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A Cartesian grid based tailored finite point method for singularly perturbed reaction-diffusion equation on complex domains

发布日期:2022-06-22点击数:

报告人:应文俊(上海交通大学)

时间2022年06月24日10:00-

地点:理科楼LA106


摘要:Singularly perturbed reaction-diffusion equations often arise from computational biology, particularly computational electrophysiology of the heart. Well-known examples are the monodomain and bidomain equations in computational cardiology. Singular perturbation in the equations characterizes slow diffusion, fast reaction and, to resolve corresponding sharp propagating wave fronts/backs, requires very fine grids and small time steps with the standard the finite difference (FD) method or finite element (FE) method as piecewise linear or quadratic basis functions used by FD/FE methods are not good ones for singularly perturbed equations. In this talk, We will present a Cartesian grid based tailored finite point method, which was originally proposed by Houde Han, Zhongyi Huang et al., for singularly perturbed reaction-diffusion equation on complex domains. The method uses special solutions to singularly perturbed equations on Cartesian grid cells as basis functions, which allow accurate approximation on coarse grids. In order to handle equations on complex domains while simultaneously working with Cartesian grids, which has several advantages including low cost in grid generation, accurate approximation on coarse grids, fast solution of resulting discrete equations etc., we incorporate the method with the kernel-free boundary integral method, a potential theory-based Cartesian grid method. We will also present numerical examples to demonstrate accuracy and efficiency of the method in the talk.


简介:应文俊,上海交通大学自然科学研究院及数学科学学院教授、博士生导师,上海交通大学重庆人工智能研究院执行院长。清华大学应用数学学士、计算数学硕士,美国杜克大学计算数学博士、生物医学工程博士后。曾任美国密西根理工大学助理教授,首批国家特聘青年专家,曾任第五届中国青年科技工作者协会常务理事,现兼任第八届中国工业应用数学学会副秘书长,上海市非线性科学学会副秘书长。

研究方向为计算和应用数学,长期从事数学算法设计与软件开发,近期主要致力于网格计算、图像处理、视频分析与相关人工智能算法。研究成果在生物医学、航空航天航海、国防、海洋建模和电力系统模拟等领域都有重要应用。


邀请人:王坤


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重庆大学数学与统计学院的前身是始建于1929年的重庆大学理学院和1937年建立的重庆大学商学院,理学院是重庆大学最早设立的三个学院之一,首任院长为数学家何鲁先生。