A field‐based finite element method for magnetostatics derived from an error minimization approach (original) (raw)

Comparison of different finite element formulations for 3D magnetostatic problems

IEEE Transactions on Magnetics, 1988

In this paper the results of several three-dimensional software packages for magnetostatlc field calculation using finite element method (FEM) are compared with regard to their accuracy and their computational time requirements. The different packages are based on the vectorpotentlal (VPOT). the reduced scalarpotential (RSP). and the total and reduced scalarpot ential (TSP+RSP). respectively.

The Finite Element Method Applied to the Magnetostatic and Magnetodynamic Problems

Finite Element Methods and Their Applications [Working Title], 2020

Modelling of realistic electromagnetic problems is presented by partial differential equations (FDEs) that link the magnetic and electric fields and their sources. Thus, the direct application of the analytic method to realistic electromagnetic problems is challenging, especially when modeling structures with complex geometry and/or magnetic parts. In order to overcome this drawback, there are a lot of numerical techniques available (e.g. the finite element method or the finite difference method) for the resolution of these PDEs. Amongst these methods, the finite element method has become the most common technique for magnetostatic and magnetodynamic problems.

Different finite element formulations of 3D magnetostatic fields

IEEE Transactions on Magnetics, 1992

Several flnlte element formulatlons of three dlmenslonal magnetostatlc flelds are reviewed In the paper. Both nodal and edge elements are consldered. The aim la to suggest remedles to some shorkomlngs of wldely used methods. Varlws formulatlons are compared based on results for Problem No. 13 of the TEAM Workshops, a nonllnear magnetostatic problem lnvolvlng thln Iron plates.

Numerical analysis of 3D magnetostatic fields

IEEE Transactions on Magnetics, 1991

The paper reviews formulations of three-dimensional magnetostatic fields for their finite element anal>sis. Partial differential equations and boundary conditions are set up f o r various kinds of potentials. Besides the method using t w o scalar potentials, several vector potential formulations are also discussed. Galerkin techniques combined with t h e finite element method are applied for the numerical solution of the boundary value problems. The effect of gauging t h e vector potential upon the numerical performance is investigated. Solutions b) different formulations t o a simple t e s t problem a s well a s t o a benchmark problem involving relatively thin saturated iron piates are presented. The latter is compared t o measured results.

A Finite Element Method for the Magnetostatic Problem in Terms of Scalar Potentials

Siam Journal on Numerical Analysis - SIAM J NUMER ANAL, 2008

The aim of this paper is to analyze a numerical method for solving the magnetostatic problem in a three-dimensional bounded domain containing prescribed currents and magnetic materials. The method discretizes a well-known formulation of this problem based on two scalar potentials: the total potential, defined in magnetic materials, and the reduced potential, defined in dielectric media and in non-magnetic conductors carrying currents. The topology of the magnetic materials is not assumed to be trivial, which leads to a multivalued potential. The resulting variational problem is proved to be well posed and is discretized by means of standard piecewise linear finite elements. Transmission conditions are imposed by means of a piecewise linear Lagrange multiplier on the surface separating the domains of both potentials. Error estimates for the numerical method are proved and the results of some numerical tests are reported to assess the performance of the method.

The Finite Element Method in Magnetics

The polarization method and the fixed point technique however, the parameter of the linear term must be selected in a special way. The last chapter is the collection of seven problems solved by the finite element method. The problems have been solved by using the user friendly graphical user interface and functions of COMSOL Multiphysics, which is a commercial finite element software. The authors want to express their grateful acknowledgement to Prof. Oszkár Bíró, Prof. Imre Sebestyén, Prof. Maurizio Repetto, Prof. Carlo Ragusa for their assistance during developing the nonlinear finite element procedures, to dr. Péter Kis and dr. János Füzi for their help in developing the scalar hysteresis measurements. The authors would like to express their thanks to Prof. György Fodor, Prof. Oszkár Bíró and Prof. Imre Sebestyén for the reading of the parts of the research and for the helpful and fruitful suggestions. The authors thank to Prof. Oszkár Bíró, dr. Péter Kis, dr. István Standeisky for reading of this book and making reviews. Their advices helped us to prepare this book better. We would like to express our special thanks to Prof. Oszkár Bíró for giving advices, many helps during studying the finite element method as well as the colleagues of the Group of Electromagnetic Theory,

A magnetostatic 2D comparison of local error estimators in FEM

IEEE Transactions on Magnetics, 1993

GRUCAD/EEL/CTC/UFSC/C.P. 476 88040-900 -Florian6polis -SC -Brasile.mai1 EELlADZ@BRUFSC.BITNET. Abstract-in this paper, three methods used in each element to test the accuracy for local error estimation to adaptive of the results.[2,3] mesh generation in finite element method are tested and compared. In the two first the errors are estimated from boundary conditions violation at the borders of the elements. In the third method, the error estimation i r reached from perturbation in the magnetic induction 8. Two examples are Or used to test the three methods: The magnetostatic analysis of a contactor and the calculation of forces exerted by permanent magnets. Al) Scalar Potential(fig.1) JB,dS = ne (1) S J~n I d s , + J~nZds, + .f~n,ds, = ne Sl s 2 s,

Comparison Between NEM and FEM in 2-D Magnetostatics Using an Error Estimator

IEEE Transactions on Magnetics, 2008

This communication deals with a comparison between two methods of discretization: the well known finite element method and the natural element method that is a meshless method. An error estimator, based on the nonverification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine.

An adaptive mixed formulation for 3D magnetostatics

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2000

ABSTRACT Cited By (since 1996): 1, Export Date: 19 July 2012, Source: Scopus, CODEN: CODUD, Language of Original Document: English, Correspondence Address: Alotto, P.; Univ of Genoa, Genoa, Italy, References: Alotto, P., Delfino, F., Molfino, P., Nervi, M., Penigia, I., A mixed face-edge finite element formulation for 3D magnetostatic problems (1998) IEEE Trans. on Magnetics, 34 (5), pp. 2445-2448;

Linear finite element method in axisymmetric magnetostatic problems

IEEE Transactions on Magnetics, 1992

If there is a long iron cylinder on the axis of rotational symmetry, the FEM with linear shape function for the computation of the angular component of the vector potential yields an i n c o m t solution. Based on a suitable weight factor in the expression for the z component of the flux density, new formulas for the coefficients of the linear