Boundary element analysis of 3-D magnetostatic problems using scalar potentials

Rucker, W.M.; Magele, Christian; Schlemmer, E.; Richter, K.R.

doi:10.1109/20.123874

Cited by 19 publications

(9 citation statements)

References 5 publications

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“…The boundary element formulation used in this study is based on eight-noded quadrilateral isoparametric surface patches [12,14]. Any point r q on the surface of a boundary element (BE) is described by second-order shape functions W fc (£ 77) and nodes r fc s Γ, = 1 k=l (23)…”

Section: Forward Calculations Using the Boundary Element Methodsmentioning

confidence: 99%

“…In the following a method is described for solving the bioelectric forward problem based on finite two-dimensional (2D) Fourier series representations. In the boundary element solution the spherical volume conductor was modeled by 256 eight-noded quadrilateral isoparametric boundary elements (BEMs) [12]. We have developed an ellipsoid approximation combined with a double Fourier series approximation method to describe the boundary surfaces of a volume conductor [19].…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Fourier Representation Used in the Bioelectric Forward Problem - Zweidimensionale Fourier-Darstellung, angewandt im bioelektrischen Vorwärtsproblem

Wach

Lafer²,

Tilg³

et al. 1999

Biomedizinische Technik/Biomedical Engineering

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The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.Schlüsselwörter: Bioelektrizität, doppelte Fourierreihen, diskrete Fouriertransformation, boundary element method, bioelektrisches Vorwärts-Problem Ziel dieser Studie war die Anwendung der diskreten zweidimensionalen Fouriertransformation zur Lösung der Integralgleichung im bioelektrischen Vorwärtsproblem. Das Potential, der Quellterm und der Kern der Integralgleichung wurden als gleichmäßig diskret abgetastet angenommen. Somit können die kontinuierlichen Funktionen des Problems durch deren diskrete Fouriertransformierte im räumlichen Frequenzbereich dargestellt werden. Die Methode wurde zur Berechnung des Potentials auf einer homogenen leitfähigen Kugel angewandt. Die Integralgleichung für das Potential wurde im räumlichen Frequenzbereich gelöst. Das Potential in den Abtastpunkten wurde durch Anwendung der inversen Fouriertransformation berechnet. Die Lösung der vorgestellten Methode wurde mit einer analytischen Lösung und mit einer Lösung durch Anwendung der Boundary Element-Methode verglichen. Isoparametrische quadrilaterale Boundary-Elemente wurden zur Modellierung des kugelförmigen Volumenleiters herangezogen. In der vorgestellten Methode wurde die sphärische Oberfläche durch eine parametrische Approximation der Randelemente beschrieben.

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Section: Forward Calculations Using the Boundary Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Fourier Representation Used in the Bioelectric Forward Problem - Zweidimensionale Fourier-Darstellung, angewandt im bioelektrischen Vorwärtsproblem

Wach

Lafer²,

Tilg³

et al. 1999

Biomedizinische Technik/Biomedical Engineering

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“…The main equations for magnetostatic problems are given by Rucker et al, 1992;Bõ Âro Â et al, 1993):…”

Section: Integral Field Equationsmentioning

confidence: 99%

Analysis of magnetostatic field for some class of inhomogeneous problems by BEM

Kurgan

2001

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Presents an application of the boundary element method to the analysis of magnetic fields in materials for which permeability depends non‐linearly on spatial co‐ordinates. A new approach is proposed, which relates the Green’s function for non‐linearly dependent permeability to Green’s function of the Laplace equation in free space by adequate variable transformation. This can be done for very broad class magnetic permeabilities. These permeable functions, which cannot be directly used in such transformations, can be approximated by series of admissible functions.

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“…The magnetostatic analysis by the boundary integral equation (BIE) derived from the scalar potential given in the book by Stratton (1941) is one of the basic numerical approaches and many papers have been reported (Rucker and Richter, 1988;Koizumi et al, 1990;Sawa and Hirano, 1990;Rucker et al, 1992, Minciunescu, 1998Buchau et al, 2003Buchau et al, , 2007. They utilize the scalar potential w H for the magnetic field H, and derive the BIEs with two unknowns of single and double layer charges,ŝ s andŝ d as the state variables.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear magnetostatic BEM formulation using one unknown double layer charge

Ishibashi

Andjelic²

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -The purpose of this paper is to solve generic magnetostatic problems by BEM, by studying how to use a boundary integral equation (BIE) with the double layer charge as unknown derived from the scalar potential. Design/methodology/approach -Since the double layer charge produces only the potential gap without disturbing the normal magnetic flux density, the field is accurately formulated even by one BIE with one unknown. Once the double layer charge is determined, Biot-Savart's law gives easily the magnetic flux density. Findings -The BIE using double layer charge is capable of treating robustly geometrical singularities at edges and corners. It is also capable of solving the problems with extremely high magnetic permeability. Originality/value -The proposed BIE contains only the double layer charge while the conventional equations derived from the scalar potential contain the single and double layer charges as unknowns. In the multiply connected problems, the excitation potential in the material is derived from the magnetomotive force to represent the circulating fields due to multiply connected exciting currents.

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Boundary element analysis of 3-D magnetostatic problems using scalar potentials

Cited by 19 publications

References 5 publications

Two-Dimensional Fourier Representation Used in the Bioelectric Forward Problem - Zweidimensionale Fourier-Darstellung, angewandt im bioelektrischen Vorwärtsproblem

Two-Dimensional Fourier Representation Used in the Bioelectric Forward Problem - Zweidimensionale Fourier-Darstellung, angewandt im bioelektrischen Vorwärtsproblem

Analysis of magnetostatic field for some class of inhomogeneous problems by BEM

Nonlinear magnetostatic BEM formulation using one unknown double layer charge

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