Application of Line-Length Related Interpolation Methods to Problems in Coal Preparation—I: Mathematical Basis and Simple Washability Data Interpolation

1993 ◽  
Vol 13 (3-4) ◽  
pp. 131-156 ◽  
Author(s):  
G. J. Lyman
Keyword(s):  
Line Length ◽  
Coal Preparation ◽  
Data Interpolation ◽  
Mathematical Basis ◽  
Interpolation Methods

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.

Research on DEM Construction Method of Interpolation

2013 ◽  
Vol 416-417 ◽  
pp. 1470-1474
Author(s):  
Shi Qing Yang ◽  
Lan Fang Miao
Keyword(s):  
Interpolation Method ◽  
Construction Method ◽  
Measured Data ◽  
Terrain Analysis ◽  
Data Interpolation ◽  
Construction Quality ◽  
The Real ◽  
Interpolation Methods ◽  
Inverse Distance

DEM construction quality directly affects a variety of applications based on DEM and terrain analysis. Giving the error in measured data, interpolation methods affect the quality of DEM. Therefore, for a certain district, choosing a better interpolation method is very important. In this paper, we constructed new DEM by three interpolation methods (inverse distance weight, spline, Kriging) on the real DEM data of loess tableland. By comparing this new DEM with the original DEM and analyzing this new DEM, we can get a better choice of interpolation for DEM construction and terrain analysis for a certain district.

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