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：
0915066
负责人：
Jie Shen
金额：
$ 32.91万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2009
资助国家：
美国
起止时间：
2009-09-01 至 2013-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915066&HistoricalAwards=false
关键词：
Fast Spectral Galerkin Methods their

项目摘要

As computer simulations are playing an ever increasing role in many branches of science and engineering and are rapidly replacing much of the expensive prototyping and testing phases in manufacturing and in science explorations, fast and robust numerical methods are becoming an indispensable tool for many scientists and engineers. The focus of this project is to design auurate, fast and robust spectral methods for solving a large class of partial differential equations, and apply them to investigate several important problems of current interest. The proposed research will result in fast and accurate numerical algorithms for a class of partial differential equations with applications in acoustic and electromagnetic scattering, complex fluids and materials science. In particular, the proposed numerical algorithms will make it possible to directly solve some important high-dimensional equations which are currently not treatable with existing numerical algorithms.It is expected that the proposed numerical simulations will enable us to handle challenging problems having stringent accuracy and/or memory requirements with a reasonable cost in CPU and turn-around time, contribute towards better understandings of the complex physical and mathematical problems, and provide valuable information for the design of advanced materials and on the rheological and hydrodynamic properties of complex fluids. Another important goal of this project is to engage graduate and undergraduate students in learning necessary skills of computational and applied mathematics so that they can pursue a successful career in sciences and engineering.

随着计算机模拟在科学和工程的许多分支中发挥着越来越多的作用，并且正在迅速取代制造业和科学探索中许多昂贵的原型制作和测试阶段，快速，鲁棒的数值方法正在成为许多科学家和工程师的必不可少工具。该项目的重点是设计静脉，快速和健壮的光谱方法来解决大量的部分微分方程，并将其应用于研究当前感兴趣的几个重要问题。拟议的研究将导致一类偏微分方程的快速，准确的数值算法，并在声学和电磁散射中应用，复杂的流体和材料科学。 In particular, the proposed numerical algorithms will make it possible to directly solve some important high-dimensional equations which are currently not treatable with existing numerical algorithms.It is expected that the proposed numerical simulations will enable us to handle challenging problems having stringent accuracy and/or memory requirements with a reasonable cost in CPU and turn-around time, contribute towards better understandings of the complex physical and mathematical problems, and provide valuable information for the高级材料以及复杂流体的流变和流体动力特性的设计。该项目的另一个重要目标是让研究生和本科生学习计算和应用数学的必要技能，以便他们可以从事科学和工程领域的成功职业。