A Comparative Study of First Order Polarization in Spherical Structures: Exploring Numerical Approaches

Abstract

The first-order polarization tensor (PT) is the basic term of the generalized polarization tensor (GPT), which represents the asymptotic series in the form of an integral equation. It is crucial in engineering applications, such as material characterization and electromagnetic modeling. Many approaches have been implemented to enhance computational efficiency and accuracy in the numerical computation of the first-order polarization tensor. Among these methods, two have received the attention of the researchers, but their comparative effectiveness remains uncertain. Hence, this study aims to analyse and compare these two methods in approximating the first-order polarization tensor for a specific object inclusion, the sphere. The methodology involves numerical simulations where the performance of both methods is observed. From the results obtained, both methods satisfy the theoretical statement that as the number of mesh discretization increases, the accuracy of the numerical simulations improves. Two types of software are used in this study: Netgen Mesh Generator and MATLAB, which assist in the pre-processing, processing, and post-processing stages of numerical computation. The simulation and numerical examples will help verify the comparative analysis of both methods.