A Potential Theory Based Cartesian Grid Method
Prof. Wen-Jun Ying
Shanghai Jiaotong University

This talk will be on a potential theory based Cartesian grid method. The method solves a boundary value or interface problem of PDE in the framework of second-kind Fredholm boundary integral equations. It avoids some limitations of the traditional boundary integral method. It does not need to know or compute the fundamental solution or Green's function of the PDE. Instead, it allows the solution of variable coefficients and nonlinear PDEs. The method evaluates boundary and volume integrals involved 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 taking advantage of the well-conditioning property of the second-kind Fredholm boundary integral equations, the method makes full use of fast solvers on Cartesian grids. The Cartesian grid method can also accurately compute nearly singular and hypersingular boundary integrals. This talk will present recent developments of the method.

About the Speaker

应文俊, 清华大学应用数学学士(1997)和计算数学硕士(2000), 美国杜克大学计算数学博士(2005)和生物医学工程系博士后(2005-2008), 曾任美国密西根理工大学数学科学系助理教授(tenure-track Assistant Professor, 2008-2010), 2010年至今在上海交通大学工作, 现为上海交通大学数学科学学院和自然科学研究院教授、博士生导师, 是中组部首批"青年千人计划"入选者, 第五届中国青年科技工作者协会常务理事。应文俊主要从事面向生物医学与航空航天的计算生物, 计算电生理, 计算空气动力学和计算流体力学等学科的应用数学研究, 致力于快速, 高效算法的开发与设计。

2019-07-23 9:00 AM
Room: A203 Meeting Room
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