Modified local singular boundary method for solution of two-dimensional diffusion equation

Engineering Analysis with Boundary Elements(2022)

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Abstract
This paper deals with a new version of the local singular boundary method (LSBM), which will allow the use of irregular node distribution and any shape of the solved area. Unlike previous modifications, it does not impose any requirements on the number of nodes in the support or the number of virtual points. Moreover, it uses radial basis functions for interpolation, not the weighted squares method. The article contains the derivation of the fundamental relations of the steady and unsteady state method and shows its effectiveness in four control examples.
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Key words
Singular boundary method,Particular solution,Radial base functions,Virtual subdomain
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