caa a22 4500 605496838 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10543-014-0487-z doi (NATIONALLICENCE)springer-10.1007/s10543-014-0487-z Regularity for Maxwell eigenproblems in photonic crystal fibre modelling [Elektronische Daten] [Monique Dauge, Richard Norton, Robert Scheichl] The convergence behaviour and the design of numerical methods for modelling the flow of light in photonic crystal fibres depend critically on an understanding of the regularity of solutions to time-harmonic Maxwell equations in a three-dimensional, periodic, translationally invariant, heterogeneous medium. In this paper we determine the strength of the dominant singularities that occur at the interface between materials. By modifying earlier regularity theory for polygonal interfaces we find that on each subdomain, where the material in the fibre is constant, the regularity of in-plane components of the magnetic field are $$H^{2-\eta }$$ H 2 - η for all $$\eta > 0$$ η > 0 . This estimate is sharp in the sense that these components do not belong to $$H^2$$ H 2 , in general. However, global regularity is restricted by the presence of an interface between these subdomains and the interface conditions imply only $$H^{3/2-\eta }$$ H 3 / 2 - η regularity across the interface. The results are useful to anyone applying a numerical method such as a finite element method or a planewave expansion method to model photonic crystal fibres or similar materials. Springer Science+Business Media Dordrecht, 2014 Sobolev regularity nationallicence Maxwell eigenproblem nationallicence Kondratiev's method nationallicence Photonics nationallicence Photonic crystal fibres nationallicence Dauge Monique IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut Norton Richard Department of Physics, University of Otago, PO Box 56, 9054, Dunedin, New Zealand aut Scheichl Robert Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 59-80 0006-3835 55:1<59 2015 55 10543 https://doi.org/10.1007/s10543-014-0487-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0487-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dauge Monique IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut NATIONALLICENCE 700 1- Norton Richard Department of Physics, University of Otago, PO Box 56, 9054, Dunedin, New Zealand aut NATIONALLICENCE 700 1- Scheichl Robert Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 59-80 0006-3835 55:1<59 2015 55 10543