Identification of conductivity and permittivity in a pulsed electric field model

Abstract

We shall investigate the mathematical identification of the conductivity and permittivity in a pulsed electric field model for biological media. The conductivity and permittivity of the media are highly discontinuous, so their identifications are formulated into an output least-squares nonlinear minimization with BV-regularization. The regularizing effects and mathematical properties of the proposed regularizing system are analysed and verified. Then, the concerned nonlinear minimization problem is approximated by a fully discrete finite element method, and the convergence of the approximation is demonstrated.

Keywords:

• Conductivity; permittivity; electric field model; identification; regularization

AMS Subject Classifications:

• 65M60; 78M30

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Jun Zou was substantially supported by Hong Kong RGC grants [Projects 405513 and 14306814].