An order-N complexity meshless algorithm based on local Hermitian interpolation

Abstract

This work describes a new numerical method utilising RBF interpolants. Based on local Hermitian interpolation of function values and boundary operators, and using an explicit time-advancement formulation, the method is of order N complexity. Computational cost to advance the solution in time is minimal, and is largely dependent on local system support size. The performance of the method is examined for a variety of linear convection-diffusion-reaction problems, featuring both steady and unsteady solutions. The technique is named the Local Hermitian Interpolation (LHI) method.