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Molecular dynamics simulations of boronnitride nanotubes embedded in amorphous SiBN
Griebel, Michael; Hamaekers, Jan (200505)In this article, we examine the elastic properties of boronnitride nanotubes, which are embedded in amorphous siliconboronnitride ceramics. We employ molecular dynamics simulations using the ParrinelloRahman approach. ... 
Molecular dynamics simulations of the mechanical properties of polyethylenecarbon nanotube composites
Griebel, Michael; Hamaekers, Jan (200505) 
Molecular dynamics simulations of the influence of chemical crosslinks on the elastic moduli of polymercarbon nanotube composites
Griebel, Michael; Hamaekers, Jan; Wildenhues, Ralf (200506)In this article we compare the Young modulus of polyethylene carbon nanotube composites with chemical crosslinks between the nanotube and the polyethylene matrix to the modulus of a composite with weak nonbonded ... 
Sparse grids for the Schrödinger equation
Griebel, Michael; Hamaekers, Jan (200512)We present a sparse grid/hyperbolic cross discretization for manyparticle problems. It involves the tensor product of a oneparticle multilevel basis. Subsequent truncation of the associated series expansion then results ... 
A wavelet based sparse grid method for the electronic Schrödinger equation
Griebel, Michael; Hamaekers, Jan (200605)We present a direct discretization of the electronic Schrödinger equation. It is based on onedimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor ... 
A molecular dynamics study on the impact of defects and functionalization on the Young modulus of boronnitride nanotubes
Griebel, Michael; Hamaekers, Jan; Heber, Frederik (2007)In this article, we examine the Young modulus of (6, <em>m</em>) boronnitride nanotubes with vacancy and functionalization defects. We employ molecular dynamics simulations using the ParrinelloRahman approach. To this ... 
A molecular dynamics study of cementitious calcium silicate hydrate (CSH) gels
Dolado, Jorge S.; Griebel, Michael; Hamaekers, Jan (200705)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 ... 
A molecular dynamics study of the aluminosilicate chains structure in Alrich calcium silicate hydrated (CSH) gels
Manzano, Hegoi; Dolado, Jorge S.; Griebel, Michael; Hamaekers, Jan (200711)Calcium silicate hydrated (CSH) 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 ... 
BOSSANOVA: A bond order dissection approach for efficient electronic structure calculations
Griebel, Michael; Hamaekers, Jan; Heber, Frederik (200801)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 dimensionwise decomposition of the space the underlying ... 
Principal manifold learning by sparse grids
Feuersänger, Christian; Griebel, Michael (200804)In this paper we deal with the construction of lowerdimensional manifolds from highdimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the ... 
Tensor product multiscale manyparticle spaces with finiteorder weights for the electronic Schrödinger equation
Griebel, Michael; Hamaekers, Jan (200907)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, ... 
A molecular dynamics study on fullerene–implanted carbon nanotori as electronmagnetic sensing and emitting devices
Griebel, Michael; Heber, Frederik (200910)Openended 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 ... 
Intraday foreign exchange rate forecasting using sparse grids
Garcke, Jochen; Gerstner, Thomas; Griebel, Michael (201011)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 ... 
The smoothing effect of integration in ℝ^{d} and the ANOVA decomposition
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (201012)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 ... 
Approximation of twovariate functions: singular value decomposition versus sparse grids
Griebel, Michael; Harbrecht, Helmut (2011)We compare the cost complexities of two approximation schemes for functions <em>f</em> ∈ <em>H<sup>p</sup></em>(<em>Ω</em><sub>1</sub> × <em>Ω</em><sub>2</sub>) which live on the product domain <em>Ω</em><sub>1</sub> × ... 
On the construction of sparse tensor product spaces
Griebel, Michael; Harbrecht, Helmut (201105)Let Ω<sub>1</sub> ⊂ ℝ<sup><em>n</em><sub>1</sub></sup> and Ω<sub>2</sub> ⊂ ℝ<sup><em>n</em><sub>2</sub></sup> be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial ... 
Coupling molecular dynamics and continua with weak constraints
Fackeldey, Konstantin; Krause, Dorian; Krause, Rolf; Lenzen, Christoph (201106)One of the most challenging problems in dynamic concurrent multiscale simulations is the reflectionless transfer of physical quantities between the different scales. In particular, when coupling molecular dynamics and ... 
Greedy and randomized versions of the multiplicative Schwarz method
Griebel, Michael; Oswald, Peter (201106)We consider sequential, i.e., GaussSeidel type, subspace correction methods for the iterative solution of symmetric positive definite variational problems, where the order of subspace correction steps is not deterministically ... 
Schwarz type solvers for hpFEM discretizations of mixed problems
Beuchler, Sven; Purrucker, Martin (201107)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 hpFEM discretizations in three dimensions
Beuchler, Sven (201107)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 ...