报告人：徐岩 教授
报告题目：Structure-Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations
报告时间：2026年4月23日（周四）下午4：30
报告地点：云龙校区6号楼318会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
徐岩，中国科学技术大学数学科学学院教授、博导， 教育部国家重大人才工程项目特聘教授，国家自然科学基金优秀青年基金获得者、教育部新世纪优秀人才计划。2005年于中国科学技术大学数学系获计算数学博士学位；2005-2007年在荷兰Twente大学从事博士后研究工作。2009年获得德国洪堡基金会的支持在德国Freiburg大学访问工作一年。主要研究领域为高精度数值计算方法。2008年度获全国优秀博士学位论文奖，2017年获中国数学会计算数学分会第二届“青年创新奖”。主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划、霍英东青年教师基础研究课题等科研项目。担任中国数学会计算数学分会理事，担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。
报告摘要：
In this talk we use Lagrange multipliers the conditions imposed by the structure 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, which is frequently encountered in constrained optimization. Since the limiter is only active in areas where positivity must be enforced it does not affect the higher order DG discretization elsewhere. The resulting non-smooth nonlinear algebraic equations have, however, a different structure compared to most constrained optimization problems. 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. Convergence of this semi-smooth Newton method is proven using a specially designed quasi-directional derivative of the time-implicit positivity preserving DG discretization. The time-implicit positivity preserving DG discretization is demonstrated for several nonlinear equations.