On the polarizability and capacitance of the cube

Helsing, J. and Perfekt, K.-M. (2013) On the polarizability and capacitance of the cube. Applied and Computational Harmonic Analysis, 34 (3). pp. 445-468. ISSN 1063-5203 doi: 10.1016/j.acha.2012.07.006

Abstract/Summary

An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually every permittivity ratio for which it exists. For example, polarizabilities accurate to between five and ten digits are obtained (as complex limits) for negative permittivity ratios in minutes on a standard workstation. In passing, the capacitance of the unit cube is determined with unprecedented accuracy. With full rigor, we develop a natural mathematical framework suited for the study of the polarizability of Lipschitz domains. Several aspects of polarizabilities and their representing measures are clarified, including limiting behavior both when approaching the support of the measure and when deforming smooth domains into a non-smooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71746
Identification Number/DOI	10.1016/j.acha.2012.07.006
Refereed	Yes
Divisions	No Reading authors. Back catalogue items
Publisher	Elsevier
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