Final Remarks and Conclusions
Chapter presents the final remarks and conclusions considering the numerical analyses and tools presented in the book.
Numerical analyses and tools presented in the book cover the most important aspects of the method of moment. In spite of the fact, that this method is not commonly used recently, it creates new possibilities in modelling the magnetic thin layers. Analyses presented in this book generalize the solution of magnetostatic systems with uniform square mesh. Moreover, practical implementation of this method in OCTAVE/MATLAB considers non-linear characteristics of magnetic materials (described e.g. by Jiles-Atherton model) as well as utilizes vectorization for efficient use of BLAS libraries. As a result, presented solutions fill important gap in the state of the art, enabling the optimisation of thin layers based magnetic devices, such as fluxgate sensors.
It should be stressed, that the results of modelling of magnetic field distribution are not always in line with intuitive expectations. These results strongly depend on the thin layer thickness. This phenomenon is especially important from the point of view of thin layer magnetic concentrators. In spite of quite large area, such concentrators may exhibit limited influence on magnetic field. In presented example the change of magnetic field was about 1.5%.
On the other hand presented methods enable optimisation of the core shapes of thin layer magnetic sensors, such as fluxgates. Example presented in the book covers ring-shaped sensors. However, presented methodology can be easily extended to frame-shaped or race track-shaped sensors, widely presented in the literature. It should be also stressed, that the result of optimisation of thin layer fluxgates are also far from intuitive guess. For example, in the presented case, achieved optimal proportion of inside/outside diameter was 0.561. This result confirms necessity of modelling such sensors during development process.
Numerical analyses in the method of moments are time and resources consuming. For this reason it is very important to develop optimised code. Presented vectorization of numerical calculations enable direct use of BLAS libraries in OCTAVE/MATLAB. This leads to radical increase of speed of calculations, which is important from the engineering point of view, and creates real possibility of including the method of moments based simulations in industrial development process.
To enable validation and further development of numerical methods presented in the book, all software used in examples is available at www.github.com/romanszewczyk/MoM/ Software is freely distributed on the base of open-source licence.
Obviously, presented book doesn’t cover all aspects of use of the method of moments for scientific and industrial purposes. However, the author hopes that it will be useful for engineers and researchers involved in development of devices utilizing different kinds of thin magnetic layers.