A Radial Basis Function Meshless Numerical Method For Solving Interface Problems In Irregular Regions

In scientific research,many practical problems can be characterized by partial differential equations with discontinuous coefficients.The true solution of this kind of problem appears to jump on the cross-section because of the discontinuity of coefficients.It is called interface problem,and the cross-section is called interface.For interface problems with large difference of magnitude in different irregular subdomains,the general numerical methods have difficulty in dealing with the information inside and outside the interface well,resulting in low numerical precision or huge calculation.problem.In order to solve such problems,this paper uses the radial basis function meshless numerical method to constructs a mathematical model by arranging discretely distributed nodes within an irregular region.The main idea is to construct corresponding radial basis functions for different regions divided by the interfaces,assemble the coefficient matrix of the interface problem and use the meshless method for interpolation.This method avoids the difficulty of mesh generation,and is efficient in the numerical simulation of partial differential equations with matrix coefficients,large jump matrix and variable matrix coefficients.We use the direct method to handle interface jump conditions.By adding nodes at the interface,the numerical error is effectively reduced.Numerical simulation results show that the radial basis function meshless numerical solution can effectively deal with various kinds of interface problems with irregular regions and sharp-edged interfaces,including Poisson equations,heat conduction equations and wave equations.