An unconditionally stable radial point interpolation meshless method with Laguerre polynomials

The time-domain radial point interpolation (RPI) meshless method has the advantage of conformal modeling of a structure with non-uniformly distributed nodes; however, the time step used is still restricted by the stability condition or distances between the nodes. The time step has to be small and computational time can be long when the distances between nodes are small. In this paper, an unconditionally stable scheme using the weighted Laguerre Polynomials is introduced into the (RPI) meshless method. The result is an always-stable RPI meshless method; it retains the advantages of both the node-based meshless method and the unconditionally stable scheme with the weighted Laguerre Polynomials. The unconditional stability, numerical accuracy and efficiency of the proposed method are verified and confirmed through numerical examples. In the case of the numerical examples computed, CPU time saving can be more than 99% in comparisons with the CPU time used with the conventional conditionally stable meshless method.