Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical
scheme, based on the multilevel combination (C) technique, to combine various levels of …

The exact numerical simulation of plasma turbulence is one of the assets and challenges in
fusion research. For grid-based solvers, sufficiently fine resolutions are often unattainable …

In this article, we analyze tensor approximation schemes for continuous functions. We
assume that the function to be approximated lies in an isotropic Sobolev space and discuss …

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 …

We compare the cost complexities of two approximation schemes for functions f∈ H p (Ω 1×
Ω 2) which live on the product domain Ω 1× Ω 2 of sufficiently smooth domains Ω 1⊂ ℝ n 1 …

In an open, bounded domain D ⊂\mathbb R^ n D⊂ R n with smooth boundary ∂ D∂ D or
on a smooth, closed and compact, Riemannian n-manifold M ⊂\mathbb R^ n+ 1 M⊂ R n+ 1 …

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty
quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin …

In this article, we show that the multilevel Monte Carlo method for elliptic stochastic partial
differential equations is a sparse grid approximation. By using this interpretation, the method …

Let $\Omega _i\subset\mathbb {R}^{n_i} $, $ i= 1,\ldots, m $, be given domains. In this
article, we study the low-rank approximation with respect to $ L^ 2 (\Omega …

Projection-free optimization via different variants of the Frank–Wolfe method has become
one of the cornerstones of large scale optimization for machine learning and computational …