Use of tensor product splines in magnet optimization

Variational metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated