Mathematisch-Naturwissenschaftliche Fakultät: Mathematisch-Naturwissenschaftliche Fakultät: Neuzugänge
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Note on “The smooting effect of integration in ℝd and the ANOVA decomposition”
(2015)This is a note on [Math. Comp. <b>82</b>, 383–400 (2013)]. We first report a mistake, in that the main result Theorem 3.1, though correct, does not as claimed apply to the Asian option pricing problem. This is because ... -
A sparse grid based method for generative dimensionality reduction of high-dimensional data
(2015-11)Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a ... -
Reproducing kernel Hilbert spaces for parametric partial differential equations
(2015-06)In this article, we present kernel methods for the approximation of quantities of interest which are derived from solutions of parametric partial differential equations. We explicitly construct a reproducing kernel Hilbert ... -
Subspace correction methods in algebraic multi-level frames
(2015-06)This study aims at introducing new algebraic multi-level solution techniques for linear systems with M-matrices. Previous optimal geometric constructions by multi-level generating systems or multi-level frames are adapted. ... -
On tensor product approximation of analytic functions
(2015)We prove sharp, two-sided bounds on sums of the form ∑<em><sub>k∈ℕ<sup>d</sup><sub>0</sub></em><sub>\<em>𝒟<sub>a</sub></em>(<em>T</em>)</sub></sub> exp(− ∑<em><sup>d</sup><sub>j</em><sub>=1</sub></sub> ... -
Variational multiscale stabilization and the exponential decay of fine-scale correctors
(2015-05)This paper reviews the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with ... -
Geographie und Recht: Gerichtsverfahren und ihre Relevanz für studying-up power bei der Kriminalitäts- und Terrorismusbekämpfung
(2023)Sarah Klosterkamp will in diesem Buch erstens bereits bestehende gerichtsethnographische Methoden für eine Humangeographie fruchtbar machen, die an Recht und seinen multiplen Wechselwirkungen im Sinne von Subjektkonstitutionen ... -
3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement
(2016-01)This paper addresses the linear independence of T-splines in three space dimensions. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear ... -
A new generalization of the P1 non-conforming FEM to higher polynomial degrees
(2015)This paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation ... -
A multiscale finite element method for Neumann problems in porous microstructures
(2015-01)In this paper we develop and analyze a Multiscale Finite Element Method (MsFEM) for problems in porous microstructures. By solving local problems throughout the domain we are able to construct a multiscale basis that can ... -
Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
(2015-03)We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number <em>κ</em> as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard ... -
Hyperbolic cross approximation in infinite dimensions
(2015)We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analytic-type smoothness in the infinite-dimensional ... -
Numerical verification of a bond-based softening peridynamic model for small displacements: Deducing material parameters from classical linear theory
(2016-12)In this article we present a systematic numerical approach for calibration and numerical verification of peridynamics models. The approach is illustrated for a two parameter exponential bond softening model, which is ... -
Extraction of fragments and waves after impact damage in particle-based simulations
(2016-12)The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process particle-based ... -
Simulation of wave propagation and impact damage in brittle materials using peridynamics
(2016-12)In this paper we present the results of simulating wave propagation and impact damage in brittle materials, like ceramics, using peridynamics, a non-local generalization of continuum mechanics. Two different bond-based ... -
Line search algorithms for locally Lipschitz functions on Riemannian manifolds
(2016-11)This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian ... -
Additive Schwarz solvers for hp-FEM discretizations of PDE-constrained optimzation problems
(2016-10)In this paper, we investigate the minimization of a quadratic functional subject to a boundary value problem of a second order linear elliptic partial differential equation. There are no inequality constraints for state ... -
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization
(2016-10)In this paper, a nonsmooth optimization method for locally Lipschitz functions on real algebraic varieties is developed. To this end, the set-valued map <em>ε</em>-conditional subdifferential <em>x</em> → ... -
Robust numerical upscaling of elliptic multiscale problems at high contrast
(2016-01)We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of <em>H<sup>1</sup></em> into the image ... -
Relaxing the CFL condition for the wave equation on adaptive meshes
(2017-02)The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size ...
