Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

The objective of this book is to introduce the reader to the Localized Orthogonal
Decomposition (LOD) method for solving partial differential equations with multiscale data …

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 …

We introduce a novel multi-resolution localized orthogonal decomposition (LOD) for time-
harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The …

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

This paper considers the numerical treatment of the time-dependent Gross–Pitaevskii
equation. In order to conserve the time invariants of the equation as accurately as possible …

In this thesis, we consider the numerical approximation of solutions of partial differential
equations that exhibit some kind of multiscale features. Such equations describe, for …

This work presents an abstract framework for the design, implementation, and analysis of the
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …

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 …

This paper studies the compression of partial differential operators using neural networks.
We consider a family of operators, parameterized by a potentially high-dimensional space of …