Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 50, Issue 10, Pages 2373-2410Publisher
WILEY
DOI: 10.1002/nme.124
Keywords
meshless method; fixed kernel technique; reproducing kernel; point collocation; finite cloud method
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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 (C) 2001 John Wiley & Sons, Ltd.
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