Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation

主讲人：邓定文

摘要：Over the years, energy-dissipation-preserving (EDP) numerical methods (EDP-NMs) for the nonlinear system of energy dissipation have attracted considerable attention because they are good at long-term computations. More recently, the invariant energy quadratization methods (IEQMs) have been proposed by Xiaofeng Yang and his collaborators to construct linearized EDP-NMs for the nonlinear system of energy dissipation, such as gradient flows. However, the system of the linear algebraic equations corresponding to the obtained EDP-NMs involves the variable coefficient matrices in general, thus resulting in complex computations. Besides, most of efficient alternating direction implicit (ADI) methods are not able to preserve the structures of continuous problem, such as, energy dissipation, energy conservation. To overcome these shortcomings, taking two-dimensional (2D) nonlinear Allen-Cahn equation for example, two energy-dissipation-preserving ADI finite difference methods (FDMs) have been developed by using IEQMs. Numerical analyses of them, such as, the discrete energy-dissipation laws, error estimations and stabilities, have been derived in detail. Numerical results support the theoretical analysis, and confirm the efficiency and accuracy of the proposed algorithms.

主讲人简介：邓定文, 博士、南昌航空大学教授、硕士研究生导师, 主要从事偏微分方程数值解的研究，主持国家自然科学基金三项  (天元，青年和地区各 1 项)，主持中国博士后科学基金、江西省杰出青年基金等各类省 (部) 级和厅级科研项目 10 余项, 正式发表科研和教研论文 40余篇， 2015年入选南昌航空大学青年英才开发计划，受国家留学基金委面上项目的资助于 2016-12-01至 2017-11-30 访问加拿大约克大学数学与统计学院。

邀请人：李东方

时间：10月13日18:00-22：30