Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem

Abstract

In this paper, the meshless local radial point interpolation (MLRPI) method is applied to one-dimensional inverse heat conduction problems. The meshless LRPIM is one of the truly meshless methods since it does not require any background integration cells. In this case, all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. A technique is proposed to construct shape functions using radial basis functions. These shape functions which are constructed by point interpolation method using the radial basis functions have delta function property. The time derivatives are approximated by the time-stepping method. Numerical experiments are carried out and compared with implicit Finite difference method