Reproducing Kernel Element Interpolation: Globally Conforming I m/C n/P k Hierarchies

2006 ◽  
pp. 109-132
Author(s):  
Shaofan Li ◽  
Daniel C. Simkins ◽  
Hongsheng Lu ◽  
Wing Kam Liu
Keyword(s):  
Reproducing Kernel ◽  
Reproducing Kernel Element

The quasi-uniformity condition for reproducing kernel element method meshes

2009 ◽  
Vol 44 (3) ◽  
pp. 333-342 ◽  
Author(s):  
Nathan Collier ◽  
Daniel Craig Simkins
Keyword(s):  
Reproducing Kernel ◽  
Uniformity Condition ◽  
Element Method ◽  
Reproducing Kernel Element

Reproducing kernel element method Part II: Globally conforming Im/Cn hierarchies

2004 ◽  
Vol 193 (12-14) ◽  
pp. 953-987 ◽  
Author(s):  
Shaofan Li ◽  
Hongsheng Lu ◽  
Weimin Han ◽  
Wing Kam Liu ◽  
Daniel C. Simkins
Keyword(s):  
Reproducing Kernel ◽  
Element Method ◽  
Reproducing Kernel Element

scholarly journals Reproducing Kernel Element Method for Galerkin Solution of Elastostatic Problems

2012 ◽  
Vol 8 (16) ◽  
pp. 71-96
Author(s):  
Mario J Juha
Keyword(s):  
Stiffness Matrix ◽  
Reproducing Kernel ◽  
Dimensional Space ◽  
Shape Functions ◽  
Computational Implementation ◽  
Galerkin Solution ◽  
Order Smoothness ◽  
High Order Smoothness ◽  
Element Method ◽  
Reproducing Kernel Element

The Reproducing Kernel Element Method (RKEM) is a relatively new technique developed to have two distinguished features: arbitrary high order smoothness and arbitrary interpolation order of the shape functions. This paper provides a tutorial on the derivation and computational implementation of RKEM for Galerkin discretizations of linear elastostatic problems for one and two dimensional space. A key characteristic of RKEM is that it do not require mid-side nodes in the elements to increase the interpolatory power of its shape functions, and contrary to meshless methods, the same mesh used to construct the shape functions is used for integration of the stiffness matrix. Furthermore, some issues about the quadrature used for integration arediscussed in this paper. Its hopes that this may attracts the attention of mathematicians.

Reproducing kernel element method Part III: Generalized enrichment and applications

2004 ◽  
Vol 193 (12-14) ◽  
pp. 989-1011 ◽  
Author(s):  
Hongsheng Lu ◽  
Shaofan Li ◽  
Daniel C. Simkins ◽  
Wing Kam Liu ◽  
Jian Cao
Keyword(s):  
Reproducing Kernel ◽  
Element Method ◽  
Reproducing Kernel Element

Reproducing kernel element method. Part I: Theoretical formulation

2004 ◽  
Vol 193 (12-14) ◽  
pp. 933-951 ◽  
Author(s):  
Wing Kam Liu ◽  
Weimin Han ◽  
Hongsheng Lu ◽  
Shaofan Li ◽  
Jian Cao
Keyword(s):  
Reproducing Kernel ◽  
Theoretical Formulation ◽  
Element Method ◽  
Reproducing Kernel Element

Reproducing kernel element method. Part IV: Globally compatible triangular hierarchy

2004 ◽  
Vol 193 (12-14) ◽  
pp. 1013-1034 ◽  
Author(s):  
Daniel C. Simkins ◽  
Shaofan Li ◽  
Hongsheng Lu ◽  
Wing Kam Liu
Keyword(s):  
Reproducing Kernel ◽  
Element Method ◽  
Reproducing Kernel Element

Treatment of discontinuity in the reproducing kernel element method

2005 ◽  
Vol 63 (2) ◽  
pp. 241-255 ◽  
Author(s):  
Hongsheng Lu ◽  
Do Wan Kim ◽  
Wing Kam Liu
Keyword(s):  
Reproducing Kernel ◽  
Element Method ◽  
Reproducing Kernel Element
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