Describing the perturbation in electric or electromagnetic fields due to conductivity contrast could be essential to improve many industrial applications. The applications include electrical imaging such as electrical impedance tomography, electrical resistivity tomography and metal detectors. In this case, understanding the perturbation helps, for examples, to improve reconstruction of images for medical purposes or reduce the possibility of detecting nonthreat objects during security screening with metal detectors. One way to describe the perturbation in electric or electromagnetic fields due to the presence of a conducting object in the region of the field is to use the terminology called as polarization tensor, where, polarization tensor can then be used to describe and characterize the presented object. Mathematically, polarization tensor can be defined in terms of boundary value problems of a PDE or also as integral equations in an asymptotic series. In this paper, the applications of polarization tensor are highlighted specifically to characterize object. The examples included are in the natural electric fish and also in an artificial intelligence. It is proposed to relate all studies in the future to improve the related applications using polarization tensor.

Throughout this paper, the translation effect on the first order polarization tensor approximation for different type of objects will be highlighted. Numerical integration involving quadratic element as well as linear element for polarization tensor approximation will be presented. Here, we used different positions of an object of fixed size and conductivity when computing the first order polarization tensor. From the numerical results of computed first order polarization tensor, the convergence for every translation is observed. Moreover, discretization of the geometric objects into triangular meshes was done by using meshing software called NETGEN mesh generator while for the numerical computation, MATLAB software was used. We found that the translation has no effect on the approximated first order PT for sphere and cube after we have computed the first order PT for both geometries with a few center of masses. The numerical results of approximated first order polarization tensor is plotted by comparing the numerical results with analytical solution provided.

Polarization tensor (PT) is a classical terminology in fluid mechanics and theory of electricity that can describe geometry in a specific boundary domain with different conductivity contrasts. In this regard, the geometry may appear in a different size, and for easy characterizing, the usage of PT to identify particular objects is crucial. Hence, in this paper, the first order polarization tensor for different types of object with a diverse range of sizes are presented. Here, we used three different geometries: sphere, ellipsoid, and cube, with fixed conductivity for each object. The software Matlab and Netgen Mesh Generator are the essential mathematical tools to aid the computation of the polarization tensor. From the analytical results obtained, the first order PT for sphere and ellipsoid depends on the size of both geometries. On the other hand, the numerical investigation is conducted for the first order PT for cube, since there is no analytical solution for the first order PT related to this geometry, to further verify the scaling property of the first order PT due to the scaling on the size of the original related object. Our results agree with the previous theoretical result that the first order polarization tensor of any geometry will be scaled at a fixed scaling factor according to the scaling on the size of the original geometry.

Presented in this paper is a computational approach that uses higher order Gaussian quadrature to improve the accuracy of the evaluation of an integral. The transformation from ξη space (standard Gaussian) to st space (higher order Gaussian) were shown throughout this paper. Not even that, the efficacy of this higher order Gaussian quadrature were tested by implementing and comparing it with standard Gaussian quadrature over the same integral. Results shown that the evaluation of an integral by using higher order Gaussian quadrature provide accurate and converge results compared to an integral using standard Gaussian quadrature.