A Generalized Discontinuous Galerkin Method and Its Applications

Kai Fan

ISBN 10: 3639108043 / ISBN 13: 9783639108040

Editore: VDM Verlag, DE, 2008

Codice articolo LU-9783639108040

Riassunto:

In this book, a new Generalized Discontinuous Galerkin (GDG) method for Schrodinger equations with nonsmooth solutions is proposed. The numerical method is based on a reformulation of Schrodinger equations, using split distributional variables and their related integration by parts formulae to account for solution jumps across material interfaces. GDG can handle time dependent and general nonlinear jump conditions. And numerical results validate the high order accuracy and the flexibility of the method for various types of interface conditions. As one of GDG's application, a new vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for wave propagations in inhomogeneous optical waveguides is also included. The resulting GDG-BPM takes on four formulations for either electric or magnetic field. GDG- BPM's unique feature of handling interface jump conditions and its flexibility in modeling wave propagations in inhomogeneous optical fibers is shown by various numerical results.

L'autore: Kai Fan holds a B.Sc (2003) in Mathematics from Hong Kong Baptist University, China, and a Ph.D (2008) in Applied Mathematics from the University of North Carolina at Charlotte, US. In 2008, he joined North Carolina State University as a research associate.

Dati bibliografici

Titolo: A Generalized Discontinuous Galerkin Method ...
Casa editrice: VDM Verlag, DE
Data di pubblicazione: 2008
Legatura: Paperback
Condizione: New