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: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=423972
• 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、物理建模和应用数学分析中的经典方法结合在一起，研究流体力学和材料科学中出现的问题。从数学上讲，要求解的方程是高阶的、非线性的偏微分方程组，而且区域往往非常复杂。基本的计算框架是在任何需要的时候使用“设计者”算法，即那些针对具体问题的算法。这些现代而强大的计算方法能够通过充分利用问题的基本分析结构来准确地捕获问题的解决方案。这与已经开发的具有最广泛应用的更标准的数值方法形成了对比。