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

Numerical homogenization aims to efficiently and accurately approximate the solution space
of an elliptic partial differential operator with arbitrarily rough coefficients in a $ d …

A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an
overlapping domain decomposition (DD) method, is proposed to efficiently construct …

We provide a concise review of the exponentially convergent multiscale finite element
method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without …

We propose a component-based (CB) parametric model order reduction (pMOR) formulation
for parameterized nonlinear elliptic partial differential equations. CB-pMOR is designed to …

We propose a local, non-intrusive model order reduction technique to accurately
approximate the solution of coupled multi-component parametrized systems governed by …

In recent years, there has been a growing interest in understanding complex microstructures
and their effect on macroscopic properties. In general, it is difficult to derive an effective …

Many complex engineering systems consist of multiple subsystems that are developed by
different teams of engineers. To analyse, simulate and control such complex systems …

We propose a probabilistic way for reducing the cost of classical projection-based model
order reduction methods for parameter-dependent linear equations. A reduced order model …

In this contribution we present a survey of concepts in localized model order reduction
methods for parameterized partial differential equations. The key concept of localized model …