Energy stable nodal discontinuous Galerkin methods for nonlinear Maxwell's equations in multi-dimensions

DOI10.1007/S10915-021-01651-4OpenAlexW3206240582MaRDI QIDQ2236544

Vrushali A. Bokil, Yingda Cheng, Maohui Lyu, Fengyan Li

Publication date: 25 October 2021

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

Full work available at URL: https://doi.org/10.1007/s10915-021-01651-4

zbMATH Keywords

Maxwell's equationshigh dimensionsenergy stablenodal discontinuous Galerkin methodsKerr and Raman nonlinear effectslinear Lorentz

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Diffraction, scattering (78A45) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Lasers, masers, optical bistability, nonlinear optics (78A60) Soliton solutions (35C08)

Related Items (6)

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 ⋮ A FETD scheme and analysis for photonic crystal waveguides comprising third-order nonlinear and linear materials ⋮ Numerical analysis of the direct method for 3D Maxwell's equation in Kerr-type nonlinear media ⋮ An energy-stable finite element method for nonlinear Maxwell's equations ⋮ An unconditionally stable modified leapfrog method for Maxwell's equation in Kerr-type nonlinear media

Cites Work

• Unnamed Item
• Unnamed Item
• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• Dispersion reducing methods for edge discretizations of the electric vector wave equation
• Comparison between staggered and unstaggered finite-difference time-domain grids for few-cycle temporal optical soliton propagation
• High spatial order energy stable FDTD methods for Maxwell's equations in nonlinear optical media in one dimension
• Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media
• Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension
• Interpolatory HDG method for parabolic semilinear PDEs
• A new FDTD scheme for Maxwell's equations in Kerr-type nonlinear media
• An efficient vector finite element method for nonlinear electromagnetic modeling
• Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model

This page was built for publication: Energy stable nodal discontinuous Galerkin methods for nonlinear Maxwell's equations in multi-dimensions