Extrinsic meshfree approximation using asymptotic expansion for interfacial discontinuity of derivative

A sharp meshfree approximation for derivative discontinuities across arbitrary interfaces is proposed. The interface can be arbitrarily located in a domain in which nodes are distributed uniformly or irregularly. The proposed meshfree approximations consist of two parts, singular and regular. The moving least square meshfree approximation is used together with the local wedge function as basis functions. The approximations for discontinuities are applied in a meshfree point collocation method to obtain solutions of the Poisson problem with a layer delta source on the interface and second order elliptic problems with discontinuous coefficients and/or the singular layer sources along the interface. The numerical calculations show that this method has good performance even on irregular node models.