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Natural neighbor (n-n) interpolation
[1,2,3] is a
multivariate data interpolation method, which has primarily
been used in data interpolation and modeling of
geophysical phenomena. See [4] for a review on
scattered data interpolation in multi-dimensions. Natural
neighbor interpolation relies on concepts, such as
Voronoi diagrams [5] and Delaunay
tessellations [6] in computational geometry
[7,8], in order to construct the
interpolant. It is a weighted average method, where the
weights are area-based, as opposed to Shepard's
interpolant (to cite an example), where distance-based
weights are used. In spite
of its fairly simple structure, sound theoretical basis for
construction, and desirable smoothness properties, n-n
interpolation has seemingly received little attention in the area
of multivariate data interpolation, when compared to
other interpolation/approximation schemes such as Shepard's
interpolant, moving least squares approximants, radial
basis functions, or Hardy's multiquadrics. Recent
work on n-n interpolation [9] and
its application to the solution of partial differential
equations [10]
does exemplify the potential of the Natural Element
Method (NEM), and hence begs the
question if it could find possible applications in the field of
computational solid/fluid mechanics. This note, in the same spirit,
attempts to give a brief introduction to the interpolation scheme
and its implementation in a Galerkin-based formulation (NEM)
to solve partial differential equations. The interested reader
can refer to the references (and the references therein)
for further details.

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*N. Sukumar*