A reproducing kernel method with nodal interpolation property

International Journal for Numerical Methods in Engineering

Volumn 56, Issue 7, 2003, Pages 935-960

  Chen, Jiun Shyan ^a   Han, Weimin ^b   You, Yang ^b   Meng, Xueping ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Essential boundary conditions; Kronecker delta properties; Meshfree method; Reproducing kernel approximation; Reproducing kernel interpolation

Indexed keywords

ESSENTIAL BOUNDARY CONDITIONS; KRONECKER DELTA PROPERTIES; MESHFREE METHOD; REPRODUCING KERNEL APPROXIMATION; REPRODUCING KERNEL INTERPOLATION;

BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; ERROR ANALYSIS; FUNCTION EVALUATION;

INTERPOLATION;

EID: 0345529301     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.592     Document Type: Article

References (24)

1. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158.
2. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
3. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
4. Belytschko T, Kronggauz Y, Organ D, Fleming M. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139:3-47.
5. Melenk JM, Babuska I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
6. Babuska I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
7. Duarte CAM, Oden JT. A h-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering 1996; 139:237-262.
8. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106.
9. Liu WK, Jun S, Li S, Adee J, Belytschko B. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering 1995; 38:1655-1679.
10. Liu WK, Li S, Belytschko T. Moving least square kernel Galerkin method. Part I. Methodology and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 143:422-433.
11. Zhu T, Atluri, SN. A modified collocation and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics 1998; 21:211-222.
12. Chen JS, Pan C, Wu CT, Liu WK. Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Computer Methods in Applied Mechanics and Engineering 1996; 139:195-227.
13. Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering 1997; 40:2953-2974.
14. Chen JS, Wang HP. New boundary condition treatments for meshless computation of contact problems. Computer Methods in Applied Mechanics and Engineering 2000; 187:441-468.
15. Gunther F, Liu WK. Implementation of boundary conditions for meshless methods. Computer Methods in Applied Mechanics and Engineering 1998; 163:205-230.
16. Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering 1996; 131:133-145.
17. Huerta A, Fernández-Méndez S. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering 2000; 48:1615-1636.
18. Wagner GJ, Liu WK. Hierarchical enrichment for bridging scales and meshfree boundary conditions. International Journal for Numerical Methods in Engineering 2001; 50:507-524.
19. Han W, Wagner GJ, Liu WK. Convergence analysis of a hierarchical enrichment of dirichlet boundary conditions in a meshfree method. International Journal for Numerical Methods in Engineering 2002; 53:1323-1336.
20. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1996; 139:49-74.
21. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulation. International Journal for Numerical Methods in Engineering 2000; 47:1189-1214.
22. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
23. Han W, Meng X. Error analysis of the reproducing kernel particle method. Computer Methods in Applied Mechanics and Engineering 2001; 190:6157-6181.
24. Brenner SC, Scott LR. The Mathematical Theory of Finite Element Methods. Springer: New York, 1994.