Parallel and energy-preserving schemes based on the partitioned averaged vector field method

讲座题目：Parallel and energy-preserving schemes based on the partitioned averaged vector field method
讲座时间 Datetime：2024年12月10日，周一，10:00-12:00
地点 Venue: 腾讯会议：471509353  密码：2024
报告人Speaker: 蔡文君 教授
单位 Affiliation: 南京师范大学
主持人 Host：李露 副教授
报告摘要 Abstract:
In this talk, we introduce a novel approach for developing highly efficient, energy-preserving methods for both conservative and dissipative partial differential equations (PDEs). Our method utilizes spatial finite difference approximations and, while it appears fully implicit, it is actually completely decoupled point by point. For the sine-Gordon and Allen-Cahn equations, our implementation only requires solving a scalar nonlinear equation successively, resulting in a complexity that scales with the degrees of freedom. Additionally, for the coupled Klein-Gordon-Schrodinger equations, the scheme enables fully explicit computation. Building on the partitioned averaged vector field method, we further generalize the proposed schemes to facilitate naturally parallel computation, significantly enhancing computational efficiency. Various numerical experiments are presented to demonstrate the performance of the proposed schemes. 
报告人简介：
蔡文君, 南京师范大学数学科学学院教授。2014年于南京师范大学获得博士学位，2014年9月到2016年9月在中国科学院大学计算地球动力学重点实验室从事博士后研究工作。主要研究兴趣是偏微分方程的保结构算法及其在守恒或者耗散系统中的应用。主持完成国家自然科学基金面上项目1项、作为主要参与人完成国家重点研发计划子课题1项，完成国家自然科学基金青年项目1项、江苏省高校自然科学重大项目1项，获2022年度教育部高等学校科学研究优秀成果二等奖，江苏省第三届“工业与应用数学奖青年奖”，入选第六期江苏省“333”工程第三层次培养对象，入选南京师范大学青年拔尖人才计划。