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美国麻省大学达特茅斯分校王成教授学术报告

时间:2019-12-25 10:27      来源:新皇冠体育

报告题目:An energy stable pseudo-spectral numerical scheme for the square phase field crystal (SPFC) equation

报 告 人:Prof. Cheng Wang美国麻省大学达特茅斯分校

报告时间:20191230日(周一)16:00

报告地点:清水河校区主楼A1-513

邀 请 人:徐立伟 教授


报告摘要:

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.


报告人简介:

王成,1993年毕业于中国科技大学获数学学士学位,2000年在美国坦普尔大学获得博士学位,2000-2003年在美国印尼安纳大学做博士后,2003-2008年在美国田纳西大学任助理教授,2008-2012年在美国麻省大学达特茅斯分校任助理教授,2012年晋升为副教授,2019年晋升为教授。主要研究领域是应用数学,包括数值分析、偏微分方程、流体力学、计算电磁学等。在Journal of Computational PhysicsSIAM Journal on Numerical AnalysisIMA Journal of Numerical Analysis等期刊上发表论文五十多篇。



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