Fachgruppe Mathematik: Fachgruppe Mathematik: Recent submissions
Now showing items 21-40 of 153
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Fast approximation of the discrete Gauss transform in higher dimensions
(2011-10)We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares ... -
Approximation of two-variate functions: singular value decomposition versus sparse grids
(2011)We compare the cost complexities of two approximation schemes for functions <em>f</em> ∈ <em>H<sup>p</sup></em>(<em>Ω</em><sub>1</sub> × <em>Ω</em><sub>2</sub>) which live on the product domain <em>Ω</em><sub>1</sub> × ... -
Coupling molecular dynamics and continua with weak constraints
(2011-06)One of the most challenging problems in dynamic concurrent multiscale simulations is the reflectionless transfer of physical quantities between the different scales. In particular, when coupling molecular dynamics and ... -
Greedy and randomized versions of the multiplicative Schwarz method
(2011-06)We consider sequential, i.e., Gauss-Seidel type, subspace correction methods for the iterative solution of symmetric positive definite variational problems, where the order of subspace correction steps is not deterministically ... -
On the construction of sparse tensor product spaces
(2011-05)Let Ω<sub>1</sub> ⊂ ℝ<sup><em>n</em><sub>1</sub></sup> and Ω<sub>2</sub> ⊂ ℝ<sup><em>n</em><sub>2</sub></sup> be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial ... -
Multiscale simulation of ion migration for battery systems
(2012-11)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 ... -
An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
(2012-09)We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions ... -
A sparse grid based generative topographic mapping for the dimensionality reduction of high-dimensional data
(2012-05)Most high-dimensional data exhibit some correlation such that data points are not distributed uniformly in the data space but lie approximately on a lower-dimensional manifold. A major problem in many data-mining applications ... -
A note on the construction of L-fold sparse tensor product spaces
(2012-04)In the present paper, we consider the construction of general sparse tensor product spaces in arbitrary space dimensions when the single subdomains are of different dimensionality and the associated ansatz spaces possess ... -
Computational 3D simulation of calcium leaching in cement matrices
(2012-02)Calcium leaching is a degradation process consisting in the progressive dissolution of the paste by the migration of calcium atoms to the aggressive solution. It is therefore, a complex phenomenon involving simultaneously ... -
An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jump-diffusion model
(2012-02)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 ... -
An adaptive sparse grid approach for time series predictions
(2012-01)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 ... -
Multiscale partition of unity
(2013-12)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 ... -
Optimal scaling parameters for sparse grid discretizations
(2013-08)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 ... -
Multiscale simulations of three-dimensional viscoelastic flows in a square-square contraction
(2015-03)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 ... -
Multiscale approximation and reproducing kernel Hilbert space methods
(2013)We consider reproducing kernels <em>K</em> : Ω x Ω → ℝ in multiscale series expansion form, i.e., kernels of the form <em>K</em> (<em>x</em>, <em>y</em>) = ∑<sub>ℓ∈ℕ</sub>λ<sub>T ... -
Dimensionality reduction of high-dimensional data with a non-linear principal component aligned generative topographic mapping
(2013-07)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 ... -
Dimension-adaptive sparse grid quadrature for integrals with boundary singularities
(2013)Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitly smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalized ... -
Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model
(2013-04)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 ... -
A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle
(2015-09)We employ a numerical simulation of the three-dimensional fluid flow and the simultaneous transport of sediment to reproduce current-driven sediment transport processes. In particular, the scouring at a rectangular obstacle ...
