Speaker: Prof. Yan Xu（徐岩教授）

Time: 10:00-11:00, 23 February 2024 (Friday) (Beijing time)

Venue: 华信书院，CC126

Tencent Meeting ID: 179-925-780

Abstract

In this talk, we discuss local discontinuous Galerkin (LDG) method for solving the nonlinear equations which contain nonlinear high order derivatives. The discretization results in an extremely local, element based discretization, which is beneficial for parallel computing and maintaining high order accuracy on unstructured meshes. 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. Convergence of this semi-smooth Newton method is proven using a specially designed quasi-directional derivative of the time-implicit positivity preserving DG discretization. Numerical experiments are carried out to illustrate the accuracy and capability of the proposed method.

About Prof. Xu

徐岩，中国科学技术大学数学科学学院教授。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年获国家自然科学基金委“优秀青年基金”, 2017年获中国数学会计算数学分会第二届“青年创新奖”。徐岩教授入选了教育部新世纪优秀人才计划，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(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。徐岩教授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。