Numerical solution of PDEs by the spectral method

点击翻译按钮获取中文摘要

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.