On optimal radius of sub-domains in meshless LBIE method

Hossein Hosseinzadeh and Ahmad Shirzadi

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 213, issue C, 145-160

Abstract: 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.

Keywords: Meshless methods; Local boundary integral equations (LBIE); Local weak formulation; Radial basis functions; Lebesgue constant (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:213:y:2023:i:c:p:145-160

DOI: 10.1016/j.matcom.2023.06.006

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