Mathematical Sciences: Development, Analysis, and Applications for Numerical Methods for Nonlinear Partial Differential Equations

数学科学：非线性偏微分方程数值方法的发展、分析和应用

• 批准号: 9404942
• 负责人: Stanley Osher
• 金额: $ 37.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404942&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Development; Analysis; Applications

The principal investigators and their collaborators study the development, analysis, and applications of numerical methods for nonlinear partial differential equations. The three main topics addressed are: (1) high resolution methods, including shock capturing, front capturing, numerical homogenization, and particle methods, (2) multiscale analysis applied to these and other related problems, and (3) fast methods for linear evolution equations based on multiscale analysis and high frequency asymptotics. Engineering and physical applications studied include combustion, fluid dynamics, crystal growth, Stefan problems, microwave scattering, and reacting gases. These innovative numerical methods are used to simulate real world problems in the areas of aeronautics, oil recovery, materials science, and environmental science. Transition to industrial and military application is made in the above areas, as well as in low observables, semiconductor device modelling, and shape recognition. These methods are applicable wherever the phenomena to be studied have sharp changes of state variables or are beyond the resolving capabilities of standard methods.

首席研究人员及其合作者研究了非线性部分微分方程的数值方法的开发，分析和应用。 所解决的三个主要主题是：（1）高分辨率方法，包括捕获冲击，前捕获，数值均质化和粒子方法，（2）应用于这些和其他相关问题的多尺度分析以及（3）基于多尺度分析和高频分析的线性进化方程的快速方法。 所研究的工程和物理应用包括燃烧，流体动力学，晶体生长，Stefan问题，微波散射和反应气体。 这些创新的数值方法用于模拟航空，石油回收，材料科学和环境科学领域的现实世界问题。 在上述领域以及低观测值，半导体设备建模和形状识别中进行过渡到工业和军事应用。 这些方法适用于要研究的现象具有急剧变化的状态变量，或者超出了标准方法的解决能力。