Meshfree point collocation method with intrinsic enrichment for interface problems

Abstract

A meshfree collocation method with an intrinsic wedge enrichment is presented for solving interface problems. To approximate the class of functions with discontinuous derivatives on the interface, the wedge is asymptotically added to the basis functions. A general class of wedge basis functions with specified orders of asymptotic behavior at the interface is developed for moving least square approximations. These are implemented in diffuse derivative methods where the shape functions are approximately differentiated. The reproducing properties of these approximations for the polynomial part and for the wedge function along straight boundaries of the basis are demonstrated. For curved boundaries, the reproducing properties of the wedge functions are more restricted. Numerical results show the ease of constructing the intrinsic enrichment and the robustness of the numerical scheme in solving interface problems.