Fachgruppe Mathematik: Fachgruppe Mathematik: Recent submissions
Now showing items 61-80 of 153
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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 ... -
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 ... -
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 ...
