On the polarizability and capacitance of the cube
(2013) In Applied and Computational Harmonic Analysis 34(3). p.445-468- 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 non-smooth 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, Karl-Mikael 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
- 1096-603X
- 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
- 1e9f3953-9013-4fbe-92f2-cd07135331f9 (old id 3053368)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/helsingACHA1252rev.pdf
- date added to LUP
- 2016-04-01 09:48:32
- date last changed
- 2022-02-17 03:27:27
@article{1e9f3953-9013-4fbe-92f2-cd07135331f9,
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 non-smooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials.}},
author = {{Helsing, Johan and Perfekt, Karl-Mikael}},
issn = {{1096-603X}},
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 = {{445--468}},
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}},
}