2020
DOI: 10.3390/en13246515
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Detailed Analytical Approach to Solve the Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) Problem for Three-Layer Objects

Abstract: This paper is devoted to an analytical approach to the magnetoacoustic tomography with magnetic induction (MAT-MI) problem for three-layer low-conductivity objects. For each layer, we determined closed-form analytical expressions for the eddy current density and Lorentz force vectors based on the separation of variables method. Next, the analytical formulas were validated with numerical solutions obtained with the help of the finite element method (FEM). Based on the acoustic dipole radiation theory, the influ… Show more

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Cited by 7 publications
(3 citation statements)
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References 33 publications
(144 reference statements)
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“…Considering the irregular conductivity distribution problem, a mathematical framework and an optimal control method for reconstructing the anisotropic conductivity tensor were proposed by the Ecole Normale Supérieure de Paris [7] , which proved the convergence of the algorithm. Researchers from the Nanjing Normal University theoretically derived a MAT-MI for a single-layer cylindrical model under an anisotropic conductivity tensor and analyzed its effect [8][9][10][11] . For cylindrical models with abrupt changes in the conductivity boundary, the signal generated at the boundary was demonstrated to be determined by the components of the anisotropic conductivity tensor along the x and y directions.…”
Section: Magnetoacoustic Tomographymentioning
confidence: 99%
“…Considering the irregular conductivity distribution problem, a mathematical framework and an optimal control method for reconstructing the anisotropic conductivity tensor were proposed by the Ecole Normale Supérieure de Paris [7] , which proved the convergence of the algorithm. Researchers from the Nanjing Normal University theoretically derived a MAT-MI for a single-layer cylindrical model under an anisotropic conductivity tensor and analyzed its effect [8][9][10][11] . For cylindrical models with abrupt changes in the conductivity boundary, the signal generated at the boundary was demonstrated to be determined by the components of the anisotropic conductivity tensor along the x and y directions.…”
Section: Magnetoacoustic Tomographymentioning
confidence: 99%
“…Due to the limitations of invasive methods of process monitoring, more and more attempts are being made to use noninvasive tomographic methods, i.e., electrical capacitance tomography (ECT) [24,44,45,47], electrical impedance tomography (EIT) [10,11,22,29,41], magnetoacoustic tomography [48,49], electrical resistance tomography [27,38,46], ultrasonic tomography [19,21,31], or computed tomography using radiation X [3,30].…”
Section: Introductionmentioning
confidence: 99%
“…It is readily available, and common, and is widely used in diagnosis and inspection. Of the numerous computed tomography methods based on physical phenomena such as electrical resistivity tomography (ERT) [4], electrical capacitance tomography (ECT) [3], electrical impedance tomography (EIT) [2], radio wave tomography and localization [5], X-ray tomography [6] or magnetism tomography [7], ultrasound tomography (UST) [8] is a commonly used method in medicine and industry [9,10]. UST is an imaging technique that exploits the properties of acoustic wave transmittance through tissues and materials [11].…”
Section: Introductionmentioning
confidence: 99%