Fachgruppe Mathematik: Fachgruppe Mathematik: Recent submissions
Now showing items 41-60 of 153
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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 ... -
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 ... -
3D incompressible two-phase flow benchmark computations for rising droplets
(2014-03)We perform 3D incompressible two-phase flow simulations of rising droplets. Based on a similar 2D benchmark, a 3D benchmark configuration with two test cases is formulated in which we compare the flow solvers DROPS, NaSt3DGPF ... -
Stable splitting of polyharmonic operators by generalized Stokes systems
(2015-12)A stable splitting of 2<em>m</em>-th order elliptic partial differential equations into 2(<em>m</em>−1) problems of Poisson type and one generalized Stokes problem is established for any space dimension <em>d</em> ≥ 2 and ... -
A new discretization for mth-Laplace equations with arbitrary polynomial degrees
(2016-07)This paper introduces new mixed formulations and discretizations for <em>m</em>th-Laplace equations of the form (−1)<em><sup>m</sup></em>∆<em><sup>m</sup>u</em> = f for arbitrary <em>m</em> = 1, 2, 3, . . . based on novel ... -
On the stability of the Rayleigh-Ritz method for eigenvalues
(2017-01-05)This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios <em>^λ<sub>k</sub></em>/<em>λ<sub>k</sub></em> of the <em>k</em>th ... -
Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations
(2015-12)This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution-free ... -
A multilevel approach to the evolutionary generation of polycrystalline structures
(2015-11)The Poisson-Voronoi tesselation is commonly used as an approximation to the microstructure of polycrystalline material. Although simple, this approximation fails to respect basic physical properties observed empirically, ...
