PDE Eigenvalue Iterations with Applications in Two-dimensional Photonic Crystals

dc.contributor.authorAltmann, Robert
dc.contributor.authorFroidevaux, Marine
dc.date.accessioned2021-12-17T10:15:35Z
dc.date.available2021-12-17T10:15:35Z
dc.date.issued2018-07-30
dc.description.abstractThe first part of this paper is devoted to the approximative solution of linear and Hermitian eigenvalue problems where the differential operator satisfies a Garding inequality. For this, known iterative schemes for the matrix case such as the inverse power or Arnoldi method are extended to the infinite-dimensional case. This formally allows one to apply different spatial discretizations in each iteration step and thus, justifies the use of adaptive methods. The second part considers eigenvalue problems as they appear in two-dimensional models of photonic crystals for the computation of band-gaps. If the permittivity of the material is frequency-dependent, then this leads to a nonlinear eigenvalue problem. For this, we consider two strategies. First, a linearization combined with the application of the inverse power method and second, a direct application of Newton's iteration.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15907
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14680
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.othernonlinear eigenvalue problemen
dc.subject.otherphotonic crystalsen
dc.subject.otherinverse poweren
dc.subject.otherNewton iterationen
dc.titlePDE Eigenvalue Iterations with Applications in Two-dimensional Photonic Crystalsen
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.issuenumber2018, 05en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065N25 Eigenvalue problemsen
tub.subject.msc200065J10 Equations with linear operatorsen

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