题目: 一个求解椭圆型偏微分方程的基于位势理论的直角网格法
报告人：应文俊
报告时间：2018年12月21号上午 9：00-11:00
报告地点：数学统计学院314会议室
报告摘要:
I will give a talk on a potential theory based Cartesian grid method for elliptic PDEs. The method solves a boundary value or interface problem of elliptic PDE in the framework of second-kind Fredholm boundary integral equations. It avoids some limitations of the traditional boundary integral method for elliptic PDEs. It does not need to know or compute the fundamental solution or Green's function of the PDE and allows the solution of variable coefficients and nonlinear PDEs. The method evaluates boundary and volume integrals indirectly by solving equivalent but much simpler interface problems on Cartesian grids, based on properties of single, double layer boundary integrals and volume integrals in potential theory. In addition to its taking advantage of the well-conditioning property of the second-kind Fredholm boundary integral equations in an iterative solution of the resulting discrete system, the method makes full use of fast elliptic solvers on Cartesian grids. The Cartesian
grid method can also accurately compute nearly singular and hypersingular boundary integrals in a natural and convenient way. In this talk, I will present several different applications of the method, including computational cardiac dynamics and fluid dynamics of incompressible flow, as well as some moving interface and free boundary problems.
报告人简介:
应文俊, 男, 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, 生物医学工程系博士后, 曾任美国密歇根理工大学助理教授, 现为上海交通大学自然科学研究院及数学科学学院教授,是中组部首批"青年千人计划"入选者. 应文俊博士的研究主要包括求解非线性双曲守恒律方程和奇异扰动反应扩散方程的时间空间自适应网格加密算法,求解刚性系统的L-稳定时间积分方法,求解椭圆型偏微分方程的边界积分方法,以及一类基于位势理论的求解复杂区域上椭圆型,抛物型偏微分方程的笛卡尔直角网格法, 研究涉及的领域包括计算空气动力学,计算生物物理学,计算电生理学和计算流体力学等. 应文俊博士的研究得到美国国家科学基金(NSF),中国自然科学基金(NSFC)和中国工程物理研究院等多家机构的支持.
