Reproducing kernel element method Part III: Generalized enrichment and applications

By Hongsheng Lu, Shaofan Li, D. Simkins, Wing Kam Liu, Jian Cao. 2004

84 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/312a056376f680b76e8ade099f7f0f7dc886bb9e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Xiaoying Zhuang
2. T. Tamai
3. Seiichi Koshizuka
4. Dae-Jin Kim
5. Timon Rabczuk
6. Carlos Armando Duarte
7. Hongsheng Lu
8. Wing Kam Liu

In Mechanics of Materials

1. Xiaoying Zhuang
2. Carlos Armando Duarte
3. Timon Rabczuk
4. T. Tamai
5. Dae-Jin Kim
6. Seiichi Koshizuka
7. Hongsheng Lu
8. Wing Kam Liu

Citations in the corpus

• The piecewise polynomial partition of unity functions for the generalized finite element methods (2008, methodology): “Another non conventional FEM, closely related to GFEM, are Meshfree Particle Methods, such as Reproducing Kernel Particle Method (RKPM)([2],[8],[9],[13]) and Reproducing Kernel Element Method (RKEM) ([9],[10],[11]).”
• Least squares moving particle semi-implicit method (2014, methodology): “The first class of meshfree/ particle methods is used with various weak formulations such as Galerkin methods, for example, diffuse element method (DEM) [73], element free Gelerkin (EFG) method [11,13– 15,67], reproducing Kernel particle method (RKPM) [21, 63–65], h-p cloud method [27,28,58,74], par”
• Reproducing Kernel Triangular B-spline-based FEM for Solving PDEs (2013, methodology): “Some examples include the moving least-square reproducing kernel method [22, 21], the reproducing kernel element method (RKEM) [29, 23, 34, 51] and the NURBS-based error reproducing kernel meshfree method (ERKM) [50].”
• Reproducing kernel element method Part II: Globally conforming Im/Cn hierarchies (2004, methodology): “The problem domain and triangle discretization are illustrated in Fig. 14. The computed deformed shape and convergence results are displayed in Fig. 15. A detailed discussion on this problem can be found in both Parts III and IV of this work [ 24 ,26].”
• Arbitrarily smooth generalized finite element approximations (2006, methodology): “The socalled Reproducing Kernel Element Method recently proposed by Liu et al. [33] [50] [51] [66] provides interpolating shape functions of arbitrary smoothness, but their supports do not coincide with the finite element mesh.”