Open Access

ARTICLE

A New Meshless Interpolation Scheme for MLPG_R Method

by

1 School of Engineering and Mathematical Sciences, City University, Northampton Square, London, UK, EC1V0HB

Computer Modeling in Engineering & Sciences 2008, 23(2), 75-90. https://doi.org/10.3970/cmes.2008.023.075

Abstract

In the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, one needs a meshless interpolation scheme for an unknown function to discretise the governing equation. The MLS (moving least square) method has been used for this purpose so far. The MLS method requires inverse of matrix or solution of a linear algebraic system and so is quite time-consuming. In this paper, a new scheme, called simplified finite difference interpolation (SFDI), is devised. This scheme is generally as accurate as the MLS method but does not need matrix inverse and consume less CPU time to evaluate. Although this scheme is purposely developed for the MLPG_R method, it may also be used for other meshless methods.

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Keywords

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