High spatial order energy stable FDTD methods for Maxwell's equations in nonlinear optical media in one dimension

DOI10.1007/s10915-018-0716-8zbMath1407.65094OpenAlexW2801879390WikidataQ129920361 ScholiaQ129920361MaRDI QIDQ1632262

Yingda Cheng, Fengyan Li, Puttha Sakkaplangkul, Yan Jiang, Vrushali A. Bokil

Publication date: 13 December 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-018-0716-8

zbMATH Keywords

nonlinear dispersionMaxwell's equationsenergy stabilitysoliton propagationhigh-order FDTD

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Nonlinear ordinary differential equations and systems (34A34) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Lasers, masers, optical bistability, nonlinear optics (78A60) Soliton solutions (35C08) Maxwell equations (35Q61)

Related Items (8)

Legendre-tau Chebyshev collocation spectral element method for Maxwell's equations with material interfaces of two dimensional transverse magnetic mode ⋮ An operator splitting Legendre-tau spectral method for Maxwell's equations with nonlinear conductivity in two dimensions ⋮ An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics ⋮ An energy-stable finite element method for nonlinear Maxwell's equations ⋮ Unnamed Item ⋮ Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension ⋮ Energy stable nodal discontinuous Galerkin methods for nonlinear Maxwell's equations in multi-dimensions ⋮ Developing and analyzing new unconditionally stable finite element schemes for Maxwell's equations in complex media

Cites Work

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• Superconvergence analysis of Yee scheme for metamaterial Maxwell's equations on non-uniform rectangular meshes
• Interior penalty DG methods for Maxwell's equations in dispersive media
• Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media
• Error analysis of finite element methods for 3-D Maxwell's equations in dispersive media
• Godunov scheme for Maxwell's equations with Kerr nonlinearity
• Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell's equations in dispersive media
• High-order scheme for a nonlinear Maxwell system modelling Kerr effect
• Comparison between staggered and unstaggered finite-difference time-domain grids for few-cycle temporal optical soliton propagation
• Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media
• An explicit fourth-order staggered finite-difference time-domain method for Maxwell's equations
• An efficient vector finite element method for nonlinear electromagnetic modeling
• Analysis of a time-domain finite element method for 3-D Maxwell's equations in dispersive media
• Analysis of spatial high-order finite difference methods for Maxwell's equations in dispersive media
• High-order DGTD methods for dispersive Maxwell's equations and modelling of silver nanowire coupling
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• On a Fourier Method for the Integration of Hyperbolic Equations
• A Convergence Analysis of Yee’s Scheme on Nonuniform Grids
• Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach
• Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
• Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion
• Spatial Finite Difference Approximations for Wave-Type Equations
• Convergence of a discontinuous Galerkin scheme for the mixed time-domain Maxwell's equations in dispersive media
• A Discontinuous Galerkin Finite Element Time-Domain Method Modeling of Dispersive Media
• Numerical Modeling of Laser Pulse Behavior in Nonlinear Crystal and Application to the Second Harmonic Generation
• Construction and analysis of higher order finite difference schemes for the 1D wave equation
• A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations

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