We propose a new method for constructing a polyspline on annuli, i.e. a C2 surface on ℝ2 \ {0}, which is piecewise biharmonic on annuli centered at 0 and interpolates smooth data at all interface circles. A unique surface is obtained by imposing Beppo Levi conditions on the innermost and outermost annuli, and one additional restriction at 0: either prescribing an extra data value, or asking that the surface is non-singular. We show that the resulting Beppo Levi polysplines on annuli are in fact thin plate splines, i.e. they minimize Duchon's bending energy.
Bejancu, A. (2013). Thin plate splines for transfinite interpolation at concentric circles. Mathematical Modelling and Analysis, 18(3), 446-460. https://doi.org/10.3846/13926292.2013.807317
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