Multiscale scattering in nonlinear Kerr-type media

DOI10.1090/mcom/3722zbMath1491.65148arXiv2011.09168OpenAlexW4205408820MaRDI QIDQ5082032

Roland Maier, Barbara Verfürth

Publication date: 15 June 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.09168

zbMATH Keywords

a priori estimatesnonlinearHelmholtz equationmultiscale methodKerr medium

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary value problems for nonlinear higher-order PDEs (35G30) A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

Numerical homogenization beyond scale separation ⋮ Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients ⋮ Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems ⋮ A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity ⋮ Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization ⋮ An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition ⋮ Higher-order finite element methods for the nonlinear Helmholtz equation

Uses Software

• GitHub
• gridlod

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