On the polarizability and capacitance of the cube
(2013) In Applied and Computational Harmonic Analysis 34(3). p.445468 Abstract
 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... (More)
 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 nonsmooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3053368
 author
 Helsing, Johan ^{LU} and Perfekt, KarlMikael ^{LU}
 organization
 publishing date
 2013
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Spectral measure, Capacitance, Polarizability, Lipschitz domain, Electrostatic boundary value problem, Continuous spectrum, Layer potential, Sobolev space, Multilevel solver, Cube
 in
 Applied and Computational Harmonic Analysis
 volume
 34
 issue
 3
 pages
 445  468
 publisher
 Elsevier
 external identifiers

 wos:000316303100007
 scopus:84875229803
 ISSN
 1096603X
 DOI
 10.1016/j.acha.2012.07.006
 language
 English
 LU publication?
 yes
 additional info
 The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematics (Faculty of Sciences) (011015002), Numerical Analysis (011015004)
 id
 1e9f395390134fbe92f2cd07135331f9 (old id 3053368)
 alternative location
 http://www.maths.lth.se/na/staff/helsing/helsingACHA1252rev.pdf
 date added to LUP
 20160401 09:48:32
 date last changed
 20220217 03:27:27
@article{1e9f395390134fbe92f2cd07135331f9, abstract = {{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 nonsmooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials.}}, author = {{Helsing, Johan and Perfekt, KarlMikael}}, issn = {{1096603X}}, keywords = {{Spectral measure; Capacitance; Polarizability; Lipschitz domain; Electrostatic boundary value problem; Continuous spectrum; Layer potential; Sobolev space; Multilevel solver; Cube}}, language = {{eng}}, number = {{3}}, pages = {{445468}}, publisher = {{Elsevier}}, series = {{Applied and Computational Harmonic Analysis}}, title = {{On the polarizability and capacitance of the cube}}, url = {{https://lup.lub.lu.se/search/files/1272239/3878561.pdf}}, doi = {{10.1016/j.acha.2012.07.006}}, volume = {{34}}, year = {{2013}}, }