A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains

Abstract

In this paper, we use the radial basis function meshless method to solve the irregular region interface problem. The key idea is to construct radial basis functions corresponding to different regions divided by the interfaces. This method avoids the difficulty of mesh generation, and is efficient in the numerical simulation of partial differential equations in irregular domain with variable matrix coefficients. The numerical error is effectively reduced by using the direct method to handle the interface jump conditions. Numerical simulation results show that the radial basis function meshless numerical method can effectively deal with various kinds of interface problems with irregular domains and sharp-edged interfaces, including Poisson equations, heat conduction equations and wave equations.