报告题目：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（University of Massachusetts Dartmouth）
邀请人：宋怀玲
时间：5月26日上午10:00-11:00
腾讯会议：617-942-424（无密码）
报告摘要：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.
报告人简介：
王成教授，1993年于中国科学技术大学数学系获得学士学位，2000年于天普大学获得博士学位。2000年至2003年于印第安纳大学担任博士后，2003年至2008年于田纳西大学担任助理教授。 2008年至2012年于University of Massachusetts Dartmouth担任助理教授， 2012年至2019年于University of Massachusetts Dartmouth担任副教授， 2019年至今于University of Massachusetts Dartmouth担任教授。王教授的研究兴趣为针对流体力学、电磁力学、 材料科学中涉及的偏微分方程的数值方法研究。主要在SIAM、JCP、JSC等发表了90余篇论文， 被引用超过2400次。
