On optimal radius of sub-domains in meshless LBIE method

Local weak based meshless methods construct weak form of governing equations on local sub-domains. In two dimensional domains, for the simplicity of computations, these sub-domains are taken as circles. In these methods, the optimal radius of sub-domains has been an open problem yet. This paper aims...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2023-11, Vol.213, p.145-160
Main Authors: Hosseinzadeh, Hossein, Shirzadi, Ahmad
Format: Article
Language:English
Subjects:
Lebesgue constant
Local boundary integral equations (LBIE)
Local weak formulation
Meshless methods
Radial basis functions
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Summary:Local weak based meshless methods construct weak form of governing equations on local sub-domains. In two dimensional domains, for the simplicity of computations, these sub-domains are taken as circles. In these methods, the optimal radius of sub-domains has been an open problem yet. This paper aims at solving this problem for meshless local boundary integral equation (LBIE) method to enhance its performance. It is proved that a sub-domain for which the Lebesgue constant takes its minimum over its boundary is the optimal sub-domain. In other words, the optimal sub-domain is one for which the solution of PDE is approximated on its boundary as accurate as possible. A comprehensive numerical study confirms the theory.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2023.06.006