Third order accurate, linear numerical scheme for epitaxial thin film growth model with energy stability
发布人:杨蓉   发表时间:2024-05-30
报告人 Cheng Wang 时间 2024年06月4日(星期二)19:00-21:00
地点 腾讯会议

主讲人:Cheng Wang (Department of Mathematics University of Massachusetts Dartmouth)






A few linear schemes for nonlinear PDE model of thin film growth model without slope selection are presented in the talk. In the first order linear scheme, the idea of convex-concave decomposition of the energy functional is applied, and the particular decomposition places the nonlinear term in the concave part of the energy, in contrast to a standard decomposition. As a result, the numerical scheme is fully linear at each time step and unconditionally solvable, and an unconditional energy stability is guaranteed by the convexity splitting nature of the numerical scheme. To improve the numerical accuracy, a linear second order scheme is presented and analyzed, so that the energy stability is assured, with a second order Douglas-Dopnt regularization. Finally, a third order accurate ETD-based scheme is proposed, in which all the nonlinear terms are updated by higher order Lagrange extrapolation formulas. Moreover, the energy stability analysis and convergence estimate are established at a theoretical Level, which is the first such result in the area. Some numerical simulation results are also presented in the talk.


王成(Cheng Wang)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等期刊上发表论文一百余篇论文。