A new interpolation method for rotation
and divergence free fields is presented. It is based on a suitable choice of a tricubic
interpolation scheme and reaches an accuracy of third order in grid size (Δx). With the interpolation method it is possible
to increase the accuracy with a factor of gridsize/distance with respect to the trilinear
interpolation method using exactly the same data points. Simulations for several
distances of dipoles (r) to the interpolation
area show that the maximum relative deviation is approximately 3(Δx/r)3 ppm.
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