报告题目：Higher order accurate structure preserving time-implicit discretizations for the nonlinear time-dependent equation

报 告 人： 徐岩教授  中国科学技术大学

报告时间： 2023年8月7日（星期一）上午9:30

报告地点： 文理楼290

报告人简介：

徐岩，中国科学技术大学数学学院教授、博士生导师。主要从事间断有限元方法的研究工作，发表高水平科研论文80余篇。近年来徐岩教授承担国家自然科学基金、中科院、教育部基金、霍英东基金等多相科学基金项目的研究。先后获得教育部新世纪优秀人才支持计划(2009) 、中国科学院/全国博士学位论文奖(2007, 2008)、中国科学技术大学优秀青年教师奖(2010, 2013, 2016) 、优秀研究生指导教师奖(2013,2016)、中国数学会计算数学学会青年创新奖(2016)、国家自然科学基金委优秀青年基金(2017)。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation等杂志的编委。

报告摘要：

 In this talk, we discuss local discontinuous Galerkin (LDG) method for solving the nonlinear time-dependent equations. We develop a novel semi-implicit spectral deferred correction (SDC) time marching method. The method can be used in a large class of problems, especially for highly nonlinear ordinary differential equations (ODEs) without easily separating of stiff and non-stiff components, which is more general and efficient comparing with traditional semi-implicit SDC methods. Using Lagrange multipliers the conditions imposed by the positivity preserving limiters are directly coupled to a DG discretization combined with implicit time integration method. The positivity preserving DG discretization is then reformulated as a Karush-Kuhn-Tucker (KKT) problem. We therefore develop an efficient active set semi-smooth Newton method that is suitable for the KKT formulation of time-implicit positivity preserving DG discretizations. Numerical experiments are carried out to illustrate the accuracy and capability of the proposed method.