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, a generalized finite element (FE) method with optimal local approximation
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …

Multiple scattering of waves is eminent in a wide range of applications and extensive
research is being undertaken into multiple scattering by ever more complicated structures …

We introduce a new efficient algorithm for Helmholtz problems in perforated domains with
the design of the scheme allowing for possibly large wavenumbers. Our method is based …