2012/03/27 by Johan Helsing, Helsing, Johan, Karl‐Mikael Perfekt +2 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Microwave and Dielectric Measurement Techniques #math-ph #math.AP #math.FA #math.MP #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1203.5997
33 pages, 7 figures
openalex publication_date 2012/03/27 · arxiv created 2012/06/14 · arxiv updated 2012/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.