Assessment and applications of point interpolation methods for computational mechanics

By Guirong Liu, Yuantong T. Gu, K. Y. Dai. 2004

87 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/685a23f49f6751811745172aeb13b8f71b0bd7de

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In Control and Systems Engineering

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation (2009, methodology): “For computations in the field of structural mechanics, the RPIM has been successfully applied [32, 33].”
Time‐dependent fractional advection–diffusion equations by an implicit MLS meshless method (2011, methodology): “This category of meshless methods includes the diffuse element method (DEM) [25], the elementfree Galerkin (EFG) method [21], the reproducing kernel particle method [26], and the point interpolation method (PIM) [27, 28], the meshless local Petrov–Galerkin (MLPG) method [29], the local radial point ”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “However, PIM shape functions cannot automatically ensure the compatibility (C0-continuity) in the whole domain, since the approximation is not continuous across the boundaries of integration cells [40].”
MLS (moving least square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement (2007, unknown): “In point interpolation, the weight-function matrix W(n) may be thought of as an identity matrix on its support, but suddenly collapsing to zero matrix outside its support, so that it has the property like the step function [28].”
An implicit RBF meshless approach for time fractional diffusion equations (2011, methodology): “This category of meshless methods includes the element-free Galerkin (EFG) method [20], the reproducing kernel particle method (RKPM)[21], and the point interpolation method (PIM) [22,23], the meshless local Petrov-Galerkin (MLPG) method [24], the local radial point interpolation method (LRPIM) [25,”
An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields (2010, unknown): “As discussed by Liu and Gu [2,30], the RBF interpolation may not satisfy the partition of unity (the summation of shape functions is 1.”
An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function (2014, background): “(The readers are referred to the literature [30] for detailed discussions on compatibility for other meshless approximations).”
The natural neighbour radial point interpolation method: dynamic applications (2009, methodology): “This property is achieved in the RPIMs using the conforming RPIM ( Liu et al. , 2004”