Speaker: Cheng Wang( professor, University of Massachusetts Dartmouth)

Title（1）: A semi-implicit projection method for the Landau-Lifshitz equation and its convergence analysis

Abstract: A second order accurate numerical scheme for the Landau-Lifshitz equation, the dynamics of magnetization in a ferromagnetic material with a non-convex constraint, is proposed and analyzed. The temporal discretization is based on the second-order backward differentiation formula, combined with the one-sided extrapolation for the coefficient function, so that the numerical method preserves a linear nature. Subsequently, a projection step is used to preserve the length of the magnetization. The unique solvability of this scheme is theoretically guaranteed with the help of monotonicity analysis. In addition, the convergence analysis for the fully discrete numerical solution is established, with second-order accuracy in both time and space. Some numerical results are also presented in the talk.

Time: 10:30Am, 5/08/2019

Location: room702, Science and technology building(south)

Title（2）: Epitaxial thin film growth model and its numerical simulation

Abstract: A nonlinear PDE model of thin film growth model, with or without slope selection, are presented in the talk. A global in time solution with Gevrey regularity is established for the one with slope selection. For the numerical simulation, an idea of convex-concave splitting of the corresponding physical energy is applied, which gives to an implicit treatment for the convex part and an explicit treatment for the concave part. That in turn leads to a numerical scheme with a non-increasing energy. A first order accurate linear splitting and a second order accurate linear iteration algorithm are also considered, with some numerical simulation results presented.

Time: 10:30Am, 6/08/2019

Location: room702, Science and technology building(south)