ncku-talk2011-05-24

NCTS(South) Seminar

DATE 2011-05-24　16:00-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. Qin Sheng（Department of Mathematics, Baylor University, Texas, USA）

TITLE An Evolution of The Splitting from Cosine To Eikonal Schemes

ABSTRACT 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. Some simulated results will be given.

NCTS(South) Seminar

DATE	2011-05-24　16:00-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. Qin Sheng（Department of Mathematics, Baylor University, Texas, USA）

TITLE	An Evolution of The Splitting from Cosine To Eikonal Schemes

ABSTRACT	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. Some simulated results will be given.