摘要：Singularly perturbed reaction-diffusion equations often arise from computational biology, particularly computational electrophysiology of the heart. Well-known examples are the monodomain and bidomain equations in computational cardiology. Singular perturbation in the equations characterizes slow diffusion, fast reaction and, to resolve corresponding sharp propagating wave fronts/backs, requires very fine grids and small time steps with the standard the finite difference (FD) method or finite element (FE) method as piecewise linear or quadratic basis functions used by FD/FE methods are not good ones for singularly perturbed equations. In this talk, We will present a Cartesian grid based tailored finite point method, which was originally proposed by Houde Han, Zhongyi Huang et al., for singularly perturbed reaction-diffusion equation on complex domains. The method uses special solutions to singularly perturbed equations on Cartesian grid cells as basis functions, which allow accurate approximation on coarse grids. In order to handle equations on complex domains while simultaneously working with Cartesian grids, which has several advantages including low cost in grid generation, accurate approximation on coarse grids, fast solution of resulting discrete equations etc., we incorporate the method with the kernel-free boundary integral method, a potential theory-based Cartesian grid method. We will also present numerical examples to demonstrate accuracy and efficiency of the method in the talk.