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 …

The current burst in research activities on disordered semiconductors calls for the
development of appropriate theoretical tools that reveal the features of electron states in …

This paper addresses the numerical solution of nonlinear eigenvector problems such as the
Gross–Pitaevskii and Kohn–Sham equation arising in computational physics and chemistry …

This paper is devoted to the numerical solution of constrained energy minimization problems
arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn …

This paper studies the J-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput.
36-4: A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space …

This paper analyzes spectral properties of linear Schrödinger operators under oscillatory
high-amplitude potentials on bounded domains. Depending on the degree of disorder, we …

We study localization properties of low-lying eigenfunctions of magnetic Schrödinger
operators (− i∇− A (x)) 2 ϕ+ V (x) ϕ= λ ϕ, where V: Ω→ R≥ 0 is a given potential and A: Ω→ …

We provide a convergence analysis of the localized orthogonal decomposition (LOD)
method for Schrödinger equations with general multiscale potentials in the semiclassical …

This paper studies the localization behavior of Bose--Einstein condensates in disorder
potentials, modeled by a Gross--Pitaevskii eigenvalue problem on a bounded interval. In the …