The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 461-480 of 4992
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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 ... -
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 ...
