Local Radial Point Interpolation Meshless Method for Transient Heat Conduction Problems

A radial point interpolation method (RPIM) was proposed by authors to overcome the possible singularity associated with only polynomial basis. The RPIM used multi-quadric (MQ) as basis function. We developed the local radial point interpolation method (LRPIM) using the Heaviside step function to solve transient heat conduction problems. The Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions. The traditional Crank-Nicolson is selected for the time discretization scheme.

Keywords:

Radial point interpolation method , Local radial point interpolation method , Transient heat conduction problems , meshfree method