Numerical Methods in Large-Scale Computation

大规模计算中的数值方法

• 批准号: 9706866
• 负责人: Steve McCormick
• 金额: $ 48.24万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-15 至 2001-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9706866&HistoricalAwards=false
• 关键词: Numerical; Methods; Large; Scale; Computation

9706866 McCormick The main thrust of the proposed research is the development of efficient numerical techniques for simulation of a wide variety of physical processes. Important applications include aerodynamics, meteorology, elasticity, electromagnetics, porous media, and particle transport. The general goal is to develop accurate discretization methods and fast algebraic solvers for the partial differential equations that govern these and other applications. The research topics include: multilevel first-order system least squares, which involves reformulation of partial differential equations as well-posed minimization principles to allow for robust and efficient solution methods; porous media problems, which will be treated by Eulerian-Lagrangian localized adjoint methods that have been successful for such multiparty and reactive flows; transport phenomena, which will be simulated using efficient and robust least-squares methods for the three-dimensional Boltzmann transport equations; and iterative methods, which is aimed at developing effective algebraic solvers for the equations that arise in many applications. The focus of this project is research in the field of computational mathematics. The purpose is to improve our understanding of the mathematics behind computer simulation of complex physical phenomena. Such simulations are key to the study and control of many important processes, including groundwater flow, global change, energy production, and material science. One of the challenges in such simulations is the development of improved mathematical methods for solving the equations that arise in these models. The basic aim of this research is dramatic improvement in our ability to model increasingly more complicated and sophisticated processes with much greater accuracy and efficiency. This will pave the way for simulations that can provide scientists, engineers, and policy-makers with much more powerful tools to understand and improve our industry, science, and environm ent.

小行星9706866 拟议的研究的主要推力是开发有效的数值技术，用于模拟各种各样的物理过程。重要的应用包括空气动力学、气象学、弹性、电磁学、多孔介质和粒子输运。 总的目标是开发精确的离散化方法和快速代数求解偏微分方程，这些和其他应用。 研究课题包括：多级一阶系统最小二乘法，其中涉及重新制定的偏微分方程作为适定的最小化原则，以允许强大的和有效的解决方法;多孔介质问题，这将是由欧拉拉格朗日本地化的伴随方法，已成功地为这样的多方和反应流处理;输运现象，将使用三维玻尔兹曼输运方程的高效和稳健的最小二乘法进行模拟;和迭代方法，其目的是为许多应用中出现的方程开发有效的代数求解器。 该项目的重点是计算数学领域的研究。 其目的是提高我们对计算机模拟复杂物理现象背后的数学的理解。 这种模拟是研究和控制许多重要过程的关键，包括地下水流、全球变化、能源生产和材料科学。 这种模拟的挑战之一是开发改进的数学方法来求解这些模型中出现的方程。 这项研究的基本目的是显着提高我们的能力，以更高的准确性和效率来模拟越来越复杂和复杂的过程。 这将为模拟铺平道路，为科学家、工程师和政策制定者提供更强大的工具，以了解和改善我们的行业、科学和技术。