On the augmented moving least squares approximation and the localized method of fundamental solutions for anisotropic heat conduction problems

Abstract

The augmented moving least squares (AMLS) approximation is a meshless scheme to construct continuous functions by using fundamental solutions as basis functions. By incorporating the AMLS approximation into the method of fundamental solutions (MFS), the localized MFS can significantly reduce the computational load and accelerate the solution progress of the MFS. In this paper, error estimates of the AMLS approximation and the localized MFS are established for anisotropic heat conduction problems. Numerical examples are also presented to verify the convergence and accuracy of the methods.