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Abstract
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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.
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