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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.
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