Magnetostatic Modelling of Thin Layers Using the Method of Moments And Its Implementation in Octave/Matlab pp 51-100 | Cite as
Analysis of 1D, 2D and 3D Systems Using the Method of Moments
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Abstract
This chapter presents the analyse of 1D, 2D and 3D systems from the point of view of the method of moments. The sets of equations for modelling of each case are elaborated. Special stress was made on the generalized description of thin layer systems, modelled as 2D systems. Chapter presents also the consideration of nonlinearity in magnetization process of thin layer (on the base of Jiles-Atherton model) as well as the vectorization of the equations for 2D systems description, enabling fast solution using recently produced processors.
References
- 1.Harrington RF (1968) Field computation by moment methods. WileyGoogle Scholar
- 2.Chadebec O, Rouve LL, Coulomb JL (2002) New methods for a fast and easy computation of stray fields created by wound rods. IEEE Trans Magn 38:517CrossRefGoogle Scholar
- 3.
- 4.
- 5.Delevoye E, Audoin M, Beranger M, Cuchet R, Hida R, Jager T (2008) Microfluxgate sensors for high frequency and low power applications. Sens Actuators A 145–146:271–277CrossRefGoogle Scholar
- 6.Soft Magnetic Materials Market by Material Type (Soft Ferrite, Electrical Steel, Cobalt), Application (Motor, Transformer, Alternator), End User Industry (Automotive, Electronics & Telecommunications, Electrical)—Global Forecast to 2026. Report CH 4731, http://www.marketsandmarkets.com/Market-Reports/soft-magnetic-material-market-206182334.html
- 7.Valadeiro J, Cardoso S, Macedo R, Guedes A, Gaspar J, Freitas PP (2016) Hybrid Integration of magnetoresistive sensors with MEMS as a strategy to detect ultra-low magnetic fields. Micromachines 7(5):88CrossRefGoogle Scholar
- 8.Golub GH, Welsch JH (1969) Calculation of gauss quadrature rules. Math Comput 23:221MathSciNetCrossRefGoogle Scholar
- 9.Burden RL, Faires JD (2000) Numerical analysis. Brooks/ColeGoogle Scholar
- 10.Szewczyk R, Nowicki M, Rzeplińska-Rykała K (2016) Models of magnetic hysteresis loops useful for technical simulations using finite elements method (FEM) and method of moments (MoM). Adv Intell Syst Comput 543:82Google Scholar
- 11.Szewczyk R, Frydrych P (2017) Optimisation of frame-shaped fluxgate sensor core made of amorphous alloy using generalized magnetostatic method of moments. Acta Phys Pol A 131:660CrossRefGoogle Scholar
- 12.Kittel C (2005) Introduction to solid state physics. WileyGoogle Scholar
- 13.Szewczyk R (2016) Technical B–H saturation magnetization curve models for SPICE, FEM and MoM simulations. J Autom Mobile Robot Intell Syst 10:3Google Scholar
- 14.Heckbert PS (1994) Graphics gems. Academic PressCrossRefGoogle Scholar
- 15.Chadebec O, Coulomb JL, Bongiraud JP, Cauffet G, Le Thiec P (2002) Recent improvements for solving inverse magnetostatic problem applied to thin shells. IEEE Trans Magn 38:1005CrossRefGoogle Scholar
- 16.Chadebec O, Coulomb J-L, Janet F (2006) A review of magnetostatic moment method. IEEE Trans Magn 42:515CrossRefGoogle Scholar
- 17.Szewczyk R (2017) Generalization of magnetostatic method of moments for thin layers with regular rectangular grids. Acta Phys Pol A 131:845CrossRefGoogle Scholar
- 18.Jackiewicz D, Szewczyk R, Bienkowski A, Kachniarz M (2015) New methodology of testing the stress dependence of magnetic hysteresis loop of the L17HMF heat resistant steel casting. J of Autom Mobile Robot Intell Syst 9:52Google Scholar
- 19.Jiles DC, Thoelke JB (1989) Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops. IEEE Trans Magn 25:3928CrossRefGoogle Scholar
- 20.Biedrzycki R, Jackiewicz D, Szewczyk R (2014) Reliability and efficiency of differential evolution based method of determination of Jiles-Atherton model parameters for X30Cr13 corrosion resisting martensitic steel. J Autom Mobile Robot Intell Syst 8:63. https://doi.org/10.14313/JAMRIS_4-2014/39CrossRefGoogle Scholar
- 21.
- 22.Kahaner D, Moler C, Nash S (1989) Numerical methods and software. Prentice–HallGoogle Scholar
- 23.Coleman TF, Li Y (1994) On the convergence of reflective newton methods for large-scale nonlinear minimization subject to bounds. Math Progr 67(2):189–224CrossRefGoogle Scholar
- 24.Huang TZ, Zhang Y, Li L, Shao W, Lai S (2009) Modified incomplete Cholesky factorization for solving electromagnetic scattering problems. Prog Electromagn Res 13:41–58CrossRefGoogle Scholar
- 25.Dongarra JJ, Du Croz J, Hammarling S, Duff IS (1990) A set of level 3 basic linear algebra subprograms. ACM Trans Math Softw 16:1CrossRefGoogle Scholar
- 26.
- 27.Zhu T, Feng P, Li X, Li F, Rong Y (2013) The study of the effect of magnetic flux concentrator to the induction heating system using coupled electromagnetic-thermal simulation model. In: 2013 International conference on mechanical and automation engineering, Jiujang, 2013, pp 123–127Google Scholar
- 28.
- 29.Varma RAR (2014) Design of degaussing system and demonstration of signature. Physics Procedia 54:174–179CrossRefGoogle Scholar
- 30.
- 31.Goto K, Van De Geijn R (2008) High-performance implementation of the level-3 BLAS. ACM Trans Math Softw 35:1MathSciNetCrossRefGoogle Scholar
- 32.Lozito GM, Fulginei FR, Salvini A (2015) On the generalization capabilities of the ten-parameter Jiles-atherton model. Math Prob Eng 2015(715018):13. https://doi.org/10.1155/2015/715018MathSciNetCrossRefGoogle Scholar
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