Numerical Computation of approximate Generalized Polarization Tensors

TL;DR

This paper introduces a semi-algebraic numerical method for computing Generalized Polarization Tensors, providing an accessible tool for analyzing steady state voltage perturbations caused by inhomogeneities.

Contribution

It presents a novel, easy-to-implement semi-algebraic approach as an alternative to integral equations for computing these tensors.

Findings

Method is easy to implement and integrate into MATLAB.

Provides a user-friendly graphical interface for non-experts.

Enables efficient computation of polarization tensors in practical scenarios.

Abstract

In this paper we describe a method to compute Generalized Polarization Tensors. These tensors are the coefficients appearing in the multipolar expansion of the steady state voltage perturbation caused by an inhomogeneity of constant conductivity. As an alternative to the integral equation approach, we propose an approximate semi-algebraic method which is easy to implement. This method has been integrated in a Myriapole, a matlab routine with a graphical interface which makes such computations available to non-numerical analysts.