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Multiscale scattering in nonlinear Kerr-type media

https://doi.org/10.1090/mcom/3722
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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For Most Frequencies, Strong Trapping Has a Weak Effect in Frequency‐Domain Scattering
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Relaxing the CFL Condition for the Wave Equation on Adaptive Meshes
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A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
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The Heterogeneous Multi-Scale Method for Homogenization Problems
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
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Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations
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A two point boundary value problem with a rapidly oscillating solution
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On a BPX-preconditioner for P1 elements
inferredcites →https://doi.org/10.1007/s00033-018-1031-9openalex-snapshot
Stability estimate for the Helmholtz equation with rapidly jumping coefficients
inferredcites →https://doi.org/10.1007/s00205-013-0664-2openalex-snapshot
Real Solutions to the Nonlinear Helmholtz Equation with Local Nonlinearity
inferredcites →https://doi.org/10.1007/s10543-018-0735-8openalex-snapshot
Explicit computational wave propagation in micro-heterogeneous media
inferredcites →https://doi.org/10.1016/0021-9991(85)90119-6openalex-snapshot
On accuracy conditions for the numerical computation of waves
inferredcites →https://doi.org/10.1016/j.cma.2015.06.017openalex-snapshot
Stable multiscale Petrov–Galerkin finite element method for high frequency acoustic scattering
inferredcites →https://doi.org/10.1016/j.crma.2014.07.006openalex-snapshot
Finite-element heterogeneous multiscale method for the Helmholtz equation
inferredcites →https://doi.org/10.1016/j.jcp.2009.02.014openalex-snapshot
A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media
inferredcites →https://doi.org/10.1016/j.jcp.2013.04.045openalex-snapshot
Generalized multiscale finite element methods (GMsFEM)
inferredcites →https://doi.org/10.1016/j.jcp.2017.04.046openalex-snapshot
Robust iterative method for nonlinear Helmholtz equation
inferredcites →https://doi.org/10.1016/j.jde.2018.08.048openalex-snapshot
The Helmholtz equation in heterogeneous media: A priori bounds, well-posedness, and resonances
inferredcites →https://doi.org/10.1016/s0045-7825(97)00130-8openalex-snapshot
A multiscale finite element method for the Helmholtz equation
inferredcites →https://doi.org/10.1017/s0962492912000025openalex-snapshot
The heterogeneous multiscale method
inferredcites →https://doi.org/10.1051/m2an/2013141openalex-snapshot
A localized orthogonal decomposition method for semi-linear elliptic problems
inferredcites →https://doi.org/10.1051/m2an/2016066openalex-snapshot
Finite element quasi-interpolation and best approximation
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XL. A new relation between electricity and light: Dielectrified media birefringent
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Elliptic Partial Differential Equations
inferredcites →https://doi.org/10.1090/conm/180/01951openalex-snapshot
Two-level additive Schwarz preconditioners for nonconforming finite elements
inferredcites →https://doi.org/10.1090/mcom/3114openalex-snapshot
Localized orthogonal decomposition method for the wave equation with a continuum of scales
inferredcites →https://doi.org/10.1090/mcom/3156openalex-snapshot
Eliminating the pollution effect in Helmholtz problems by local subscale correction
inferredcites →https://doi.org/10.1090/mcom/3457openalex-snapshot
Stability and finite element error analysis for the Helmholtz equation with variable coefficients
inferredcites →https://doi.org/10.1090/mcom/3529openalex-snapshot
Computational high frequency scattering from high-contrast heterogeneous media
inferredcites →https://doi.org/10.1090/s0025-5718-2014-02868-8openalex-snapshot
Localization of elliptic multiscale problems
inferredcites →https://doi.org/10.1093/imanum/drz020openalex-snapshot
Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems
inferredcites →https://doi.org/10.1103/physrevlett.53.910openalex-snapshot
Intrinsic Optical Bistability in Nonlinear Media
inferredcites →https://doi.org/10.1103/physrevlett.85.3966openalex-snapshot
Negative Refraction Makes a Perfect Lens
inferredcites →https://doi.org/10.1126/science.1096796openalex-snapshot
Metamaterials and Negative Refractive Index
inferredcites →https://doi.org/10.1126/science.1125907openalex-snapshot
Controlling Electromagnetic Fields
inferredcites →https://doi.org/10.1137/060662575openalex-snapshot
Wave-Number-Explicit Bounds in Time-Harmonic Scattering
inferredcites →https://doi.org/10.1137/120888223openalex-snapshot
Multiscale Hybrid-Mixed Method
inferredcites →https://doi.org/10.1137/120900332openalex-snapshot
Oversampling for the Multiscale Finite Element Method
inferredcites →https://doi.org/10.1137/130921520openalex-snapshot
Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates
inferredcites →https://doi.org/10.1137/16m1108820openalex-snapshot
A New Heterogeneous Multiscale Method for the Helmholtz Equation with High Contrast
inferredcites →https://doi.org/10.1137/17m111314xopenalex-snapshot
Finite Element Method and its Analysis for a Nonlinear Helmholtz Equation with High Wave Numbers
inferredcites →https://doi.org/10.1137/17m1133932openalex-snapshot
Numerical Homogenization of H(curl)-Problems
inferredcites →https://doi.org/10.1137/18m1189701openalex-snapshot
Numerical Homogenization of Elliptic PDEs with Similar Coefficients
inferredcites →https://doi.org/10.1137/19m1255616openalex-snapshot
A Multiscale Hybrid-Mixed Method for the Helmholtz Equation in Heterogeneous Domains
inferredcites →https://doi.org/10.1137/19m1278211openalex-snapshot
Numerical Upscaling of Perturbed Diffusion Problems
inferredcites →https://doi.org/10.1137/19m1293818openalex-snapshot
Computational Homogenization of Time-Harmonic Maxwell's Equations
inferredcites →https://doi.org/10.1137/s0036142994269186openalex-snapshot
Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
inferredcites →https://doi.org/10.1142/s0218202519500106openalex-snapshot
Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions
inferredcites →https://doi.org/10.1364/josaa.27.002347openalex-snapshot
A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects
inferredcites →https://doi.org/10.1364/ol.18.001654openalex-snapshot
Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion
inferredcites →https://doi.org/10.1785/0120170268openalex-snapshot
An Efficient Multiscale Finite‐Element Method for Frequency‐Domain Seismic Wave Propagation
inferredcites →https://doi.org/10.4310/cms.2003.v1.n1.a8openalex-snapshot
The Heterognous Multiscale Methods
inferredcites →https://doi.org/10.5167/uzh-157650openalex-snapshot
Stability estimate for the Helmholtz equation with rapidly jumping coefficients

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/s10915-024-02459-8openalex-snapshot
Higher-Order Finite Element Methods for the Nonlinear Helmholtz Equation
inferred← citeshttps://doi.org/10.1016/j.cma.2025.118426openalex-snapshot
Linearized localized orthogonal decomposition for quasilinear nonmonotone elliptic PDE
inferred← citeshttps://doi.org/10.1016/j.cma.2026.119136openalex-snapshot
Linear CIP-FEM for nonlinear Helmholtz systems at high wavenumbers
inferred← citeshttps://doi.org/10.1016/j.cnsns.2023.107422openalex-snapshot
A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity
inferred← citeshttps://doi.org/10.1017/s0956792526100539openalex-snapshot
Adaptive FEM and CIPFEM for a nonlinear Helmholtz equation with high wave number
inferred← citeshttps://doi.org/10.1051/m2an/2026006openalex-snapshot
A generalized framework for higher-order Localized Orthogonal Decomposition methods
inferred← citeshttps://doi.org/10.1098/rsta.2024.0353openalex-snapshot
A high-order perturbation method for analysing the Dirichlet–Neumann operator for a nonlinear Kerr medium
inferred← citeshttps://doi.org/10.1137/21m1414607openalex-snapshot
Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems
inferred← citeshttps://doi.org/10.1137/21m1438244openalex-snapshot
Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients
inferred← citeshttps://doi.org/10.1137/21m1460016openalex-snapshot
An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition
inferred← citeshttps://doi.org/10.1137/22m1524278openalex-snapshot
Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization
inferred← citeshttps://doi.org/10.1186/s13662-022-03702-yopenalex-snapshot
Operator compression with deep neural networks
inferred← citeshttps://doi.org/10.2139/ssrn.5366225openalex-snapshot
Neural Numerical Homogenization Based on Deep Ritz Corrections
inferred← citeshttps://doi.org/10.2139/ssrn.5367853openalex-snapshot
Linearized Localized Orthogonal Decomposition for Quasilinear Nonmonotone Elliptic Pde
inferred← citeshttps://doi.org/10.2139/ssrn.5709804openalex-snapshot
CIP-FEM for Nonlinear Helmholtz Systems at High Wavenumbers
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