吕茂辉 博士, (ICMSEC, AMSS)

Energy preserving nodal discontinuous Galerkin method for nonlinear Maxwell's equations

10 月 27 日（周三） 下午 16:00-17:00 数学院南楼 202 教室

When light propagates in the optical media, it interacts with the media, giving extraordinary optical phenomena, such as nonlocal effects and high order harmonic generations. In this talk, we present a class of high order nodal discontinuous Galerkin methods for nonlinear Maxwell’s equations that encode linear Lorentz, nonlinear Kerr and Raman effects in multi-dimensions. With special treatments of the nonlinearities, discrete analogue of the energy relation at continuous level is identified for the proposed schemes. Under some assumptions on the strength of nonlinearities, error estimates for the semi-discrete in space DG schemes are established for Qk type approximations on Cartesian grids. To avoid nonlinear iterations, we further propose a strategy based on dual grids to linearly solve the nonlinear system. Numerical experiments are provided to demonstrate the accuracy, energy conserving property of the proposed schemes. We further illustrate the performance of the schemes through physically relevant simulations involving spatial soliton propagations and airhole scattering in realistic glasses. 

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