In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic ...

In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of ...

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system ...

In this article, we present a new decomposition approach for the efficient approximate calculation of the electronic structure problem for molecules. It is based on a dimension-wise decomposition of the space the underlying ......

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 ...

The Poisson-Voronoi tesselation is commonly used as an approximation to the microstructure of polycrystalline material. Although simple, this approximation fails to respect basic physical properties observed empirically, ......