Numerical solution of Allen–Cahn model on surfaces via an effective method based on generalized moving least squares (GMLS) approximation and the closest point approach

Abstract

A numerical method has been designed for solving the surface Allen–Cahn model. The proposed numerical procedure is based on the generalized moving least-squares approximation and the closest point method. This approach is free from the structure of the underlying surface. It only needs a set of arbitrarily distributed mesh-free points on the surface.