Smoothed Point Interpolation Methods

10.1142/8742 ◽  
2013 ◽  
Author(s):  
G R Liu ◽  
G Y Zhang
Keyword(s):  
Interpolation Methods ◽  
Point Interpolation

Application of the smoothed point interpolation methods in computational geomechanics: A comparative study

2020 ◽  
Vol 126 ◽  
pp. 103714
Author(s):  
A. Khoshghalb ◽  
A. Shafee ◽  
A. Tootoonchi ◽  
O. Ghaffaripour ◽  
S.A. Jazaeri
Keyword(s):  
Comparative Study ◽  
Interpolation Methods ◽  
Point Interpolation

Mathematical Basis of G Spaces

2016 ◽  
Vol 13 (04) ◽  
pp. 1641007 ◽  
Author(s):  
Meng Chen ◽  
Ming Li ◽  
G. R. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Weak Formulation ◽  
Mathematical Basis ◽  
Numerical Examples ◽  
Interpolation Methods ◽  
Point Interpolation ◽  
Theoretical Frame ◽  
Lower Boundedness ◽  
Numerical Approaches

This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.

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