Computation of the band structure of two-dimensional photonic crystals with \(hp\) finite elements

DOI10.1016/j.cma.2008.06.009zbMath1157.78355OpenAlexW2077763481MaRDI QIDQ1008928

Peter Kauf, Kersten Schmidt

Publication date: 30 March 2009

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2008.06.009

zbMATH Keywords

corner singularitiesexponential convergence\(hp\)-FEMphotonic crystalsphotonic band structurequasi-periodic boundary condition

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10)

Related Items

CONVERGENT ADAPTIVE FINITE ELEMENT METHODS FOR PHOTONIC CRYSTAL APPLICATIONS, Linearization techniques for band structure calculations in absorbing photonic crystals, Rational eigenvalue problems and applications to photonic crystals, On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model, Periodic band structure calculation by the Sakurai-Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation, On the homogenization of the Helmholtz problem with thin perforated walls of finite length, A High Order Method for the Approximation of Integrals Over Implicitly Defined Hypersurfaces, A multiscale \(hp\)-FEM for 2D photonic crystal bands, Adaptive finite element methods for computing band gaps in photonic crystals, Dispersion relation reconstruction for 2D photonic crystals based on polynomial interpolation, An a posteriori error estimator for \(hp\)-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals, Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations, An a posteriori error estimator for \(hp\)-adaptive continuous Galerkin methods for photonic crystal applications, Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications, Non-conforming Galerkin finite element methods for local absorbing boundary conditions of higher order, Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides, Complex dispersion relation calculations with the symmetric interior penalty method, An analysis of Feng’s and other symmetric local absorbing boundary conditions, PDE eigenvalue iterations with applications in two-dimensional photonic crystals, Singular Value Decompositions for Single-Curl Operators in Three-Dimensional Maxwell's Equations for Complex Media

Uses Software

• Concepts
• SuperLU

Cites Work

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• Modified edge finite elements for photonic crystals
• An efficient method for band structure calculations in 2D photonic crystals
• An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I: Scalar case
• The computation of spectra of some 2D photonic crystals
• An adaptive refinement strategy for \(hp\)-finite element computations
• An efficient method for band structure calculations in 3D photonic crystals
• Convergence of an adaptive \( hp\) finite element strategy in one space dimension
• Separation of Variables in the Computation of Spectra in 2-D Photonic Crystals
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• Singularities of Maxwell interface problems
• Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data
• A Supernodal Approach to Sparse Partial Pivoting
• The h–p version of the finite element method for problems with interfaces
• Concepts—An Object-Oriented Software Package for Partial Differential Equations
• EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• Floquet theory for partial differential equations