报告人：王成
       Department of Mathematics, UMass Dartmouth

报告题目：Numerical approximation for  Phase Field Crystal (PFC) equations

报告地点：管理科研楼1518

报告时间：2013年7月5日星期五  上午10:00―11:00

Abstract: Highly efficient, unconditionally energy stable and uniquely solvable finite difference schemes for the Phase Field Crystal (PFC) equation, a nonlinear sixth order parabolic equation, are discussed.

A convex splitting of the corresponding physical energyis utilized. As a result, a combination of an implicit treatment for the convex part and an explicit treatment for the concave part leads to a numerical scheme with a non-increasing energy.Both the first and second order splittings in time,both the centered difference and the fourth order long stencildifference spatial approximations, are analyzed and proven to be unconditionally stable. In turn, a local in time numericalconvergence can be derived.

These ideas can be applied to other models of gradient systems, such as Cahn-Hilliard equations,a modified PFC model, epitaxial thin film growth models, etc.Some numerical simulation results are also presented.

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