学术报告

报告题目：Solution of the Dirichlet problem by a finite differenceanalog of the 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 the past years, we have been working on a finite difference analogof the boundary integral equation method for elliptic and parabolic partialdifferential equations. We call it as the kernel-free boundary integral (KFBI)method. In this talk, I will present a proof for the validity of a simplifiedversion of this method for the Dirichlet problem in a general domain in two orthree space dimensions. Given a boundary value, the simplified method solvesfor a discrete version of the density of the double layer potential using a loworder interface method. It produces the Shortley-Weller solution for the unknownharmonic function with second-order accuracy. The unique solvability for thedensity, with bounds in norms based on the energy or Dirichlet norm is proved,using techniques which mimic those of exact potentials. The analysis revealsthat the crude method maintains much of the mathematical structure of theclassical integral equation. Numerical examples are included. This is jointwork with J. Thomas 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