报告题目：Efficient high order semi-implicit spectral deferred correction time discretization
报告人： 徐岩 教授
报告时间：2025年4月29日（周二）下午2:30-3:30
报告地点：藕舫楼 724室
主持人： 徐玮玮 教授
报告摘要：In this talk, we will present high order spectral deferred correction time discretization methods. We introduce L-stable spectral deferred correction methods with low stages, initiated by the Crank-Nicolson method. By employing a linear stabilization approach for phase field models, we derive a linear implicit SDC scheme. This involves adding and subtracting linear stabilization operators tailored for various phase field problems. We also incorporate an extrapolation technique in the prediction step of the semi-implicit SDC method without compromising the low-stage property. We also adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Furthermore, we construct high-order stabilization terms for semi-implicit deferred correction methods, focusing on convection-diffusion-reaction problems. We investigate optimal choices for stability parameters and analyze the upper bound of the time step to ensure both stability and high-order accuracy. Utilizing Fourier analysis, we apply von Neumann stability and Schur theory to the proposed single-step and multi-step deferred correction methods. Numerical experiments validate the analysis of the stability parameter bounds and time step constraints for these methods.
报告人简介：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。
欢迎广大师生踊跃参加！
数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2025年4月27日
