Title: A second order scalar auxiliary variable (SAV) numerical method for the square phase field crystal (SPFC) equation and its comparison with direct nonlinear solver
报告人：王成教授（美国麻塞诸塞立大学达特茅斯分校）

地点：数学与统计学院310报告厅

时间：2023年6月2日15:30-16:30

Abstract: A second order accurate (in time), scalar auxiliary variable (SAV)-based 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. 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 combined with the SAV approach. In particular, an appropriate decomposition for the physical energy functional is formulated, so that the nonlinear energy part has a well-established global lower bound, and the rest terms lead to constant-coefficient diffusion terms with positive eigenvalues. In turn, the numerical scheme could be very efficiently implemented by constant-coefficient Poisson-like type solvers (via FFT), and energy stability is established by introducing an auxiliary variable, and an optimal rate convergence analysis is provided for the proposed SAV method. A few numerical experiments are presented, and a careful numerical comparison with direct nonlinear solvers is also undertaken.  

个人简介：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 Physics，SIAM Journal on Numerical Analysis，IMA Journal of Numerical Analysis等期刊上发表论文五十多篇。