Institut für Numerische Simulation (INS): Browsing Institut für Numerische Simulation (INS) by Title
Now showing items 50-69 of 153
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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 ... -
Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1
Peter Oswald (2018-09)We show that the <em>d</em>-dimensional Haar system <em>H<sup>d</sup></em> on the unit cube <em>I<sup>d</sup></em> is a Schauder basis in the classical Besov space B<em><sup>s</sup><sub>p,q,1</sub></em>(<em>I<sup>d</sup></em>), ... -
Hyperbolic cross approximation in infinite dimensions
Dũng, Dinh; Griebel, Michael (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 ... -
In-situ Estimation of Time-averaging Uncertainties in Turbulent Flow Simulations
Rezaeiravesh, Saleh; Gscheidle, Christian; Peplinski, Adam; Garcke, Jochen; Schlatter, Philipp (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 ... -
Incremental kernel based approximations for Bayesian inverse problems
Rieger, Christian (2018-05)We provide an interpretation for the covariance of the predictive process of Bayesian Gaussian process regression as reproducing kernel of a subset of the Cameron Martin space of the prior. We demonstrate that this ... -
Inexact additive Schwarz solvers for hp-FEM discretizations in three dimensions
Beuchler, Sven (2011-07)In this paper, a boundary value problem of second order in three space dimensions is discretized by means of the <em>hp</em>-version of the finite element method. The system of linear algebraic equations is solved by the ...