Modern numerical methods for problems in physics

物理问题的现代数值方法

• 批准号: 203326-2007
• 负责人: Kropinski, MaryCatherine
• 金额: $ 1.38万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=392800
• 关键词: Modern; numerical; methods; problems; physics

The primary theme in this research program is to bring together state-of-the-art methods in scientific computing, physical modeling, and classical methods in applied mathematical analysis for studying problems that arise in fluid dynamics and material science. Mathematically, the equations to be solved are high-order, nonlinear partial differential equations, and the domains are often extremely complex. The underlying computational framework is to employ, whenever indicated, ``designer'' algorithms, i.e. those that target specific problems. These modern and powerful computational methods are able to accurately capture the solution of a problem by fully exploiting its underlying analytical structure. This is in contrast to more standard numerical methods that have been developed to have the widest possible application.

该研究计划的主要主题是将科学计算，物理建模和经典方法中的最新方法汇总到应用数学分析中，以研究流体动力学和材料科学中出现的问题。从数学上讲，要解决的方程是高阶，非线性偏微分方程，并且域通常非常复杂。基本的计算框架是在指示``设计师''算法时使用的，即针对特定问题的算法。这些现代强大的计算方法能够通过充分利用其潜在的分析结构来准确捕获问题的解决方案。这与已开发的更为标准的数值方法相反，该方法具有最广泛的应用。