Numerical solution of PDEs by the spectral method

谱法的偏微分方程数值解

• 批准号: 250303-2006
• 负责人: Lui, ShiuHong
• 金额: $ 0.73万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=394745
• 关键词: Numerical; solution; PDEs; spectral; method

Many problems in the physical sciences and engineering (weather forecasting and flow of air over an aircraft to name two examples) are posed as partial differential equations (PDEs).  The main challenge is to solve these PDEs accurately and efficiently.  Spectral method is a class of algorithms for solving PDEs and they have proven to be accurate and efficient for rectangular domains. However, many problems involve irregular domains.  We intend to study spectral methods applied to problems with irregular domains.  As a specific example, we study the flow of air over a golf ball.  The dimples on the ball cause great difficulties for any numerical algorithm. A second goal of this project is to create a general purpose software which solves linear PDEs on essentially arbitrary geometry using spectral methods.  This will provide the scientific and engineering community with an easy-to-use program which can solve their PDEs efficiently.

物理科学和工程中的许多问题（如天气预报和飞行器上的气流问题）都是由偏微分方程（PDE）求解的，如何准确有效地求解这些偏微分方程是当前的主要挑战，谱方法是求解偏微分方程的一类算法，它在矩形区域上具有很好的精度和效率。然而，许多问题涉及到不规则区域.我们打算研究谱方法应用于不规则区域的问题.作为一个具体的例子，我们研究了空气流动的高尔夫球.球上的酒窝造成很大的困难，任何数值算法.该项目的第二个目标是创建一个通用软件，使用谱方法求解基本上任意几何形状的线性偏微分方程，这将为科学和工程界提供一个易于使用的程序，可以有效地解决他们的偏微分方程。