Institut für Numerische Simulation (INS)
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Operator based multi-scale analysis of simulation bundles
(2015-11)We propose a new mathematical data analysis approach, which is based on the mathematical principle of symmetry, for the post-processing of bundles of finite element data from computer-aided engineering. Since all those ... -
Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
(2015)An approach to solve finite time horizon suboptimal feedback control problems for partial differential equations is proposed by solving dynamic programming equations on adaptive sparse grids. A semi-discrete optimal control ... -
Sparse grids for the Schrödinger equation
(2005-12)We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results ... -
Molecular dynamics simulations of the influence of chemical cross-links on the elastic moduli of polymer-carbon nanotube composites
(2005-06)In this article we compare the Young modulus of polyethylene carbon nanotube composites with chemical cross-links between the nanotube and the polyethylene matrix to the modulus of a composite with weak non-bonded ... -
Multiscale simulation of polymeric fluids using the sparse grid combination technique
(2017-10)We present a computationally efficient sparse grid approach to allow for multiscale simulations of non-Newtonian polymeric fluids. Multiscale approaches for polymeric fluids often involve model equations of high dimensionality. ... -
A wavelet based sparse grid method for the electronic Schrödinger equation
(2006-05)We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor ... -
Molecular dynamics simulations of boron-nitride nanotubes embedded in amorphous Si-B-N
(2005-05)In this article, we examine the elastic properties of boron-nitride nanotubes, which are embedded in amorphous silicon-boron-nitride ceramics. We employ molecular dynamics simulations using the Parrinello-Rahman approach. ... -
A molecular dynamics study of the aluminosilicate chains structure in Al-rich calcium silicate hydrated (C-S-H) gels
(2007-11)Calcium silicate hydrated (C-S-H) gel is the principal binding phase of the cement paste and responsible for its strength. It is basically composed of silicate chains held together with CaO layers, where different guest ... -
A molecular dynamics study on the impact of defects and functionalization on the Young modulus of boron-nitride nanotubes
(2007)In this article, we examine the Young modulus of (6, <em>m</em>) boron-nitride nanotubes with vacancy and functionalization defects. We employ molecular dynamics simulations using the Parrinello-Rahman approach. To this ... -
BOSSANOVA: A bond order dissection approach for efficient electronic structure calculations
(2008-01)In this article, we present a new decomposition approach for the eff cient approximate calculation of the electronic structure problem for molecules. It is based on a dimension-wise decomposition of the space the underlying ... -
A molecular dynamics study of cementitious calcium silicate hydrate (C-S-H) gels
(2007-05)In this article we study the polymerization of silicic acids (Si(OH)<sub>4</sub>) in the presence of calcium ions by molecular dynamics simulations. We focus on the formation and structure of cementitious calcium silicate ... -
Principal manifold learning by sparse grids
(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 molecular dynamics study on fullerene–implanted carbon nanotori as electronmagnetic sensing and emitting devices
(2009-10)Open-ended carbon nanotubes have been found to form toroidal structures [17]. These specific structures bear striking resemblance to electrographic coils. Two modes of action can be thought of: Either the metallic conductivity ... -
Tensor product multiscale many-particle spaces with finite-order weights for the electronic Schrödinger equation
(2009-07)In this article we combine the favorable properties of efficient Gaussian type orbitals basis sets, which are applied with good success in conventional electronic structure methods, and tensor product multiscale bases, ... -
The smoothing effect of integration in ℝd and the ANOVA decomposition
(2010-12)This paper studies the ANOVA decomposition of a <em>d</em>-variate function <em>f</em> defined on the whole of ℝ<em><sup>d</sup></em>, where <em>f</em> is the maximum of a smooth function and zero (or <em>f</em> could ... -
Intraday foreign exchange rate forecasting using sparse grids
(2010-11)We present a machine learning approach using the sparse grid combination technique for the forecasting of intraday foreign exchange rates. The aim is to learn the impact of trading rules used by technical analysts just ... -
Schwarz type solvers for hp-FEM discretizations of mixed problems
(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 ... -
Inexact additive Schwarz solvers for hp-FEM discretizations in three dimensions
(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 ... -
Solving incompressible two-phase flows on multi-GPU clusters
(2011-10)We present a fully multi-GPU-based double-precision solver for the three-dimensional two-phase incompressible Navier-Stokes equations. It is able to simulate the interaction of two fluids like air and water based on a ...
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