报告题目：一个求解隐式界面椭圆型偏微分方程基于修正函数的无核边界积分方法（A correction function-based kernel-free boundary integral method for elliptic PDEs with implicitly defined interfaces）

报告人 (Speaker)：应文俊 教授（上海交通大学）

报告时间 (Time)：2023年11月7日(周二) 10：00

报告地点 (Place)：腾讯会议：440-650-222

邀请人(Inviter)：刘东杰

主办部门：理学院数学系

报告摘要：

In this talk, I will present a new version of the kernel-free boundary integral（KFBI）method for elliptic PDEs with implicitly defined irregular boundaries and interfaces. The KFBI method evaluates boundary or volume integrals indirectly by solving equivalent but much simpler interface problems. A correction function is introduced for both evaluation of right hand side correction terms and interpolation of a non-smooth potential function. It allows the new method to avoid computation of high-order partial derivatives on interfaces or boundaries, greatly reducing the algorithm complexity and improving the efficiency, especially for fourth-order methods in three space dimensions. Challenging numerical examples including high-contrast coefficients, arbitrarily close interfaces and heterogeneous interface problems, will be reported to demonstrate the efficiency and accuracy of the method.