Compact RBF meshless methods for photonic crystal modelling
Compact RBF meshless methods for photonic crystal modelling
Meshless methods based on compact radial basis functions (RBFs) are proposed for modelling photonic crystals (PhCs). When modelling two-dimensional PhCs two generalised eigenvalue problems are formed, one for the transverse-electric (TE) mode and the other for the transverse-magnetic (TM) mode. Conventionally, the Band Diagrams for two-dimensional PhCs are calculated by either the plane wave expansion method (PWEM) or the finite element method (FEM). Here, the eigenvalue equations for the two-dimensional PhCs are solved using RBFs based meshless methods. For the TM mode a meshless local strong form method (RBF collocation) is used, while for the tricker TE mode a meshless local weak form method (RBF Galerkin) is used (so that the discontinuity of the dielectric function epsilon (Porson)(x) can naturally be modelled). The results obtained from the meshless methods are found to be in good agreement with the standard PWEM. Thus, the meshless methods are proved to be a promising scheme for predicting photonic band gaps
photonic crystal, meshless methods, compactly supported radial basis functions
4910-4921
Hart, E.E.
d4df69be-0324-4f86-b84d-1644b7eea603
Cox, S.J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
1 June 2011
Hart, E.E.
d4df69be-0324-4f86-b84d-1644b7eea603
Cox, S.J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Hart, E.E., Cox, S.J. and Djidjeli, K.
(2011)
Compact RBF meshless methods for photonic crystal modelling.
Journal of Computational Physics, 230 (12), .
(doi:10.1016/j.jcp.2011.03.010).
Abstract
Meshless methods based on compact radial basis functions (RBFs) are proposed for modelling photonic crystals (PhCs). When modelling two-dimensional PhCs two generalised eigenvalue problems are formed, one for the transverse-electric (TE) mode and the other for the transverse-magnetic (TM) mode. Conventionally, the Band Diagrams for two-dimensional PhCs are calculated by either the plane wave expansion method (PWEM) or the finite element method (FEM). Here, the eigenvalue equations for the two-dimensional PhCs are solved using RBFs based meshless methods. For the TM mode a meshless local strong form method (RBF collocation) is used, while for the tricker TE mode a meshless local weak form method (RBF Galerkin) is used (so that the discontinuity of the dielectric function epsilon (Porson)(x) can naturally be modelled). The results obtained from the meshless methods are found to be in good agreement with the standard PWEM. Thus, the meshless methods are proved to be a promising scheme for predicting photonic band gaps
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e-pub ahead of print date: 12 March 2011
Published date: 1 June 2011
Keywords:
photonic crystal, meshless methods, compactly supported radial basis functions
Organisations:
Civil Engineering & the Environment
Identifiers
Local EPrints ID: 179525
URI: http://eprints.soton.ac.uk/id/eprint/179525
ISSN: 0021-9991
PURE UUID: 678c57b0-fe94-4bd2-9153-e64541b4f358
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Date deposited: 08 Apr 2011 08:32
Last modified: 14 Mar 2024 02:49
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Author:
E.E. Hart
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