报告题目： Stochastic Multi-symplectic Methods for StochasticMaxwell Equations with Additive Noise

报告人：洪佳林教授（中科院数学与系统科学研究院）  

报告时间： 2015年7月5日（周日）上午9:20—10:20

报告地点：知新楼B1248

摘要： I In this talk we first review main resultson stochastic symplectic methods for stochastic Hamiltonian systems, then weintroduce the stochastic multi- symplectic structure for stochastic Hamiltonianpartial differential equations (PDEs), and show that stochastic Maxwellequations are of the stochastic Hamiltonian PDEs. We also show that theaveraged energy increases linearly as the growth of time with a precisely givenincreasing rate. It is proved that the phase flow of stochastic Maxwellequations preserves the divergence in the sense of expectation. In order topreserve the above properties numerically, we present three stochasticmulti-symplectic methods for stochastic Maxwell equations. We obtain thecorresponding dissipative property of the discrete averaged energy satisfied byeach method. Furthermore, utilizing the adaptedness of solutions to stochasticMaxwell equations and properties of Wiener process, we estimate the dissipativerates with respect to time for three methods in our consideration, and we showthat the discrete averaged energies evolve at most linearly with respect totime under certain assumptions. As for divergence, we show that all of thethree methods preserve the discrete conservation law of averaged divergencewell. The work in this talk is in collaboration with Chuchu Chen and LiyingZhang.

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