Magnetostatic Modelling of Thin Layers Using the Method of Moments And Its Implementation in OCTAVE/MATLAB (eBook)

Foreword 6
Contents 7
1 Introduction 9
2 Magnetic Materials and Magnetization Process 11
2.1 Maxwell Equations and Magnetostatic Simplification 11
2.2 Physical Principles of Magnetization Process 13
2.3 Overview of Soft Magnetic Materials 17
2.4 Models of Magnetic Characteristics of Soft Magnetic Materials 20
2.4.1 Phenomenological Models 20
2.4.2 Jiles-Atherton Model 22
2.4.3 Preisach Model 27
References 29
3 Thin-Layer Based Devices 32
3.1 Fluxgates with Thin Layer Cores 32
3.2 Thin Layer Magnetic Flux Concentrators 38
3.3 Ships and Other Nut-Shell Objects 40
References 42
4 Magnetostatic Modelling 43
4.1 Finite Elements Method 43
4.1.1 Principles of Finite Elements Method 43
4.1.2 Meshing and Discretization 44
4.1.3 Solving Partial Differential Equations 46
4.1.4 Interpolation and Presentation of the Results 47
4.1.5 Limitations of the Finite Element Method 51
4.2 Method of the Moments 53
4.2.1 Magnetic Dipole 53
4.2.2 Demagnetization of Magnetic Elements 54
References 55
5 Analysis of 1D, 2D and 3D Systems Using the Method of Moments 57
5.1 Thin Rod 57
5.2 Cylindrical Rod 61
5.3 Flat Rod 67
5.4 Generalization of the Method of Moments for Rods 70
5.5 Thin Layer 74
5.5.1 Thin Layer with Uniform Mesh 74
5.5.2 Thin Layer with Adaptive Mesh 86
5.6 3D Objects 90
5.6.1 Thin Shells 90
5.6.2 Bulk Objects 93
5.7 Considering Non-linear Magnetization Characteristic 93
5.8 Solving Large Systems of Linear Equations 101
5.9 Optimisation of Calculations 102
References 105
6 Practical Examples 107
6.1 Optimisation of the Shape of Thin Layer, Ring-Shaped Fluxgate Sensor 107
6.2 Analysis of Thin Layer Magnetic Flux Concentrator 108
Reference 112
7 Final Remarks and Conclusions 113