Numerical computation of approximate generalized polarization tensors

Abstract

In this article 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.

Keywords:

• generalized polarization tensors
• impedance tomography
• layer potentials
• semi-algebraic numerical method

AMS Subject Classifications::

• 35J25
• 45Q05; 45B05
• 65N38
• 78M25

Acknowledgements

Yves Capdeboscq is supported by the EPSRC Science and Innovation award to the Oxford Centre for Nonlinear PDE (EP/E035027/1). This work was completed in part while Anton Bongio Karrman was visiting OxPDE during a Summer Undergraduate Research Fellowship awarded by the California Institute of Technology in 2010, and he would like to thank the Centre for the wonderful time he had there.