A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM)

An efficient nodal integration with quadratic exactness for three-dimensional meshfree Galerkin methods

“…2. Such partition technology is used in [22,23] with tetrahedral mesh. However, hexahedral mesh of the approximation nodes is employed in this paper and the benefit is that it generates less surface elements for each nodal integration sub-domain.…”

“…Consequently, SCNI has been widely applied in various studies, see [12][13][14][15][16][17][18]. The technique of strain smoothing has also been extended to natural-element method [19], radial point interpolation method [20] and even finite element method [21] and has been applied to various 3D problems such as heat transfer [22], adaptive analysis [23,24], fluid-structure interaction (FSI) [25], etc.…”

Adaptive Analysis Using S-PIMs

“…In this section, we define an error indicator which uses the difference between the computed values at different identities (field nodes, background cells or smoothing cells) in a particular norm. Using this error indicator, adaptive analysis is performed using NS-PIM and ES-PIM, and very good results have been obtained for a number of 2D and 3D benchmark problems [41,43].…”

Adaptive radial basis function–generated finite differences method for contact problems

“…The basic idea behind the proposed indicator, also known as ZZ or Z 2 is based on the assumption that the error of the solution can be approximated as the difference between the numerically obtained solution and a recovered solution, ie, a more accurate solution computed by appropriate post‐processing. This approach has been later successfully extended to the meshless solutions of elasticity problems, both weak form, using meshless finite volume method, node‐based smoothed point interpolation method, and strong form, using FPM . In RBF‐FD context, a ZZ type of error indicator has been discussed in a solution of Laplace equation in the work of Oanh et al An alternative class of error indicators is available for commonly used least squares–based meshless methods, which relies on the least squares approximation residual .…”