A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis

In this paper, a stabilized radial point collocation method (RPCM) that uses locally supported nodes is proposed using least-squares stabilization technique. The focus of this work is to stabilize the solution of the RPCM in order to perform adaptive analysis. Good stiffness matrix properties such as symmetric and positive definite (SPD) are gained via a least-squares procedure, and yet the formulation procedure of the stabilized LS-RPCM is still kept simple and straightforward. Adaptive analysis study has then been successfully carried out using the stabilized LS-RPCM. Error indicator based on interpolation error is adopted in the adaptive scheme for nodal refinement. Thanks for the meshfree features of the RPCM, refinement process can be easily done by inserting additional nodes based on the Voronoi diagram, without worrying about nodal connectivity in the formulation of system equations. Good numerical performance has been shown in the numerical examples presented in this paper.