On the polarizability and capacitance of the cube
Författare
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.
Avdelning/ar
- Matematik LTH
- Matematik (naturvetenskapliga fakulteten)
- Harmonic Analysis and Applications
- eSSENCE: The e-Science Collaboration
Publiceringsår
2013
Språk
Engelska
Sidor
445-468
Publikation/Tidskrift/Serie
Applied and Computational Harmonic Analysis
Volym
34
Issue
3
Fulltext
- Available as PDF - 951 kB
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Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- Spectral measure
- Capacitance
- Polarizability
- Lipschitz domain
- Electrostatic boundary value problem
- Continuous spectrum
- Layer potential
- Sobolev space
- Multilevel solver
- Cube
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 1096-603X