Numerical homogenization beyond scale separation

R Altmann, P Henning, D Peterseim - Acta Numerica, 2021 - cambridge.org
Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment

K Smetana, T Taddei - SIAM Journal on Scientific Computing, 2023 - SIAM
We propose a component-based (CB) parametric model order reduction (pMOR) formulation
for parameterized nonlinear elliptic partial differential equations. CB-pMOR is designed to …

On optimal convergence rates for discrete minimizers of the Gross–Pitaevskii energy in localized orthogonal decomposition spaces

P Henning, A Persson - Multiscale Modeling & Simulation, 2023 - SIAM
In this paper we revisit a two-level discretization based on localized orthogonal
decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D …

Multiscale scattering in nonlinear Kerr-type media

R Maier, B Verfürth - Mathematics of Computation, 2022 - ams.org
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 …

On optimal convergence rates for discrete minimizers of the Gross-Pitaevskii energy in LOD spaces

P Henning, A Persson - arxiv preprint arxiv:2112.08485, 2021 - arxiv.org
In this paper we revisit a two-level discretization based on the Localized Orthogonal
Decomposition (LOD). It was originally proposed in [P. Henning, AM {\aa} lqvist, D …