Fig 3 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
The average elements, a of the approximated first order PT by quadratic elements for cube (size 0.04 0.04 0.04 and conductivity 1.5 k = ) against the total surface elements for the mesh, where, the center of the mass for the cube are respectively (0, 0, 0) , ( 0.02, 0, 0) − and (0.02, 0.02, 0.02) .
Source publication
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 co...
Context in source publication
Context 1
... this case, a is computed by the formula ( ) Finally, Fig. 3 shows the average of the elements for the approximated first order PT for cube against the total surface elements for each mesh used. Here, the total surface elements or the size of the mesh for the cube generated automatically in Netgen are 192, 768, and 3072. In addition, the first order PT for the cube of size 0.04 0.04 0.04 , in ...
Citations
... They also mentioned that the determinant for the first order PT of the spheroid remains the same before and after the spheroid is rotated. Morever, the study by Sukri et al., [24] had numerically shown that the first order PT of a few objects do not depend on the location of objects that is, the first order PT for an object does not change even though the center of gravity for the object is changed. Similarly, the numerical examples of the first order PT for translated and rotated objects was also conducted by Khairuddin et al., [25]. ...
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.
