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 consider reproducing kernels K : Ω x Ω → ℝ in multiscale series expansion form, i.e., kernels of the form K (x, y) = ∑_ℓ∈ℕλ_ℓ∑_j∈Iℓ

Most high-dimensional real-life data exhibit some dependencies such that data points do not populate the whole data space but lie approximately on a lower-dimensional manifold. A major problem in many data mining applications ...

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 ...

We apply the multiscale FENE model to a 3D square-square contraction flow problem and to two 2D benchmark experiments. For this purpose, we couple the stochastic Brownian configuration field method (BCF) with our fully ...

We apply iterative subspace correction methods to elliptic PDE problems discretized by generalized sparse grid systems. The involved subspace solvers are based on the combination of all anisotropic full grid spaces that ...

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 ...

A real valued, deterministic and stationary time series can be embedded in a — sometimes high-dimensional — real vector space. This leads to a one-to-one relationship between the embedded, time dependent vectors in ......

We use a sparse grid approach to discretize a multi-dimensional partial integro-differential equation (PIDE) for the deterministic valuation of European put options on Kou’s jump-diffusion processes. We employ a generalized ......

Let Ω₁ ⊂ ℝ^n₁ and Ω₂ ⊂ ℝ^n₂ be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness ......