Compact RBF meshless methods for photonic crystal modelling
| Autor: | E. E. Hart, Kamal Djidjeli, Simon J. Cox |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Regularized meshless method Physics and Astronomy (miscellaneous) Plane wave expansion method Applied Mathematics Mathematical analysis Geometry Computer Science::Computational Geometry Computer Science::Numerical Analysis Finite element method Mathematics::Numerical Analysis Computer Science Applications Computational Mathematics Discontinuity (linguistics) Computer Science::Computational Engineering Finance and Science Modeling and Simulation Meshfree methods Radial basis function Galerkin method Mathematics Photonic crystal |
| Zdroj: | Journal of Computational Physics. 230:4910-4921 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2011.03.010 |
| Popis: | 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 @e(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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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