地 点:理科楼 LD202
摘 要: In ferromagnets, the intrinsic magnetic order, known as magnetization, makes these materials ideal for information storage and manipulation. From the modeling perspective, magnetization dynamics is described by the Landau-Lifshitz equation with pointwise length constraint. From the numerical perspective, typically, second-order in time schemes are either explicit with strong stability restriction on the stepsize due to the high nonlinearity or implicit with a nonlinear system of equations to be solved at each step. In the talk, we will introduce several second-order semi-implicit schemes based on the second-order backward-differentiation-formula and the one-sided interpolation from former steps with a projection step. For these schemes, we are able to prove the uniqueness of the numerical solution to the linear system of equations at each step. For one of these schemes, we then prove its second-order accuracy under the mild condition that the stepsize in time is proportional to the gridsize in space. Examples in 1D and 3D are given to verify the analysis results. A benchmark problem from National Institute of Standards and Technology is also tested to varify the applicability of these schemes.
报告人简介：陈景润，苏州大学数学科学学院教授，博士生导师，2015年入选青年千人计划。2005年毕业于南京大学，获学士学位；2010年毕业于中国科学院，获博士学位，导师为鄂维南院士和明平兵教授；2010-2015年，在美国加州大学圣芭芭拉分校先后担任博士后和访问助理教授；主要研究兴趣为与材料相关的数学建模、分析与应用等。在J. Comput. Phys., Math. Comp., SIAM Multiscale Model. Simul.等期刊上发表论文20余篇。