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Analysis of a dimension splitting scheme for Maxwell equations with low regularity in heterogeneous media [revised]

Zerulla, Konstantin ORCID iD icon

Abstract:

We analyze a dimension splitting scheme for the time integration of linear Maxwell equations in a heterogeneous cuboid. The domain contains several homogeneous subcuboids, and serves as a model for a rectangular embedded waveguide. Due to discontinuities of the material parameters and irregular initial data, the solution of the Maxwell system has regularity below H$^{1}$. The splitting scheme is adapted to the arising singularities, and is shown to converge with order one in L$^{2}$. The error result only imposes assumptions on the model parameters and the initial data, but not on the unknown solution. To achieve this result, the regularity of the Maxwell system is analyzed in detail, giving rise to sharp explicit regularity statements. In particular, the regularity parameters are given in explicit terms of the largest jump of the material parameters. The analysis is based on semigroup theory, interpolation theory, and regularity analysis for elliptic transmission problems.


Volltext (Version 2) §
DOI: 10.5445/IR/1000142206/v2
Veröffentlicht am 05.05.2022
Volltext (Version 1) §
DOI: 10.5445/IR/1000142206
Veröffentlicht am 25.01.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 05.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000142206
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 38 S.
Serie CRC 1173 Preprint ; 2022/6
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Bemerkung zur Veröffentlichung Version 1 (01.2022) u.d.T.: Construction and analysis of an ADI splitting for Maxwell equations with low regularity in heterogeneous media
Externe Relationen Siehe auch
Schlagwörter Maxwell equations, heterogeneous media, splitting method, error bound, regularity analysis, elliptic transmission problem
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