2018, a new year including new possibilities, new investigations and new discoveries.  We wish you all a successful and prosperous year!

With the release of SONOPEC (read here), Bonphysics B.V. ended the year 2017 well. To start 2018 well, we want to present you a publication by Bonphysics from 2013. Without the knowledge from the past, this new year might miss its chances.

The publication ‘Fully and partly divergence and rotation free interpolation of Magnetic fields’ is accepted by the ‘Journal of Electromagnetic Analysis and Applications’ at 9th of july in 2013 (click here for the original).
Results of the investigation of a new interpolation method, conducted and described by V.O. de Haan, lead to a substantiated recommendation for the use of this method in magnetic fields without rotation and divergence. This interpolation procedure uses the properties of a magnetic field in homogeneous linear materials without conducting current. By using this technique, the accuracy can be increased with a factor of ∆x/r (∆x refers to the grid size and r to the distance between the source and the interpolation point) with respect to the trilinear interpolation using exactly the same data points.

This study has been conducted because there was a lack of sufficient methods to obtain accurate knowledge about a vector field including an adequate spatial resolution in a short period of time.

Especially in the case of magnetic fields, calculations are time consuming and often impossible due to the required spatial resolution. Therefore, the magnetic fields have to be measured, these measurements are very time consuming too and the needed spatial resolution cannot be obtained.
Higher order interpolation schemes are needed because of these problems. Several interpolation procedures are known for the described magnetic field (rotation and divergence free) in absence of conducting currents and in a homogenous material. As stated in the publication, these have limitations such as not reaching the required accuracy or needing a large number of grid points. In general, these methods result in a field in the grid with finite divergence and rotation, which could possibly lead to unphysical results. These inadequacies can be remedied with the suggested new procedure: a divergence and rotation free interpolation of a vector field inside a 3D-rectangular grid, with an accuracy that is third order in grid size.

When you are interested in the complete methods, results and other conclusions, we recommend you to read the whole publication or contact us. This way knowledge acquired in 2013, can be used in 2018 to conduct further research.

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