The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 481-500 of 4994
-
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, ... -
Convergence of nonsmooth descent methods via Kurdyka–Lojasiewicz inequality on Riemannian manifolds
(2015-11)We develop a subgradient-oriented descent method in nonsmooth optimization on Riemannian manifolds and prove convergence of the method in the sense of subsequences for nonsmooth functions whose standard models are strict. ... -
Generalized finite element methods for quadratic eigenvalue problems
(2015-10)We consider a large-scale quadratic eigenvalue problem (QEP), formulated using P1 finite elements on a fine scale reference mesh. This model describes damped vibrations in a structural mechanical system. In particular we ... -
Complexity of hierarchical refinement for a class of admissible mesh configurations
(2015-09)An adaptive isogeometric method based on <em>d</em>-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of ... -
Regularized kernel based reconstruction in generalized Besov spaces
(2015)We present a theoretical framework for reproducing kernel based reconstruction methods in certain generalized Besov spaces based on positive, essentially self-adjoint operators. An explicit representation of the reproducing ... -
A generalized multiscale finite element method for poroelasticity problems I: linear problems
(2015-04)In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow ... -
CLSVOF as a fast and mass-conserving extension of the level-set method for the simulation of two-phase flow problems
(2015-07)The modeling of two-phase flows in computational fluid dynamics is still an area of active research. One popular method is the coupling of level-set and volume-of-fluid (CLSVOF), which benefits from the advantages of both ...
