solving stiff systems arising from the discretization of partial differential equations. These methods will be designed for both additively and nonlinearly partitioned problems, allowing the implicitness to be distributed in the most computationally efficient way. Moreover, the project will investigate differing types of implicitness, including fully-implicit methods that can leverage modern developments in preconditioning. Method design will draw on ideas from a recently introduced time integration framework that utilizes interpolating polynomials to greatly simplify the construction of multivalued integrators. Lastly, all the methods developed as part of this work will be validated and applied to solve a range of practical problems arising from the fields of plasmas, radiative transport, and fluid dynamics.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.

复杂动力现象的建模对于许多科学和工程领域至关重要。特别是，数值模拟为我们提供了对自然过程的更多了解，并在工程系统的设计和优化中起着至关重要的作用。在许多情况下，这些模拟需要解决时间依赖性的部分微分方程的解决方案。由于存在广泛的空间和时间尺度，求解此类方程式具有挑战性。因此，持续需要精心设计的时间集成算法，使建模者能够更有效，更准确地模拟复杂的物理系统。此EPSCOR RII TRECK-4奖为Tulane University的助理教授提供了奖学金，并为研究生提供了支持。它将通过使多次访问与主要的数学家和科学家进行合作和互动，从而加强杜兰大学和洛斯阿拉莫斯国家实验室之间的合作。该项目将开发新的隐式通用线性方法，以解决由部分微分方程离散化引起的刚性系统。这些方法将针对添加性和非线性分区的问题设计，从而使隐性性以最有效的方式分布。此外，该项目将研究不同类型的内在性，包括可以利用现代发展的完全无限方法。方法设计将借鉴最近引入的时间集成框架的想法，该框架利用插值多项式来大大简化多价集成器的构建。最后，将对这项工作的一部分开发的所有方法都将得到验证并应用于解决由等离程度，辐射运输和流体动力学领域引起的一系列实际问题。该奖项反映了NSF的法定任务，并认为通过基金会的知识分子和更广泛的影响，通过评估来审查Criteria。