The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 621-640 of 5047
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Finite differences on sparse grids for continuous time heterogeneous agent models
(2019-09)We present a finite difference method working on sparse grids to solve higher dimensional heterogeneous agent models. If one wants to solve the arising Hamilton-Jacobi-Bellman equation on a standard full grid, one faces ... -
Convergence of the SQP method for quasilinear parabolic optimal control problems
(2019-11)Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a ... -
EXAHD - A massively parallel fault tolerant sparse grid approach for high-dimensional turbulent plasma simulations
(2020-03)Plasma fusion is one of the promising candidates for an emission-free energy source and is heavily investigated with high-resolution numerical simulations. Unfortunately, these simulations suffer from the curse of ... -
Multivariate Haar systems in Besov function spaces
(2020-03)We determine all cases for which the d-dimensional Haar wavelet system <em>H<sup>d</sup></em> on the unit cube <em>I<sup>d</sup></em> is a conditional or unconditional Schauder basis in the classical isotropic Besov function ... -
Note on 1D quarklet approximation
(2020-03)On the example of the simplest <em>C<sup>0</sup></em> spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval ... -
Optimal control of quasilinear parabolic PDEs with state-constraints
(2020-12)We discuss state-constrained optimal control of a quasilinear parabolic PDE. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in ... -
A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
(2020-12)We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore ... -
Sparse tensor product approximation for a class of generalized method of moments estimators
(2020-12)Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models with not analytically ... -
A fault-tolerant domain decomposition method based on space-filling curves
(2021-03)We propose a simple domain decomposition method for d-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to ... -
Deep neural networks and PIDE discretizations
(2021-08)In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN). As an alternative to increasing the network’s depth or width to improve performance, ... -
Multi-resolution dynamic mode decomposition for early damage detection in wind turbine gearboxes
(2021-10)We introduce an approach for damage detection in gearboxes based on the analysis of sensor data with the multi-resolution dynamic mode decomposition (mrDMD). The application focus is the condition monitoring of wind turbine ... -
A dimension-oblivious domain decomposition method based on space-filling curves
(2021-10)In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve ... -
On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data
(2021-12)Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro–differential equations with uncertainties in the ... -
Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
(2022-01)We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls ... -
Sparse optimal control of a quasilinear elliptic PDE in measure spaces
(2022-03)We prove existence of optimal controls for sparse optimal control of a quasilinear elliptic equation in measure spaces and derive first-order necessary optimality conditions. Under additional assumptions also second-order ... -
Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness
(2022-03)Let Ω<sub><em>i</em></sub> ⊂ R<em><sup>n<sub>i</sub></sup></em> , <em>i</em> = 1, . . . , <em>m</em>, be given domains. In this article, we study the low-rank approximation with respect to L<sup>2</sup>(Ω<sub>1</sub> × · ... -
In-situ Estimation of Time-averaging Uncertainties in Turbulent Flow Simulations
(2022)The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. The techniques available in the literature to accurately estimate these uncertainties typically only work in an ... -
A dimension-adaptive combination technique for uncertainty quantification
(2022-04)We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The ... -
A note on source term representation for control-and-state-constrained parabolic control problems with purely time-dependent control
(2022-06)We revisit the concept of source term representation, originally developed for boundary control problems subject to pointwise state constraints in the domain, and apply it to linear-quadratic parabolic control problems ... -
Knowledge discovery assistants for crash simulations with graph algorithms and energy absorption features
(2022)We propose the representation of data from finite element car crash simulations in a graph database to empower analysis approaches. The industrial perspective of this work is to narrow the gap between the uptake of modern ...
