Institut für Numerische Simulation (INS): Browsing Institut für Numerische Simulation (INS) by Title
Now showing items 115-134 of 153
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Principal manifold learning by sparse grids
Feuersänger, Christian; Griebel, Michael (2008-04)In this paper we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the ... -
A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints
Neitzel, Ira; Wollner, Winnifried (2016-03)In this paper, an elliptic optimization problem with pointwise inequality constraints on the state is considered. The main contribution of this paper are a priori <em>L<sup>2</sup></em>-error estimates for the discretization ... -
A priori error estimates for state constrained semilinear parabolic optimal control problems
Ludovici, Francesco; Neitzel, Ira; Wollner, Winnifried (2016-02)We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In contrast to many results in numerical analysis ... -
Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
Hoppe, Fabian; Neitzel, Ira (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 ... -
Regularized kernel based reconstruction in generalized Besov spaces
Griebel, Michael; Rieger, Christian; Zwicknagl, Barbara (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 ... -
Relaxing the CFL condition for the wave equation on adaptive meshes
Peterseim, Daniel; Schedensack, Mira (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 ... -
A representer theorem for deep kernel learning
Bohn, Bastian; Griebel, Michael; Rieger, Christian (2019-05)In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical ... -
Reproducing kernel Hilbert spaces for parametric partial differential equations
Griebel, Michael; Rieger, Christian (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 ... -
Robust numerical upscaling of elliptic multiscale problems at high contrast
Peterseim, Daniel; Scheichl, Robert (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 ... -
Sampling inequalities for anisotropic tensor product grids
Rieger, Christian; Wendland, Holger (2018-04)We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in ... -
Sampling inequalities for sparse grids
Rieger, Christian; Wendland, Holger (2015)Sampling inequalities play an important role in deriving error estimates for various reconstruction processes. They provide quantitative estimates on a Sobolev norm of a function, defined on a bounded domain, in terms of ... -
Schwarz iterative methods: Infinite space splittings
Griebel, Michael; Oswald, Peter (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 ... -
Schwarz type solvers for hp-FEM discretizations of mixed problems
Beuchler, Sven; Purrucker, Martin (2011-07)The Stokes problem and linear elasticity problems can be viewed as a mixed variational formulation. These formulations are discretized by means of the <em>hp</em>-version of the finite element method. The system of linear ... -
Second order optimality conditions for optimal control of quasilinear parabolic equations
Bonifacius, Lucas; Neitzel, Ira (2017-03)We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality ... -
Simrank-based prediction of crash simulation similarities
Pakiman, Anahita; Garcke, Jochen; Schumacher, Axel (2022)Data searchability has been utilized for decades and is now a crucial ingredient of data reuse. However, data searchability in industrial engineering is essentially still at the level of individual text documents, while ... -
Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model
Griebel, Michael; Rüttgers, Alexander (2013-04)We apply the multiscale FENE model to a 3D square-square contraction flow problem. For this purpose, wecouple the stochastic Brownian configuration field method (BCF) with our fully parallelized three-dimensional Navier-Stokes ... -
Simulation of droplet impact with dynamic contact angle boundary conditions
Griebel, Michael; Klitz, Margrit (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 ... -
Simulation of micron-scale drop impact
Klitz, Margrit; Griebel, Michael (2018-10)The numerical simulation of droplet impact 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 is a key ... -
Simulation of the oil storage process in the scopa of specialized bees
Rüttgers, Alexander; Griebel, Michael; Pastrik, Lars; Schmied, Heiko; Wittmann, Dietmar; Scherrieble, Andreas; Dinkelmann, Albrecht; Stegmaier, Thomas (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 ... -
Simulation of wave propagation and impact damage in brittle materials using peridynamics
Diehl, Patrick; Schweitzer, Marc Alexander (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 ...