Helmholtz equation in periodic media with a line defect

DOI10.1016/J.JCP.2011.10.022zbMath1242.65228OpenAlexW2023172943MaRDI QIDQ422988

Julien Coatléven

Publication date: 18 May 2012

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.10.022

zbMATH Keywords

convergencenumerical resultsquadrature ruleHelmholtz equationsemidiscretizationLippmann-Schwinger equationline defectsexact-boundary conditionsFloquet-Block transformunbounded defectsunbounded media

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Method of lines for boundary value problems involving PDEs (65N40)

Related Items (16)

An integral equation method for the Helmholtz problem in the presence of small anisotropic inclusions ⋮ Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides ⋮ The Floquet-Bloch transform and scattering from locally perturbed periodic surfaces ⋮ Explicit formula for amplitudes of waves in lattices with defects and sources and its application for defects detection ⋮ A High Order Numerical Method for Scattering from Locally Perturbed Periodic Surfaces ⋮ Numerical methods for scattering problems from multi‐layers with different periodicities ⋮ A Floquet--Bloch Transform Based Numerical Method for Scattering from Locally Perturbed Periodic Surfaces ⋮ A volume integral method for solving scattering problems from locally perturbed infinite periodic layers ⋮ Reconstruction of local perturbations in periodic surfaces ⋮ Wave propagation through periodic lattice with defects ⋮ Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides ⋮ A modification of the invariant imbedding method for a singular boundary value problem ⋮ Numerical methods for scattering problems in periodic waveguides ⋮ Near-field imaging of locally perturbed periodic surfaces ⋮ Time-Harmonic Acoustic Scattering from Locally Perturbed Periodic Curves ⋮ Algebra of multidimensional periodic operators with defects

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact artificial boundary conditions for problems with periodic structures
• Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media
• A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations
• Dirichlet-to-Neumann Map Method with Boundary Cells for Photonic Crystals Devices
• Convergence of the Supercell Method for Defect Modes Calculations in Photonic Crystals
• Floquet theory for partial differential equations

This page was built for publication: Helmholtz equation in periodic media with a line defect