On the polarizability and capacitance of the cube

Summary, in English

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.

• Author: Johan Helsing; Karl-Mikael Perfekt
• Department/s: Mathematics (Faculty of Engineering); Mathematics (Faculty of Sciences); Harmonic Analysis and Applications; eSSENCE: The e-Science Collaboration
• Publishing year: 2013
• Language: English
• Pages: 445-468
• Publication/Series: Applied and Computational Harmonic Analysis
• Volume: 34
• Issue: 3
• Full text: - 951 kB; Download statistics
• Links: http://www.maths.lth.se/na/staff/helsing/helsingACHA1252rev.pdf; http://dx.doi.org/10.1016/j.acha.2012.07.006
• Document type: Journal article
• Publisher: Elsevier
• Topic: Mathematics
• Keywords: Spectral measure; Capacitance; Polarizability; Lipschitz domain; Electrostatic boundary value problem; Continuous spectrum; Layer potential; Sobolev space; Multilevel solver; Cube
• Status: Published
• Research group: Harmonic Analysis and Applications; Harmonic Analysis and Applications
• ISBN/ISSN/Other: ISSN: 1096-603X