Some Properties of the First Order Polarization Tensor for 3-D Domains

Abstract

In this paper, numerical approximation and two properties of first order Polarization Tensor for 3-D domain are highlighted. Based on the definition of the generalized polarization tensor by integral equation, the quadrature method is adapted to simplify the approximation of the first order polarization tensor. Furthermore, the softwares MATLAB and Netgen Mesh Generator are used for computation purpose. Here, the numerical results obtained by following the method show reasonable convergence to the exact first order polarization tensor but at several known factors. Finally, these results are further discussed to demonstrate the transformation and types of the first order polarization tensor for few different objects. Keywords: Matrix; Mesh; Quadrature 2010 Mathematics Subject Classification: 65D30; 15A04; 45G05