Multiscale Scattering in Nonlinear Kerr-Type Media
Preprint, 2020

We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the coefficients and combines the multiscale technique known as Localized Orthogonal Decomposition with an adaptive iterative approximation of the nonlinearity. We rigorously analyze the method in terms of well-posedness and convergence properties based on suitable assumptions on the initial data and the discretization parameters. Numerical examples illustrate the theoretical error estimates and underline the practicability of the approach.

Helmholtz equation

multiscale method


a priori estimates

Kerr medium


Roland Maier

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Barbara Verfürth

Karlsruher Institut für Technologie (KIT)



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