The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 521-540 of 5046
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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 ... -
Fast discrete Fourier transform on generalized sparse grids
(2013-03)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 ... -
On the convergence of the combination technique
(2013)Sparse tensor product spaces provide an efficient tool to discretize higher dimensional operator equations. The direct Galerkin method in such ansatz spaces may employ hierarchical bases, interpolets, wavelets or multilevel ... -
Simulation of droplet impact with dynamic contact angle boundary conditions
(2013-01)The numerical simulation of dynamic wetting processes is of interest for a vast variety of industrial processes, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle ... -
On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions
(2013-01)We first discretize the <em>d</em>-dimensional Laplacian in (0, 1)<sup><em>d</em></sup> for varying <em>d</em> on a full uniform grid and build a new preconditioner that is based on a multilevel generating system. We show ... -
Schwarz iterative methods: Infinite space splittings
(2014-12)We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hilbert space. For the greedy case, we show ... -
Error estimates for multivariate regression on discretized function spaces
(2016-03)In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling ... -
Efficient Visual Perception for Soccer Robots, Motion Segmentation, and Video Prediction
(2024-08-23)A robot’s ability to perceive the state of its environment is crucial for successful autonomous behavior and complex interactions, such as those in robot-robot and human-robot scenarios. For robot perception systems to ... -
Eliminating the pollution effect in Helmholtz problems by local subscale correction
(2014-11)We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝ<sup>d</sup>. The discrete trial and test spaces are ... -
A multiscale method for porous microstructures
(2014-11)In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and ... -
Analysis-suitable adaptive T-mesh refinement with linear complexity
(2014-07)We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, this is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays ... -
Non-intrusive uncertainty quantification with sparse grids for multivariate peridynamic simulations
(2014-06)Peridynamics is an accepted method in engineering for modeling crack propagation on a macroscopic scale. However, the sensitivity of the method to two important model parameters – elasticity and the particle density – has ... -
Efficient neighbor search for particle methods on GPUs
(2014-06)In this paper we present an efficient and general sorting-based approach for the neighbor search on GPUs. Finding neighbors of a particle is a common task in particle methods and has a significant impact on the overall ... -
Simulation of the oil storage process in the scopa of specialized bees
(2014-06)Several species of specialized bees possess special structures to store and transport floral oils. By using closely spaced hairs at their back legs, the so called scopa, these bees can absorb and release oil droplets without ... -
The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
(2014)The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many ... -
A bond order dissection ANOVA approach for efficient electronic structure calculations
(2014-03)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 ...
