A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model

dc.contributor.authorSchmidt, Kersten
dc.contributor.authorChernov, Alexey
dc.date.accessioned2021-12-17T10:10:02Z
dc.date.available2021-12-17T10:10:02Z
dc.date.issued2012-11-05
dc.description.abstractWe introduce tools for a unified analysis and a comparison of impedance transmission conditions (ITCs) for thin conducting sheets within the time-harmonic eddy current model in two dimensions. The first criterion is the robustness with respect to the frequency or skin depth, that means if they give meaningful results for small and for large frequencies or conductivities. As a second tool we study the accuracy for a range of sheet thicknesses and frequencies for a relevant example, and analyse finally their asymptotic order in different asymptotic regimes. For the latter we write all the ITCs in a common form and show how they can be realised within the finite element method. Two new conditions which we call ITC-2-0 and ITC-2-1 are introduced in this article which appear in a symmetric form. They are derived by asymptotic expansions in the asymptotic regime of constant ratio between skin depth and thickness like those in [26]. We analyse these ITCs in comparison with the often used perfect electric boundary condition, the shielding element by Nakata et.al. [23], the thin layer impedance boundary conditions by Mayergoyz and Bedrosian [22] and a family of ITCs derived by asymptotic expansions in the asymptotic regime of constant shielding by Schmidt and Tordeux [28]. Our analysis shows the superiority of the transmission conditions derived by asymptotic expansions where especially the worst-case error level of the ITC-2-1 is remarkably lower than for all the other conditions.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15732
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14505
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherimpedance transmission conditionsen
dc.subject.otherthin conducting sheetsen
dc.subject.otherasymptotic expansionsen
dc.titleA unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current modelen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2012, 36en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsen
tub.subject.msc200035C20 Asymptotic expansionsen
tub.subject.msc200035J25 Boundary value problems for second-order, elliptic equationsen
tub.subject.msc200041A60 Asymptotic approximations, asymptotic expansionsen
tub.subject.msc200035B40 Asymptotic behavior of solutionsen
tub.subject.msc200078M30 Variational methodsen
tub.subject.msc200078M35 Asymptotic analysisen

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