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A multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient is presented. 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. The method is rigorously analyzed 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. | A multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient is presented. 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. The method is rigorously analyzed 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. | ||
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== Video == | == Video == | ||
{{#evt:service=cloudfront|id=258786|alignment=center|filename=79.mp4}} | {{#evt:service=cloudfront|id=258786|alignment=center|filename=79.mp4}} | ||
Latest revision as of 15:54, 26 June 2021
Summary
A multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient is presented. 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. The method is rigorously analyzed 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.
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Published on 26/06/21
Accepted on 26/06/21
Submitted on 26/06/21
Volume CT09 - Multiscale, Multimodel and Multiphysics, 2021
DOI: 10.23967/admos.2021.060
Licence: CC BY-NC-SA license
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