This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal ...

In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr¨odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the bond ...

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence ...

We apply the multiscale FENE model to a 3D square-square contraction flow problem. For this purpose, wecouple the stochastic Brownian configuration field method (BCF) with our fully parallelized three-dimensional Navier-Stokes ...

This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the ...

We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous ......