Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation

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Abstract
We introduce fixed, moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points. We show that for a particular choice of nodal volumes, the fixed, moving and multiple fixed kernel approaches are identical to the fixed, moving and multiple fixed least squares approaches. A finite cloud method, which combines collocation with a fixed kernel technique for the construction of interpolation functions, is presented as a true meshless technique for the numerical solution of partial differential equations. Numerical results are presented for several one‐and two‐dimensional problems, including examples from elasticity, heat conduction, thermoelasticity, Stokes flow and piezoelectricity. Copyright © 2001 John Wiley & Sons, Ltd.

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