Institut für Numerische Simulation (INS): Browsing Institut für Numerische Simulation (INS) by Title
Now showing items 45-64 of 153
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Deep neural networks and PIDE discretizations
Bohn, Bastian; Griebel, Michael; Kannan, Dinesh (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, ... -
A dimension-adaptive combination technique for uncertainty quantification
Griebel, Michael; Seidler, Uta (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 ... -
Dimension-adaptive sparse grid quadrature for integrals with boundary singularities
Griebel, Michael; Oettershagen, Jens (2013)Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitly smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalized ... -
A dimension-oblivious domain decomposition method based on space-filling curves
Griebel, Michael; Schweitzer, Marc Alexander; Troska, Lukas (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 ... -
Dimensionality reduction of high-dimensional data with a non-linear principal component aligned generative topographic mapping
Griebel, Michael; Hullmann, Alexander (2013-07)Most high-dimensional real-life data exhibit some dependencies such that data points do not populate the whole data space but lie approximately on a lower-dimensional manifold. A major problem in many data mining applications ... -
Efficient neighbor search for particle methods on GPUs
Diehl, Patrick; Schweitzer, Marc Alexander (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 ... -
Efficient solution of ill-posed integral equations through averaging
Griebel, Michael; Jahn, Tim (2024-01)This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly ... -
Eliminating the pollution effect in Helmholtz problems by local subscale correction
Peterseim, Daniel (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 ... -
Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
Li, Guanglian; Peterseim, Daniel; Schedensack, Mira (2016-06)We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard ... -
Error estimates for multivariate regression on discretized function spaces
Bohn, Bastian; Griebel, Michael (2016-03)In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling ... -
Estimates for generalized sparse grid hierarchical basis preconditioners
Peter Oswald (2018-03)We reconsider some estimates from the 1994 paper [6] concerning the hierarchical basis preconditioner for sparse grid discretizations. The improvement is in three directions: We consider arbitrary space dimensions <em>d</em> ... -
EXAHD - A massively parallel fault tolerant sparse grid approach for high-dimensional turbulent plasma simulations
Lago, Rafael; Obersteiner, Michael; Pollinger, Theresa; Rentrop, Johannes; Bungartz, Hans-Joachim; Dannert, Tilman; Griebel, Michael; Jenko, Frank; Pflüger, Dirk (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 ... -
Extraction of fragments and waves after impact damage in particle-based simulations
Diehl, Patrick; Bußler, Michael; Pflüger, Dirk; Frey, Steffen; Ertl, Thomas; Sadlo, Filip; Schweitzer, Marc Alexander (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 ... -
Fast approximation of the discrete Gauss transform in higher dimensions
Griebel, Michael; Wissel, Daniel (2011-10)We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares ... -
Fast discrete Fourier transform on generalized sparse grids
Griebel, Michael; Hamaekers, Jan (2013-03)In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of ... -
A fault-tolerant domain decomposition method based on space-filling curves
Griebel, Michael; Schweitzer, Marc Alexander; Troska, Lukas (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 ... -
Finite differences on sparse grids for continuous time heterogeneous agent models
Jochen Garcke; Steffen Ruttscheidt (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 ... -
Generalized finite element methods for quadratic eigenvalue problems
Målqvist, Axel; Peterseim, Daniel (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 ... -
Generalized sparse grid interpolation based on the fast discrete Fourier transform
Michael Griebel; Jan Hamaekers (2019-03)In [9], an algorithm for trigonometric interpolation involving only so-called <em>standard information</em> of multivariate functions on generalized sparse grids has been suggested and a study on its application for the ... -
Greedy and randomized versions of the multiplicative Schwarz method
Griebel, Michael; Oswald, Peter (2011-06)We consider sequential, i.e., Gauss-Seidel type, subspace correction methods for the iterative solution of symmetric positive definite variational problems, where the order of subspace correction steps is not deterministically ...