Fast Spectral-Galerkin Methods and their Applications

快速谱伽辽金方法及其应用

基本信息

批准号：
0610646
负责人：
Jie Shen
金额：
--
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2006
资助国家：
美国
起止时间：
2006-09-15 至 2010-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0610646&HistoricalAwards=false
关键词：
Fast Spectral Galerkin Methods their

项目摘要

As computer simulations are playing an ever increasing role in manybranches of science and engineering and are rapidly replacing much ofthe expensive prototyping and testing phases in manufacturing and inscience explorations, fast and robust numerical methods are becomingan indispensable tool for many scientists and engineers. The focus ofthis project is to design fast and robust spectral-Galerkin methodsfor solving a large class of partial differential equations, and applythem to investigate several important problems of current interest.The proposed research will result in fast and accurate numericalalgorithms for a class of partial differential equations withapplications in acoustic and electromagnetic scattering, fluiddynamics and materials science. It is expected that the proposed numerical algorithms will allowsimulations of three-dimensional time-dependent problems within areasonable turn-over time, and provide capabilities to numericallyattack challenging problems arising from emerging engineering andscientific applications. In particular, the proposed numericalsimulations will contribute towards better understandings of thecomplex physical and mathematical problems, and provide valuableinformation for the design of advanced materials and on therheological and hydrodynamic properties of complex fluids. Theproposed research will also generate opportunities for undergraduateresearch projects such as software development, parallel computationand numerical simulation.

随着计算机模拟在科学和工程的许多文化中发挥着越来越多的作用，并且正在迅速取代制造业和Inscience探索中的许多昂贵的原型制作和测试阶段，因此，快速，强大的数值方法正在成为许多科学家和工程师的不可错过的工具。该项目的重点是设计快速，稳健的光谱 - 加勒金方法来解决大量部分差分方程，并应用于调查当前兴趣的几个重要问题。拟议的研究将导致在与声学和电子磁性散射的一类偏微分方程中，对具有偏差的偏微分方程进行快速，准确的数值。预计拟议的数值算法将允许在令人难以置信的转换时间内允许三维时间依赖时间的问题，并为新兴工程和得科应用程序带来的数值攻击挑战性问题提供了能力。特别是，所提出的数值模拟将有助于更好地理解对物理和数学问题的理解，并为高级材料的设计以及复杂流体的治疗学和流体动力学特性提供宝贵的信息。该研究还将为本科生搜索项目（例如软件开发，并行计算和数值模拟）带来机会。