On using enriched cover function in the partition-of-unity method for singular boundary-value problems
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...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/103089 http://hdl.handle.net/10220/19236 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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