An Efficient Scheme for Meshless Analysis Based on Radial Basis Functions

Date of Online Publication: 02/11/2010
Keywords: Partial Differential Equations, Meshless Method, Radial Basis Function, Radial
Point Interpolation

Abstract: A meshless method based on radial point interpolation was recently developed as
an effective tool for solving partial differential equations, and has been widely applied to a
number of different problems. In addition to the primary advantage of the meshless methods
that the computation is performed without any connectivity information between field
nodes, the radial point interpolation-based meshless method has several advantages such
as the stability of the shape functions and simple implementation of boundary condition
enforcement. This paper introduces a new scheme for the radial point interpolation-based
meshless method. This method enables fast computation by modifying the construction
and evaluation of the shape functions. Numerical examples are also presented to show that
a reliable solution can be obtained with low computational cost.


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