Numerical methods for linear and nonlinear implicit PDE simulation ---- Domain Decomposition and Nonlinear Multigrid Methods

线性和非线性隐式PDE模拟的数值方法----域分解和非线性多重网格方法

• 批准号: 1115759
• 负责人: Xuemin Tu
• 金额: $ 7.94万
• 依托单位: University of Kansas Center for Research Inc
• 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: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115759&HistoricalAwards=false
• 关键词: Numerical; methods; linear; nonlinear; implicit

This project combines mathematical analysis and numerical algorithm design for the solution of linear and nonlinear partial differential equations (PDEs). Algorithms will be incorporated in the scientific software library PETSc which is widely used in the scientific community for physical modeling. These algorithms are bscalable, and easily parallelizable, and thus useful for large scale multidisciplinary simulations. Additionally the PI's research provides a solid theoretical support for the algorithms. The PI's research promises to have a major impact in several areas: computational fluid dynamics, material sciences, and acoustic scattering. The PI and her collaborators plan to publish archival articles on the new algorithms and also present results in conferences. Graduate students at the University of Kansas are impacted through the PI's plans to incorporate research results into her graduate level class on numerical methods. This course is available to a broad group of students from mathematical and engineering departments.

该项目结合了数学分析和数值算法设计，用于解决线性和非线性偏微分方程（PDE）。算法将被纳入科学软件库PETSc，这是广泛使用的科学界的物理建模。这些算法是可扩展的，并且容易并行化，因此对于大规模的多学科模拟是有用的。另外PI的研究为算法的实现提供了坚实的理论支持。PI的研究有望在几个领域产生重大影响：计算流体动力学，材料科学和声散射。PI和她的合作者计划发表关于新算法的档案文章，并在会议上展示结果。研究生在堪萨斯大学的影响，通过PI的计划，将研究成果纳入她的研究生水平类的数值方法。本课程适用于数学和工程系的广泛学生群体。