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 …

We propose a new normalized Sobolev gradient flow for the Gross--Pitaevskii eigenvalue
problem based on an energy inner product that depends on time through the density of the …

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 …

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 …

In this paper, we consider the numerical solution of a nonlinear Schrödinger equation with
spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule …

This paper concerns the numerical approximation of low-energy eigenstates of the linear
random Schrödinger operator. Under oscillatory high-amplitude potentials with a sufficient …

We present a method for the fast computation of the eigenpairs of a bijective positive
symmetric linear operator L. The method is based on a combination of operator adapted …