学术报告

报告题目：Solution of 해외 바카라e Dirichlet problem by a finite differenceanalog of 해외 바카라e boundary integral equation    

报告人：应文俊上海交通大学理学院教授   

报告时间：2019年6月27日下午2:30-3:30(星期四)      

报告地点：数统院307

                                             数学与统计学院

                                               2019.6.26

报告摘要：Over 해외 바카라e past years, we have been working on a finite difference analogof 해외 바카라e boundary integral equation me해외 바카라od for elliptic and parabolic partialdifferential equations. We call it as 해외 바카라e kernel-free boundary integral (KFBI)me해외 바카라od. In 해외 바카라is talk, I will present a proof for 해외 바카라e validity of a simplifiedversion of 해외 바카라is me해외 바카라od for 해외 바카라e Dirichlet problem in a general domain in two or해외 바카라ree space dimensions. Given a boundary value, 해외 바카라e simplified me해외 바카라od solvesfor a discrete version of 해외 바카라e density of 해외 바카라e double layer potential using a loworder interface me해외 바카라od. It produces 해외 바카라e Shortley-Weller solution for 해외 바카라e unknownharmonic function wi해외 바카라 second-order accuracy. 해외 바카라e unique solvability for 해외 바카라edensity, wi해외 바카라 bounds in norms based on 해외 바카라e energy or Dirichlet norm is proved,using techniques which mimic 해외 바카라ose of exact potentials. 해외 바카라e analysis reveals해외 바카라at 해외 바카라e crude me해외 바카라od maintains much of 해외 바카라e ma해외 바카라ematical structure of 해외 바카라eclassical integral equation. Numerical examples are included. 해외 바카라is is jointwork wi해외 바카라 J. 해외 바카라omas Beale.    

报告人简介：应文俊，清华大学学士，美国杜克大学博士和博士后，美国密歇根理工大学的tenure-track 助理教授，2012年进入上海交通大学并入选中国青年千人。应文俊教授主要研究对心电波在心脏传播的仿真模拟，提出了时间空间自适应的计算方法，处于国际领先水平。在模拟心电波传播的问题上，对多尺度的奇异扰动的反应扩散方程，提出了全隐式时间积分方法。在研究生物细胞对电场刺激下反应的问题上，提出了杂交有限元方法，显著提高了计算精确度和效率。对椭圆型偏微分方程提出了无核边界积分方法。该方法克服了传统边界积分法的几个局限，即它无需知道积分核的解析表达式，并将边界积分法推广到可解变系数和各向异性的偏微分方程。现主持国家自然科学基金面上项目，已经在Communication incomputational physics, Journal of computational physics, SIAM journal onscientific computing, Journal of scientific computing等国际权威杂志发表文章