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Search: WFRF:(Maier Roland 1993) > (2020)

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1.
  • Caiazzo, A., et al. (author)
  • Reconstruction of Quasi-Local Numerical Effective Models from Low-Resolution Measurements
  • 2020
  • In: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 85:1
  • Journal article (peer-reviewed)abstract
    • We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward models that are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that an identification of the matrix representation related to these effective models is possible. On the one hand, this provides a reasonable surrogate in cases where a direct reconstruction is unfeasible due to a mismatch between the coarse data scale and the microscopic quantities to be reconstructed. On the other hand, the approach allows us to investigate the requirement for a certain non-locality in the context of numerical homogenization. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.
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2.
  • Maier, Roland, 1993, et al. (author)
  • Multiscale Scattering in Nonlinear Kerr-Type Media
  • 2020
  • In: ArXiv Preprint 2011.09168.
  • Other publication (other academic/artistic)abstract
    • 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.
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  • Result 1-2 of 2
Type of publication
other publication (1)
journal article (1)
Type of content
other academic/artistic (1)
peer-reviewed (1)
Author/Editor
Maier, Roland, 1993 (2)
Caiazzo, A. (1)
Peterseim, D. (1)
Verfürth, Barbara (1)
University
University of Gothenburg (2)
Chalmers University of Technology (2)
Language
English (2)
Research subject (UKÄ/SCB)
Natural sciences (2)
Year
2020 (2)Undo refine

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