On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents

Bíró, Oszkár; Preis, Kurt

doi:10.1109/20.34388

Cited by 641 publications

(211 citation statements)

References 20 publications

Supporting

Mentioning

210

Contrasting

Unclassified

Order By: Relevance

“…Different formulations using tree-cotree, or loop-tree decomposition [12][13][14][15][16], have to be sought when the frequency is low or the wavelength is long. Due to the low-frequency catastrophe encountered by E-H formulation, the vector potential formulation has become popular for solving low frequency problems [17][18][19][20][21][22][23][24][25][26][27][28][29]. This work will arrive at a general theory of vector potential formulation for inhomogeneous anisotropic media, together with the pertinent integral equations.…”

Section: Introductionmentioning

confidence: 99%

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

131

View full text Add to dashboard Cite

Abstract-The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic solutions that straddle both the quantum and classical physics regimes. The vector potential formulation using A and Φ (or A-Φ formulation) is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetics problems in inhomogenous media that can be extended to the anistropic case. An advantage of the resulting equations is their absence of catastrophic breakdown at low-frequencies. Hence, the usual differential equation solvers can be used to solve them over a wide range of scales and bandwidth. It is shown that the interface boundary conditions from the resulting equations reduce to those of classical Maxwell's equations. Also, the classical Green's theorem can be extended to such a formulation, resulting in an extinction theorem and a surface equivalence principle similar to the classical case. Moreover, surface integral equation formulations can be derived for piecewise homogeneous scatterers. Furthermore, the integral equations neither exhibit the low-frequency catastrophe nor the frequency imbalance observed in the classical formulation using E-H fields. The matrix representation of the integral equation for a PEC (perfect electric conductor) scatterer is given.

show abstract

Section: Introductionmentioning

confidence: 99%

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

131

View full text Add to dashboard Cite

show abstract

“…This problem can be solved using the finite element method [27,28], finite difference method [29] or boundary element method [30]. The latter technique is known to be fast compared to FEM or FDM, since it only discretizes the boundaries of the background and the internal features, and can be found appropriate for a limited range of problems including shape reconstruction of objects with homogeneous material distribution, whereas FEM or FDM are more general however they require meshing the entire problem leading to larger number of unknowns [20].…”

Section: Forward Model and Sensitivity Matrixmentioning

confidence: 99%

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

Dekdouk¹,

Ktistis²,

Armitage³

et al. 2016

PIER

View full text Add to dashboard Cite

Abstract-Magnetic Induction Tomography (MIT) is a newly developing technique of electrical tomography that in principle is able to map the electrical conductivity distribution in the volume of objects. The image reconstruction problem in MIT is similar to electrical impedance tomography (EIT) in the sense that both seek to recover the conductivity map, but differ remarkably in the fact that data being inverted in MIT is derived from induction theory and related sources of noise are different. Progress in MIT image reconstruction is still limited, and so far mainly linear algorithms have been implemented. In difference imaging, step inversion was demonstrated for recovering perturbations within conductive media, but at the cost of producing qualitative images, whilst in absolute imaging, linear iterative algorithms have mostly been employed but mainly offering encouraging results for imaging isolated high conductive targets.In this paper, we investigate the possibility of absolute imaging in 3D MIT of a target within conductive medium for low conductivity application (σ < 5 Sm −1 ). For this class of problems, the MIT image reconstruction exhibits non-linearity and ill-posedness that cannot be treated with linear algorithms. We propose to implement for the first time in MIT two effective inversion methods known in non-linear optimization as Levenberg Marquardt (LMM) and Powell's Dog Leg (PDLM) methods. These methods employ damping and trust region techniques for controlling convergence and improving minimization of the objective function. An adaptive version of Gauss Newton is also presented (AGNM), which implements a damping mechanism to the regularization parameter. Here, the level of penalty is varied during the iterative process. As a comparison between the methods, different criteria are examined from image reconstructions using the LMM, PDLM and AGNM. For test examples, volumetric image reconstruction of a perturbation within homogeneous cylindrical background is considered. For inversion, an independent finite element FEM software package Maxwell by Ansys is employed to generate simulated data using a model of a 16 channel MIT system. Numerical results are employed to show different performance characteristics between the methods based on convergence, stability and sensitivity to the choice of the regularization parameter. To demonstrate the effect of scalability of absolute imaging in MIT for more realistic problems, a human head model with an internal anomaly is used to produce reconstructions for different finer resolutions. AGNM is adopted here and employs the Krylov subspace method to replace the computationally demanding direct inversion of the regularized Hessian.

show abstract

“…Applying Equation (3) into the Galerkin's approximation using edge element basis function [13][14][15] can yield…”

Section: Forward Problem -Eddy Current Modelingmentioning

confidence: 99%

Two-Phase Low Conductivity Flow Imaging Using Magnetic Induction Tomography

Wei¹,

Soleimani²

2012

PIER

View full text Add to dashboard Cite

Abstract-Magnetic Induction Tomography (MIT) is a new and emerging type of tomography technique that is able to map the distribution of all three passive electromagnetic properties, however most of the current interests are focusing on the conductivity and permeability imaging. In an MIT system, coils are used as separate transmitters or sensors, which can generate the background magnetic field and detect the perturbed magnetic field respectively. Through switching technique the same coil can work as transceiver which can generate field at a time and detect the field at another time. Because magnetic field can easily penetrate through the non-conductive barrier, the sensors do not need direct contact with the imaging object. These non-invasive and contactless features make it an attractive technique for many applications compared to the traditional contact electrode based electrical impedance tomography. Recently, MIT has become a promising monitoring technique in industrial process tomography, for example MIT has been used to determine the distribution of liquidised metal and gas (high conductivity two phase flow monitoring) for metal casting applications. In this paper, a low conductivity two phase flow MIT imaging is proposed so the reconstruction of the low contrast samples (< 6 S/m) can be realised, e.g., gas/ionised liquid. An MIT system is developed to test the feasibility. The system utilises 16 coils (8 transmitters and 8 receivers) and an operating frequency of 13 MHz. Three different experiments were conducted to evaluate all possible situations of two phase flow imaging: 1) conducting objects inside a non-conducting background, 2) conducting objects inside a conducting background (low contrast) and 3) non-conducting objects inside a conducting background. Images are reconstructed using the linearised inverse method with regularisation. An experiment was designed to image the non-conductive samples inside a conducting

show abstract

On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents

Cited by 641 publications

References 20 publications

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

Two-Phase Low Conductivity Flow Imaging Using Magnetic Induction Tomography

Contact Info

Product

Resources

About