Efficient integral equation method for the solution of 3-D magnetostatic problems

Hafla, W.; Buchau, A.; Groh, Friedemann; Rucker, W.M.

doi:10.1109/tmag.2005.844342

Cited by 29 publications

(11 citation statements)

References 12 publications

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“…The disadvantages of the collocation method are known and are noted by many authors who are investigating the method of boundary integral equations. In some works, it is proposed to solve the problem of collocation points using the Galerkin method to obtain a SLAE from the corresponding boundary integral equation [17][18][19]. Mathematically, this method leads to SLAE, the coefficients of which are expressed in terms of double integrals.…”

Section: Comparison Of a Constructed Numerical Model With Existing Apmentioning

confidence: 99%

“…At the same time, a simple solution was immediately found that allows one to escape from degeneracy. Obviously, SLAE obtained in [17] by the Galerkin method is also degenerate, but the authors do not write about this. -The approach proposed in this article can be generalized to other types of boundary secondary sources, for example, on sources such as a simple layer of magnetization currents [20][21][22].…”

Section: Comparison Of a Constructed Numerical Model With Existing Apmentioning

confidence: 99%

See 1 more Smart Citation

Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

Filippov¹,

Shuyskyy²

2019

PIER M

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A mathematical model is constructed for calculating a three-dimensional quasistationary electromagnetic field in a piecewise-homogeneous medium containing massive conductors which is excited by a variable magnetic field. The field is varying in time according to an arbitrary law. It is proposed to use the integral relation instead of the boundary condition written at a point, which allows one to get away from the problem of collocation points and at the same time increase the computational efficiency of the numerical model. The magnetic field is calculated for the case of the excitation of eddy currents in a conducting sample containing a cut of finite size. The results obtained are confirmed by natural experiments.

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Section: Comparison Of a Constructed Numerical Model With Existing Apmentioning

confidence: 99%

Section: Comparison Of a Constructed Numerical Model With Existing Apmentioning

confidence: 99%

Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

Filippov¹,

Shuyskyy²

2019

PIER M

View full text Add to dashboard Cite

show abstract

“…Usually, as � becomes higher, the computing accuracy by the SCM becomes worse because of the cancellation errors [8]- [11]. When � r = 1000, the results of the conventional method by use of Eq.…”

Section: Dielectric Cubic In Uniform Fieldmentioning

confidence: 99%

“…However, when the dielectric permittivity � becomes higher, the SCM is incapable of obtaining accurately E i because of the cancellation errors [8][9][10][11]. In order to investigate the electrostatic analyses in design of high voltage devices with high � from the viewpoint of industrial applications [12], we apply the BIEM for the magnetostatic analysis [7] so as to overcome the deficiency.…”

Section: Introductionmentioning

confidence: 99%

Electrostatic Analysis by Boundary Integral Equation with Loop Current and Surface Charge as Unknowns

Andjelic

Ishibashi

2013

Journal of the Japan Society of Applied Electromagnetics and Me

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In the electrostatic analysis, we usually treat the effect of polarization charges on dielectric surface and true charges on conductor surface. When we solve problems with high permittivity using the surface charge method, we cannot get accurate solutions due to cancellation errors. In this paper we propose a novel approach to solve the problems with high permittivity. The boundary integral equation in the proposed method is derived by replacing the polarization charges by loop currents instead of surface charges used in the surface charge method. The proposed method is effectively applicable because it contains only one unknown. Besides, even though the loop current gives originally scalar potentials, Biot-Savart law gives directly the electric flux density. Finally, we have compared the proposed method and surface charge method by solving some typical examples.

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“…The semi-analytical model presented in this paper addresses the more general case of the non linear regime by taking into account the nonlinearity of the B-H curve, characterizing the materials constituting the yoke and the pipe under test. For solving such a non-linear magnetostatic problem, the generalized boundary element method (BEMG) is widely used since the statement of the problem is determined by two equivalent scalar potentials: the surface charge density and the volume charge density [3,4,5]. Such numerical approach has the capability to compute the response of an arbitrary defect in the pipe.…”

Section: Introductionmentioning

confidence: 99%

Simulation of magnetic flux leakage: Application to tube inspection

Prémel¹,

Fnaeich²,

Djafa³

et al. 2012

AIP Conference Proceedings

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The detection of flaws in steel pipes using Magnetic Flux Leakage (MFL) consists in detecting magnetic flux leaks outside the pipe, either with a magnetic sensor or with an induction coil, while the pipe is rotating. In the Vallourec group, many NDT units use MFL for testing ferromagnetic pipes. In order to improve the performances of flaw detection, CEA LIST and the Vallourec Research Aulnoye (VRA) group are collaborating on MFL modelling. The aim is to be able to perform parametric studies thanks to a fast 3D numerical model dedicated to MFL systems. A simplified 2D geometry has already been derived for the development of first simulation tools. When considering the B-H curve of ferromagnetic materials, the non-linear magnetostatic problem can be solved with the generalized boundary element method (BEMG), which comes to the evaluation of two equivalent scalar potentials: the surface charge density and the volume charge density. When applying the Galerkin method for the discretization of integral equations, the particularity of this numerical model lies in the implementation of high order basis functions for the interpolation of the scalar unknowns. This paper presents some first numerical results for the numerical validation of the semi-analytical model.

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Efficient integral equation method for the solution of 3-D magnetostatic problems

Cited by 29 publications

References 12 publications

Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

Electrostatic Analysis by Boundary Integral Equation with Loop Current and Surface Charge as Unknowns

Simulation of magnetic flux leakage: Application to tube inspection

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