Algorithm Design and Analysis for High Order Numerical Methods

高阶数值方法的算法设计与分析

• 批准号: 1112700
• 负责人: Chi-Wang Shu
• 金额: $ 35.43万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1112700&HistoricalAwards=false
• 关键词: Algorithm; Design; Analysis; Order; Numerical

In this project, research in the algorithm design and analysis of high order numerical methods, including the finite difference and finite volume weighted essentially non-oscillatory (WENO) schemes and discontinuous Galerkin finite element methods, for solving hyperbolic and other convection dominated partial differential equations, will be carried out. While the emphasis of this project is on algorithm design and analysis, close attention will be paid to efficient parallel implementation and applications. The intellectual merit of the proposed activity lies in its comprehensive coverage of algorithm development, analysis, implementation and applications. Problems in applications motivate the design of new algorithms or new features in existing algorithms; mathematics tools are used to analyze these algorithms to give guidelines for their applicability and limitations; practical considerations including parallel implementation issues are addressed to make the algorithms competitive in large scale calculations; and collaborations with engineers and other applied scientists enable the efficient application of these new algorithms or new featuresin existing algorithms.The broader impacts resulting from the proposed activity will be a suite of powerful computational tools, suitable for various applications with involving convection dominated partial differential equations, in adaptive, multiscale and uncertain environments. These tools are expected to make positive contributions to computer simulations of the complicated solution structure in these applications. The application areas include (but are not limited to) computational fluid dynamics, traffic flow problems, semiconductor device simulations, and computational biology. Graduate students will be involved in this project, and will get training in performing mathematics research on problems closely related to applications. Special attention will be paid to the recruitment and training of Ph.D. students from under-represented groups including women.

在该项目中，研究高阶数值方法的算法设计和分析，包括有限差分和有限体积加权本质上非振荡（WENO）格式和间断伽辽金有限元方法，用于求解双曲和其他对流主导的偏微分方程，将进行。 该项目的重点是算法设计和分析，同时也会密切关注高效的并行实现和应用。该活动的智力优势在于其全面覆盖算法开发、分析、实现和应用。 应用中的问题激发了新算法的设计或现有算法的新功能；使用数学工具来分析这些算法，以为其适用性和局限性提供指导；解决了包括并行实现问题在内的实际考虑因素，以使算法在大规模计算中具有竞争力；与工程师和其他应用科学家的合作使得这些新算法或现有算法中的新功能得到有效应用。拟议活动产生的更广泛影响将是一套强大的计算工具，适用于涉及对流主导偏微分方程的各种应用，在自适应、多尺度和不确定的环境中。 这些工具有望为这些应用中复杂解决方案结构的计算机模拟做出积极贡献。 应用领域包括（但不限于）计算流体动力学、交通流问题、半导体器件模拟和计算生物学。研究生将参与该项目，并接受对与应用密切相关的问题进行数学研究的培训。 重点关注博士生的招募和培养。来自包括女性在内的代表性不足群体的学生。