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.

复杂动力学现象的建模对于科学和工程的许多领域都至关重要。特别是，数值模拟使我们能够更好地理解自然过程，并在工程系统的设计和优化中发挥重要作用。在许多情况下，这些模拟需要求解瞬态偏微分方程。由于存在广泛的空间和时间尺度，求解此类方程具有挑战性。因此，持续需要精心设计的时间积分算法，使建模者能够更有效、更准确地模拟复杂的物理系统。EPSCoR RII Track-4 奖项为杜兰大学助理教授提供奖学金，并为研究生提供支持。它将通过多次访问与领先的数学家和科学家合作和互动，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一般线性方法来求解由偏微分方程离散化产生的刚性系统。这些方法将针对加性和非线性划分问题而设计，允许以计算最有效的方式分布隐式。此外，该项目将研究不同类型的隐式，包括可以利用现代预处理发展的完全隐式方法。方法设计将借鉴最近推出的时间积分框架的思想，该框架利用插值多项式来大大简化多值积分器的构造。最后，作为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等离子体、辐射传输和流体动力学领域产生的一系列实际问题。该奖项反映了 NSF 的法定使命，并被认为值得支持通过使用基金会的智力优点和更广泛的影响审查标准进行评估。