Fully and Partly Divergence and Rotation Free Interpolation of Magnetic Fields

¹ BonPhysics Research and Investigations B.V., Laan van Heemstede 38, 3297 AJ Puttershoek, The Netherlands.

Abstract

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 (Δ x ). With the interpolation method it is possible to increase the accuracy with a factor of grid size/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(Δ x / r ) 3 ppm.

KeywordsMagnetic FieldsInterpolationMagnetic Field Measurement

F. Mezei, C. Pappas and T. Gutberlet, “Neutron Spin Echo Spectroscopy. Basics, Trends and Applications,” Lecture Notes in Physics, Vol. 601, 2003. doi:10.1007/3-540-45823-9
G. Paschmann and P. W. Daly, “Analysis Methods for Multi-Spacecraft Data,” ESA Publications Division Keplerlaan, Noordwijk, 1998.
M. T. Vlaardingerbroek and J. A. den Boer, “Magnetic Resonance Imaging: Theory and Practice,” Springer-Verlag, Berlin, 2002.
C. P. McNally, “Divergence-Free Interpolation of Vector Fields from Point Values—Exact ▽B = 0 in Numerical Simulations,” Monthly Notices of the Royal Astronomical Society: Letters, Vol. 413, No. 1, 2011, pp. L76-L80. doi:10.1111/j.1745-3933.2011.01037.x
H. R. Kang, “Computational Color Technology,” SPIE Press Book, Cardiff, Vol. 159, 2006.
F. Lekien and J. Marsden, “Tricubic Interpolation in Three Dimensions,” Journal of Numerical Methods and Engineering, Vol. 63, No. 3, 2005, pp. 455-471. doi:10.1002/nme.1296

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Fully and Partly Divergence and Rotation Free Interpolation of Magnetic Fields

Abstract

References (6)