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.
A Generalized Discontinuous Galerkin Method & Its Applications
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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.
The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The...
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as...
This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential...
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars...
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