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美國麻省大學達特茅斯分校王成教授學術報告

時間:2019-12-25 10:27??????來源:研究生辦公室????? ????? 點擊量:
報告地點 主講人

報告題目:An energy stable pseudo-spectral numerical scheme for the square phase field crystal (SPFC) equation

報 告 人:Prof. Cheng Wang美國麻省大學達特茅斯分校

報告時間:20191230日(周一)16:00

報告地點:清水河校區主樓A1-513

邀 請 人:徐立偉 教授


報告摘要:

An energy stable numerical scheme is proposed and analyzed for the square phase field crystal (SPFC) equation, a gradient flow to model the crystal dynamics at the atomic scale in space but on diffusive scales in time. In particular, a modification of the free energy potential to the standard phase field crystal model leads to a composition of the 4-Laplacian and the regular Laplacian operators. The Fourier pseudo-spectral approximation is taken in space, so that the summation in parts formulas enable one to study the discrete energy stability for such a high order spatial discretization. In the temporal approximation, a second order BDF stencil is applied in the time direction, combined with an appropriate extrapolation for the concave diffusion term. At a theoretical level, the unique solvability, energy stability are established, and an optimal rate convergence analysis is derived. In the numerical implementation, the preconditioned steepest descent (PSD) iteration is applied to solve for the composition of the highly nonlinear 4-Laplacian term and the standard Laplacian term, and a geometric convergence is assured for such an iteration.A few numerical experiments are also presented.


報告人簡介:

王成,1993年畢業于中國科技大學獲數學學士學位,2000年在美國坦普爾大學獲得博士學位,。2000-2003年在美國印尼安納大學做博士后,2003-2008年在美國田納西大學任助理教授,2008-2012年在美國麻省大學達特茅斯分校任助理教授,2012年晉升為副教授,2019年晉升為教授。主要研究領域是應用數學,包括數值分析、偏微分方程、流體力學欧洲杯官方网投-首页、計算電磁學等。在Journal of Computational Physics欧洲杯官方网投-首页,SIAM Journal on Numerical Analysis,IMA Journal of Numerical Analysis等期刊上發表論文五十多篇欧洲杯官方网投-首页。



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