Splitting Methods for Nonlinear Waves: from Cosine To Eikonal Schemes

发布者:系统管理员发布时间:2011-06-20浏览次数:539

报告题目: Splitting Methods for Nonlinear Waves: from Cosine To Eikonal Schemes
报 告 人: Qin Sheng
  Department of Mathematics Baylor University
报告时间: 6月22日下午2点
报告地点: 第一报告厅
相关介绍:
Splitting methods have been playing a remarkably important role in the numerical solution of linear and nonlinear partial differential equations
due to their remarkable efficiency, simplicity and flexibility in
computations as compared with their peers. This presentation will focus on
several specially designed split-step finite difference methods for solving
the sine-Gordon and paraxial Helmholtz equations in electromagnetical wave
applications. Highly oscillated solutions are often a concern. Cosine methods
and eikonal transformation based ADI/LOD procedures will be introduced and
utilized. We will show that, while the former scheme is numerical stable,
the latter is asymptotically stable in anticipated computations. In fact, the
eikonal transformation effectively maps a complex differential equation system to coupled real differential equations. Operator splitting is then
introduced to decompose the equations obtained. A Crank-Nicolson type
discretization is adopted to incorporate an overall accuracy and efficiency.
The finite difference schemes constructed are easy to use and highly reliable.
Interesting computational results will be given.