A Program on Solidification and Fast Algorithms

固化和快速算法程序

• 批准号: 9114308
• 负责人: Robert Langlands
• 金额: $ 23.24万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9114308&HistoricalAwards=false
• 关键词: Program; Solidification; Fast; Algorithms

Solidification processes are ubiquitous in modern technology. They are important whenever a substance changes from a liquid or gas to a solid, for example when ice melts or freezes, when silicon or gallium arsenide crystals are grown for use in semiconductor devices or silver halide crystals grown for film production, when Alaskan soil freezing patterns are altered by an oil pipeline, or when zinc dendrites pierce the walls of a lead- zinc battery. Computer simulation of solidification processes, the subject of this activity, serves two purposes. When the fundamental physics is under investigation, the theoretical predictions of any proposed model must be produced and compared with other models and with experiment. Solidification is sufficiently complex that this must be done by careful numerical simulation; exact solutions almost never exist. Once the fundamental physics is well understood, numerical calculations can produce data inaccessible to experiment and in some situations can even substitute for experiment. Considerable savings in time and money can be realized if numerical simulation can be substituted for experiments. The goal of the research is to develop technology to solve solidification problems which are presently beyond the reach of numerical simulation. To achieve this goal, the investigators will combine the best numerical methods available and extend them to solve more complex problems.

在现代技术中，凝固过程无处不在。每当一种物质从液体或气体转变为固体时，例如当冰融化或冻结时，当生长用于半导体器件的硅或镓砷化物晶体或为电影制作而生长的卤化银晶体时，当阿拉斯加的土壤冻结模式被输油管道改变时，或者当锌树枝晶刺穿铅锌电池的壁时，它们都是重要的。计算机模拟凝固过程，这项活动的主题，有两个目的。在研究基础物理时，必须给出所提出的任何模型的理论预测，并将其与其他模型和实验进行比较。凝固过程非常复杂，必须通过仔细的数值模拟来完成；精确的解决方案几乎永远不存在。一旦很好地理解了基本物理学，数值计算就可以产生实验无法获得的数据，在某些情况下甚至可以取代实验。如果能用数值模拟代替实验，可以节省大量的时间和金钱。这项研究的目标是开发技术来解决目前数值模拟无法解决的凝固问题。为了实现这一目标，研究人员将结合现有的最好的数值方法，并将其扩展到解决更复杂的问题。