Resolution of Nonlinear Magnetostatic Problems With a Volume Integral Method Using the Magnetic Scalar Potential | IEEE Journals & Magazine | IEEE Xplore

Resolution of Nonlinear Magnetostatic Problems With a Volume Integral Method Using the Magnetic Scalar Potential

Publisher: IEEE

Abstract:

An integral method using the magnetic scalar potential to solve nonlinear magnetostatic problems is developed. This method uses the range interactions between magnetizabl...View more

Abstract:

An integral method using the magnetic scalar potential to solve nonlinear magnetostatic problems is developed. This method uses the range interactions between magnetizable elements and it is particularly well suited to compute field in the air domain which do not need to be meshed. The collocation and Galerkin approaches are presented and compared to solve the nonlinear magnetostatic equation. Both methods need the construction of full interaction matrices which may be computed with analytical formulae. A Newton-Raphson method, in which the interaction matrix must be built at each solver iteration, is used to solve the nonlinear formulation. A modified fixed point scheme, in which the interaction matrix is built only once, is also proposed. 3-D numerical examples are given and results of the different methods are compared.
Published in: IEEE Transactions on Magnetics ( Volume: 49, Issue: 5, May 2013)
Page(s): 1685 - 1688
Date of Publication: 07 May 2013

ISSN Information:

Publisher: IEEE

I. Introduction

For devices with a huge volume free space compared to the active structure or high ratio between the object geometries, the finite element method leads to problems of accuracy and convergence to the solution [1]. In such case, integral methods can be attractive alternatives [2], [3]. Integral formulations of the magnetostatic field problems are particularly advantageous for the numerical solution of open-boundary problems which include ferromagnetic materials since only the active regions containing these materials need to be discretized. This paper gives in the first part a magnetostatic formulation in the framework of the integral volume methods in which the collocation and Galerkin methods are used to solve the magnetostatic equations. The computation of the source potential and of the integrals to built the interaction matrix are so presented in this part. The second part proposes the Newton-Raphson and modified fixed point method to solve the nonlinear formulation. The last one presents the results obtained for different applications.

References

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