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(a) The first main diagonal of approximated first order PT, í µí± (( for an ellipsoid where í µí± = 444 triangles at different values of conductivity, í µí± = 0.25, 0.5, 1.5, 10, 10 * , 10 U , 10 » and 10 ½ . (b) The second and third main diagonal of approximated first order PT, í µí± )) and í µí± ** for an ellipsoid where í µí± = 444 triangles at different values of conductivity, í µí± = 0.25, 0.5, 1.5, 10, 10 * , 10 U , 10 » and 10 ½ .
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Polarization tensor (PT) has been widely used in engineering application, particularly in electric and magnetic field areas. In this case, suitable method must be employed in the evaluation of PT in order to make sure that the tensor obtained is higher in its accuracy. Our aim in this paper is to provide simple and easy implemented method to comput...
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... if we use more elements (finer meshes) the numerical results would converge to the analytical solution. Figure 6 illustrates the behavior of first order PT as the conductivity increased. Similar patterns can be noticed in both sphere and ellipsoid geometry as we increase the conductivity. ...
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Citations
... Therefore, researchers have made numerous attempts to derive the formulas of the PT for some objects [10,11]. Conversely, some researchers focus on implementing different approaches to numerically compute the PT since it cannot be computed analytically [12,13]. Meanwhile, some researchers focus on exploring the properties of the PT theoretically [14,15] and validating the theoretical findings by presenting some numerical examples [16]. ...
The polarization tensor (PT) has been utilized in numerous applications involving electric and electromagnetic fields, such as metal detection, landmine detection, and electrical imaging. In these applications, the PT is implemented in the process of identifying object, where the object can be represented in the form of the first order PT. Thus, it is crucial to have an application that provides easy access to calculate the first order PT for the object. However, the existing application in the literature has some limitations, focusing solely on computing the first order PT for a prolate spheroid with semi axes and an oblate spheroid with semi axes . Therefore, the purpose of this study is to invent a graphical user interface (GUI) for the Spheroidal First Order Polarization Tensor (SFOPT) Toolkit which facilitates efficient computations and visualizations related to spheroids. The SFOPT Toolkit will be developed by using App Designer in MATLAB. The SFOPT interface integrates four essential functions: computation of the first order PT for a spheroid, classification of spheroidal types, three-dimensional visualization of spheroids, and determination of semi axes from the computed first order PT. Through illustrative examples, we demonstrate the effectiveness and versatility of the SFOPT framework, offering insights into its practical utility and potential applications in diverse fields. The reliability of the toolkit is also presented, and the findings shows the error of computations are small. The toolkit is a user-friendly application since the users can easily access it by downloading the application instead of running the coding themselves. Moreover, this toolkit can be a reference for researchers to compute the first order PT for a spheroid and determine the semi axes (size) of the spheroid from the given first order PT.
... For complex geometries, the computation of the related PT using BEM++ can be found in the study by Amad et al., [19]. Besides, Sukri et al., [20] has investigated the different orders of Gaussian quadrature in solving integral equations when computing the PT. In contrast to Khairuddin et al., [15][16][17], Sukri et al., [20] that used linear element in geometrical modelling for all involved objects, Sukri et al., [21] has proposed to use quadratic element in presenting three dimensional objects before computing the related PT. ...
... Besides, Sukri et al., [20] has investigated the different orders of Gaussian quadrature in solving integral equations when computing the PT. In contrast to Khairuddin et al., [15][16][17], Sukri et al., [20] that used linear element in geometrical modelling for all involved objects, Sukri et al., [21] has proposed to use quadratic element in presenting three dimensional objects before computing the related PT. ...
In order to enhance identification of objects in electrical imaging or metal detection, the polarization tensor is used to characterize the perturbation in electric or electromagnetic field due to the presence of the conducting objects. This is similar as describing the uniform fluid flow that is disturbed after a solid is immersed in the fluid during the study of fluid mechanics. Moreover, in some applications, it is beneficial to determine a spheroid based on the first order polarization tensor in order to understand what is actually represented by the tensor. The spheroid could share similar physical properties with the actual object represented by the polarization tensor. The purpose of this paper is to present how scaling on the matrix for the first order polarization tensor will affect the original spheroid represented by that first order polarization tensor. In the beginning, we revise the mathematical property regarding how scaling the semi axes of a conducting spheroid has an effect to its first order polarization tensor. After that, we give theoretical results with proofs on how scaling the matrix for the first order polarization tensor affects the volume and semi axes of the spheroid. Following that, some numerical examples are provided to further justify the theory. Here, different scalar factors will be used on the given first order polarization tensor before the new volume and semi axes of the spheroid are computed. In addition, we also investigate how the size of the scale on the first order polarization tensor influence the accuracy of computing the related volume and semi axes. In this case, it is found that a large error could occur to the volume and the semi axes when finding them by solving the first order PT with that has being scaled by a very large scaling factor or a too small scaling factor. A suggestion is then given on how to reduce the errors.
