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

We introduce xed, moving and multiple xed 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 xed, moving and multiple xed kernel approaches are identical to the xed, moving and multiple xed least squares approaches. A nite cloud method, which combines collocation with a xed kernel technique for the construction of interpolation functions, is presented as a true meshless technique for the numerical solution of partial di erential equations. Numerical results are presented for several oneand two-dimensional problems, including examples from elasticity, heat conduction, thermoelasticity, Stokes ow and piezoelectricity