报告题目：Solution of the Dirichlet problem by a finite difference analog of the boundary integral equation

报 告 人：应文俊教授（上海交通大学理学院）

报告时间：2019年6月27日 14:30-15:30

报告地点：数统院307学术报告厅

报告摘要：

Over the past years, we have been working on a finite difference analog of the boundary integral equation method for elliptic and parabolic partial differential 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 simplified version of this method for the Dirichlet problem in a general domain in two or three space dimensions. Given a boundary value, the simplified method solves for a discrete version of the density of the double layer potential using a low order interface method. It produces the Shortley-Weller solution for the unknown harmonic function with second-order accuracy. The unique solvability for the density, with bounds in norms based on the energy or Dirichlet norm is proved, using techniques which mimic those of exact potentials. The analysis reveals that the crude method maintains much of the mathematical structure of the classical integral equation. Numerical examples are included. This is joint work 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 in computational physics, Journal of computational physics, SIAM journal on scientific computing, Journal of scientific computing等国际权威杂志发表文章。