Premium
Treatment of discontinuity in the reproducing kernel element method
Author(s) -
Lu Hongsheng,
Wan Kim Do,
Kam Liu Wing
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1284
Subject(s) - discontinuity (linguistics) , partition of unity , interpolation (computer graphics) , finite element method , mathematics , kernel (algebra) , meshfree methods , mathematical optimization , extended finite element method , convergence (economics) , algorithm , mathematical analysis , computer science , discrete mathematics , structural engineering , animation , computer graphics (images) , engineering , economics , economic growth
A discontinuous reproducing kernel element approximation is proposed in the case where weak discontinuity exists over an interface in the physical domain. The proposed method can effectively take care of the discontinuity of the derivative by truncating the window function and global partition polynomials. This new approximation keeps the advantage of both finite element methods and meshfree methods as in the reproducing kernel element method. The approximation has the interpolation property if the support of the window function is contained in the union of the elements associated with the corresponding node; therefore, the continuity of the primitive variables at nodes on the interface is ensured. Furthermore, it is smooth on each subregion (or each material) separated by the interface. The major advantage of the method is its simplicity in implementation and it is computationally efficient compared to other methods treating discontinuity. The convergence of the numerical solution is validated through calculations of some material discontinuity problems. Copyright © 2005 John Wiley & Sons, Ltd.