Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/103089
Title: On using enriched cover function in the partition-of-unity method for singular boundary-value problems
Authors: Fan, S. C.
Liu, X.
Lee, Chi King
Keywords: DRNTU::Engineering::Civil engineering::Structures and design
Issue Date: 2002
Source: Liu, X., Lee, C. K., & Fan, S. C. (2002). On using enriched cover function in the Partition-of-unity method for singular boundary-value problems. Computational Mechanics, 29(3), 212-225.
Series/Report no.: Computational mechanics
Abstract: Amongst the various approaches of ‘meshless’ method, the Partition-ofunity concept married with the traditional finite-element method, namely PUFEM, has emerged to be competitive in solving the boundary-value problems. It inherits most of the advantages from both techniques except that the beauty of being ‘meshless’ vanishes. This paper presents an alternative approach to solve singular boundary-value problems. It follows the basic PUFEM procedures. The salient feature is to enhance the quality of the influence functions, either over one single nodal cover or multi-nodal-covers. In the vicinity of the singularity, available asymptotic analytical solution is employed to enrich the influence function. The beauty of present approach is that it facilitates easy replacement of the influence functions. In other words, it favors the ‘influence-function refinement’ procedure in a bid to search for more accurate solutions. It is analogous to the ‘p-version refinement’ in the traditional finite-element procedures. The present approach can yield very accurate solution without adopting refined meshes. As a result, the quantities around the singularity can be evaluated directly once the nodal values are solved. No additional post-processing is needed. Firstly, the formulation of the present PUFEM approach is described. Subsequently, illustrative examples show the application to three classical singular benchmark problems having various orders of singularity. Results obtained through mesh refinements, singlenodal- cover refinements or multi-nodal-cover refinements are compared.
URI: https://hdl.handle.net/10356/103089
http://hdl.handle.net/10220/19236
ISSN: 0178-7675
DOI: 10.1007/s00466-002-0335-x
Rights: © 2002 Springer-Verlag. This is the author created version of a work that has been peer reviewed and accepted for publication by Computational Mechanics, Springer-Verlag. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI:http://dx.doi.org/10.1007/s00466-002-0335-x].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:CEE Journal Articles

Files in This Item:
File Description SizeFormat 
LCK_CM1.pdf401.99 kBAdobe PDFThumbnail
View/Open

SCOPUSTM   
Citations 20

7
Updated on Jan 15, 2023

Web of ScienceTM
Citations 20

6
Updated on Feb 4, 2023

Page view(s) 50

396
Updated on Feb 6, 2023

Download(s) 20

269
Updated on Feb 6, 2023

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.