The Effect of Translation on the Approximated First Order Polarization Tensor of Sphere and Cube

Abstract

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.