bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Posteriori Estimates for Modelling Errors of the Stationary Diffusion Equation with Complicated Coefficients
Authors: Repin Sergej , Samrowski Tatiana , Sauter Stefan 
Published: November 2010

AbstractIn this paper, we suggest a new computational strategy for diffusion type problems with coefficients that may sharply change values and have a complicated distribution over the domain. We solve models, which approximate the coefficients, numerically and estimate the corresponding approximation errors by the a posteriori estimates of functional type. We show that the modelling error can be also explicitly calculated. This allows to obtain numerical solutions of complicated diffusion problems by solving much simpler problems that do not require full detailization of the structure of coefficients. Balancing modelling and discretization errors provides an economical way of getting an approximate solution with an a priori given accuracy. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical treatment of a free surface problem in ferrohydrodynamics
Authors: Knobloch Petr , Schütze Stephan , Tobiska Lutz 
Published: November 2010

AbstractThe interactions between a ferrofluid with a free surface and an immersed permanent magnet are studied. We consider a strategy for the computation of equilibrium positions of the free surface for various geometric positions of the magnet. It will be used for the numerical simulation of devices that are used in spacecraft technology to damp oscillations of satellites. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Solving optimal control problems by using inherent dynamical properties
Authors: Flaßkamp Kathrin , Ober‐Blöbaum Sina , Kobilarov Marin 
Published: November 2010

AbstractWe present a technique for computing optimal control trajectories by exploiting the inherent structure of the dynamics arising from symmetries and invariant (un)stable manifolds of fixed points. Our approach is based on sequencing motions along relative equilibria and invariant manifolds joined by simple optimized maneuvers. Our main goal is to compute an approximate globally optimal solution which can serve as a good initial guess for iterative nonlinear control optimization. The described approach is exemplified by the optimal control of the spherical pendulum. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shape Optimization for Stokes Flows using Conformal Metrics
Authors: Leithäuser Christian , Feßler Robert , Pinnau René 
Published: November 2010

AbstractWe derive a shape optimization approach for a two‐dimensional Stokes flow problem. Our goal is to compute a geometry whose wall shear stress is L2‐close to a desired target stress. Computations are carried out on a fixed domain, while shape variations are described through conformal metric changes. Tools from differential geometry are used to handle metric dependent operators. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Error analysis and improvement of first‐order design sensitivity relations
Authors: Materna Daniel , Barthold Franz‐Joseph 
Published: November 2010

AbstractThis contribution is concerned with novel approaches for error estimation and the improvement of first‐order design sensitivities for the state. These approaches are based on an exact representation of the design sensitivity of the state, which is obtained by performing different Taylor expansions with integral remainders. We consider a general variational framework and present the application of the proposed approach to shape sensitivity for the model problem of nonlinear elasticity. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reconstruction of Geophysical Layers with Shape Optimization and Level Set Methods
Authors: Papadopoulos Dimitrios , Herty Michael , Behr Marek , Rath Volker 
Published: November 2010

AbstractA shape optimization method is used to reconstruct the unknown shape of geophysical layers from boundary heat flux measurements by the use of adjoint fields and level sets. The identification of the shape of the geophysical layers by boundary heat flux measurements is necessary for the efficient use of geothermal energy. The method of speed is used to calculate the shape sensitivities, and the continuous adjoint approach is followed for the computation of the shape derivatives. The unknown shape is described with the help of the level set function; the advantage of the shape function is that no mesh movement or remeshing is necessary, but an additional Hamilton‐Jacobi equation has to be solved. This equation is solved in an artificial time, where the velocity represents the movement in the direction of the normal vector of the interface. For large optimization steps, re‐initialization of the level set function is also necessary, in order to keep the magnitude of the level set function near unity and also to smooth the level set function. Numerical results are given for measured heat fluxes on the boundary of the domain for different time steps and conductivity ratios. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adjoint Based Optimization of a Free Surface Flow for Film Casting
Authors: Repke Sabine , Marheineke Nicole 
Published: November 2010

AbstractMotivated by the industrial process of film casting, we discuss an optimal control approach for a viscous free surface flow that is asymptotically described by 2d Stokes equations. The aim is to optimize the shape of the free boundaries by adjusting the ambient pressure. A PDE‐constrained optimization problem is set up, where the free surfaces are described as graphs. The first‐order optimality system is derived via the Lagrangian formalism. The resulting minimization problem is solved by a steepest descent method, where the gradient is expressed in terms of the adjoint variables. Numerical results are presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Suboptimality Estimates for the Semi‐Discretized LQR Problem for Parabolic PDEs
Authors: Benner Peter , Saak Jens 
Published: November 2010

AbstractThe linear quadratic regulator problem (LQR) for parabolic partial differential equations (PDEs) has been understood to be an infinite‐dimensional Hilbert space equivalent of the finite‐dimensional LQR problem known from mathematical systems theory. The matrix equations from the finite‐dimensional case become operator equations in the infinite‐dimensional Hilbert space setting. A rigorous convergence theory for the approximation of the infinite‐dimensional problem by Galerkin schemes in the space variable has been developed over the past decades. Numerical methods based on this approximation have been proven capable of solving the case of linear parabolic PDEs. Embedding these solvers in a model predictive control (MPC) scheme, also nonlinear systems can be handled. Convergence rates for the approximation in the linear case are well understood in terms of the PDE's solution trajectories, as well as the solution operators of the underlying matrix/operator equations. However, in practice engineers are often interested in suboptimality results in terms of the optimal cost, i.e., evaluation of the quadratic cost functional. In this contribution, we are closing this gap in the theory. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Identification of Temperature Dependent Parameters in Radiative Heat Transfer
Authors: Tse Oliver , Pinnau René , Siedow Norbert 
Published: November 2010

AbstractLaser‐induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimizing irradiation planning in LITT. Optical attributes (absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal Control of the Euler Equations via Relaxation Approaches
Authors: Veelken Sonja , Herty Michael , Ngnotchouye Jean‐Medard T. , Banda Mapundi K. 
Published: November 2010

AbstractWe discuss two linear relaxation approaches to the optimal control of nonlinear hyperbolic systems, in particular the control of Euler flows in gas dynamics. The first method is a relaxation system that is due to Jin and Xin [2], the second one is a Lattice‐Boltzman approach [3], where we use one spatial dimension and five velocities (D1Q5 model). Both methods are incorporated in an adjoint based steepest‐descent algorithm for the optimisation. Convincing numerical results are presented for both methods for an example with discontinuous solutions. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Positivity inheritance for linear problems
Authors: Baum A.K. , Mehrmann Volker 
Published: November 2010

AbstractWe discuss the numerical solution of positive Differential‐Algebraic‐Equations (DAEs). For Ordinary Differential Equations (ODEs) where the system matrix is a ‐M‐Matrix, Runge‐Kutta‐ or Multistep‐Method are positive if the stepsize is chosen within the absolutely monotonicity radius of the considered method. We extend this concept to matrix pairs and present conditions for positivity preserving discretizations of linear, time‐invariant DAEs. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Worst case vs. average performance estimates for unconstrained NMPC schemes
Authors: Grüne Lars 
Published: November 2010

AbstractWe consider performance estimates for unconstrained NMPC schemes under a controllability assumption. By means of worst case and average estimates, we investigate the effect of varying control horizons on the performance and compare the results with numerical simulations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Multi‐Layered Potential Field Method for Multi‐Agent Navigation, Searching and Tracking
Authors: Hackbarth Axel , Hedrick Karl , Kreuzer Edwin 
Published: November 2010

AbstractCollaborating multi‐agent systems can handle complex tasks with several or changing mission objectives. We developed a potential field method that allows various information layers to influence the control over a group of vehicles. The gradient of the potential field is the driving force for local action, whereas the global waypoint is determined by the minimum of the agent's potential field. The driving force to the global waypoint is a virtual spring‐mass‐damper system that pulls the agent towards its waypoint, restricted by the local gradient of the agent's potential field. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Flatness based trajectory planning for the shallow water equations
Authors: Knüppel Torsten , Woittennek Frank , Rudolph Joachim 
Published: November 2010

AbstractA flatness based feed‐forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluice gate. In order to compute the trajectory of the control input, the problem is reduced to an initial value problem w.r.t. the spatial coordinate. The solution to this problem can be obtained with the method of characteristics. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Certification with optimal control strategies
Authors: Leyendecker Sigrid , Lucas Leonard J. , Owhadi Houman , Ortiz Michael 
Published: November 2010

AbstractThe optimal control methodology called concentration‐of‐measure optimal control (COMOC), seeks to minimise a concen‐ tration‐of‐measure upper bound on the probability of failure of an uncertain system. This bound is computed for a system characterised by a single performance measure depending on random inputs.This work considers controlled multibody dynamics taking place in an uncertain environment. The goal is to quantify uncertainty in a controlled robot manoeuvre and to minimise the probability of failure with regard to a performance measure. First, a deterministic optimal control problem is solved, yielding state and control trajectories that minimise an objective function. Boundary conditions for the optimal control problem are chosen such that the system performs ideally in the sense of the performance measure. Secondly, the obtained manoeuvre is reconsidered in the presence of uncertainty. Using a concentration‐of‐measure inequality, a rigorous upper bound for the probability of failure is derived. Finally, an optimisation is performed that searches for a control sequence (in the neighbourhood of the given one), that minimises the probability of failure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Passivity‐Based Control of Non‐Classical Electromechanical Systems
Authors: Müller Andreas , Jungnickel Uwe , Kielau Gerald , Maiser Peter 
Published: November 2010

AbstractPassivity‐based control has exclusively been pursued for dynamical systems possessing energetic state functions that are quadratic in the generalized velocities. This assumption does not apply to many dynamical systems, for instance in electromechanics, thus passivity‐based control has not been established for these classes of systems. This contribution presents an augmented PD control scheme for such systems. To this end the system dynamics is represented in the event space considered as a Finsler space. It is shown that in this setting the skew symmetry property is retained. A passivity‐based augmented PD controller is designed in the event space, and restricted to the configuration space giving rise to a passivity‐base control law. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modal Coupling for Active Damping of Load Swing of Container Cranes
Authors: Kreuzer Edwin , Rapp Christian 
Published: November 2010

AbstractOscillation control of container handling is dominated by open‐loop or closed‐loop control of the crane trolley, which highly effects the crane operator's well‐being. An alternative actuating approach is presented using the hoists of the crane system. Simulation and test stand results prove the effect of modal coupling control of container handling and its capability to assure improved work environment conditions for the operator of container cranes. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Flatness‐based control without prediction: example of a vibrating string
Authors: Rudolph Joachim , Woittennek Frank 
Published: November 2010

AbstractStable trajectory tracking by boundary control is discussed for a string with a mass at its free end. Based on the known fact that the ring of operators used to describe the system is a Bézout ring it is shown that predictions are not required for stabilization if distributed delays are admitted. The method is rather general for systems of boundary coupled wave equations with boundary control that can be modeled as delay systems with commensurate delays. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proper Orthogonal Decomposition for steady aerodynamic applications
Authors: Vendl Alexander , Faßbender Heike 
Published: November 2010

AbstractAn approach combining proper orthogonal decomposition (POD) with linear regression, which is called gappy POD, is used to obtain complete flow solutions in steady aerodynamic applications from knowledge of a (suitable) POD basis and the solution at very few points. In aerodynamics the partial or gappy data can be gathered by wind tunnel experiments. The effectiveness of the Gappy POD will be demonstrated on an industrial testcase of the wing‐body configuration MEGAFLUG. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Displacement Regularization with Application to Image Zooming
Authors: Lenzen Frank 
Published: November 2010

AbstractWe study the problem of displacement errors, i.e. errors induced by a sampling process with distorted locations of the sampling points. Starting with a non‐convex regularization method, we apply a semi‐group concept and derive a partial differential equation, which allows for correcting displacement errors.As main application for correction of displacement errors we consider image interpolation, in particular zooming, of digital color images. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Some contributions to the model order reduction of large scale non‐linear electric circuits
Authors: Amorocho D. Juan Pablo , Faßbender Heike 
Published: November 2010

AbstractModel order Reduction (MOR) has become an ubiquitous technique in the simulation of large‐scale dynamical systems (i.e. 104 and more equations). One technique for non‐linear MOR is the trajectory piecewise‐linear approach (TPWL) [1]. TPWL approximates a non‐linear differential system by a weighted sum of linear systems which have a significantly reduced number of equations. One open question is which weight representations provide physical meaning of the weighted sum [2]. In this article we propose two representations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Highly scalable multigrid algorithm for particle simulation
Authors: Bolten Matthias 
Published: November 2010

AbstractWe present a highly scalable method for the calculation of effects due to the Coulomb potential in atomistic systems. The method is based on a mathematical consistent formulation of the Coulomb problem in terms of the solution of a special Poisson equation. For the solution of these PDE a multigrid method is used. The whole method is parallelized using domain splitting and shows a very good strong scaling behavior. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Aspects of the Facet‐Edge Data Structure for the Construction of Voronoi Cells
Authors: Weber Christoph , Loehnert Stefan , Wriggers Peter 
Published: November 2010

AbstractThe construction of Voronoi diagrams has two main aspects: The construction algorithm and the data structure. For the construction of planar Voronoi diagrams e.g. the well known plane sweep algorithm can be applied. Another efficient method is the incremental construction of the Delaunay triangulation by using the quad‐edge data structure. Within this data structure the Delaunay triangulation is treated as a planar graph. Incremental construction implies that manipulations of the triangulation are allowed. Its Voronoi diagram is obtained simply by accessing the triangulation's dual graph. We extend this method to tree dimensions, by implementing a 3D Delaunay triangulation on the facet‐edge data structure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Heterogeneous Coupling: A Comparison of two Approaches for the Modeling of thin Structures
Authors: Groß Christian , Krause Rolf , Steiner Johannes 
Published: November 2010

AbstractTwo different approaches for the modeling of a heterogeneous model consisting of, e.g., bone and ligaments, are presented and compared along a simple model problem. We describe both methods and briefly discuss their advantages and disadvantages. Furthermore, we present first numerical results in 3D. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Verified Distance Computation Between Convex Hulls of Octrees Using Interval Optimization Techniques
Authors: Dyllong Eva , Kiel Stefan 
Published: November 2010

AbstractDistance computation is an important task in many application areas, including biomechanics, robot systems and computer games. Depending on the intended use, requirements differ. For example, in a medical context, a verified result may be of interest. In this paper we will demonstrate the use of an interval optimization algorithm for computing a verified enclosure of the minimum distance between the convex hulls of two octrees. We will also discuss runtime improvements. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical modelling of surface water waves generated by moving underwater landslide on irregular bottom
Authors: Shokina Nina 
Published: November 2010

AbstractThe numerical modelling of surface water waves generated by a moving underwater landslide on irregular bottom is considered. The non‐linear shallow water model is used with taking into account bottom mobility. The equations are obtained for an underwater landslide movement under the action of gravity force, buoyancy force, friction force and water resistance force. The predictor‐corrector scheme [5], preserving the monotonicity of the numerical solution profiles in a linear case, is used on adaptive grids. The scheme is validated on the problem with a known analytical solution. The analysis is done for the dependencies of wave regimes on bottom slope, initial landslide depth, its length and width. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model reduction via quasistatic approximations
Authors: Weber Steffen , Arnold Martin 
Published: November 2010

AbstractStiff terms in second‐order differential equations may cause long computation time due to high frequencies. Quasi‐static approximations eliminate these high frequency solution components by neglecting inertia forces. In this interpretation, the equations of motion of systems with small masses correspond to a singularly perturbed problem. Results from singular perturbation theory will be extended to problems with perturbations of more than two different orders of magnitude. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Machine of Bohnenberger: Bicentennial of the Gyro with Cardanic Suspension
Authors: F. Wagner Jörg , Trierenberg Andor 
Published: November 2010

AbstractIn 2004, a gyro with cardanic suspension was recovered in the physical collection of a school in Tübingen, Germany. Up to now, this instrument seems to be the only original corresponding explicitly with the first systematic explanation of such an apparatus. This description dates back to 1817 and was written by the inventor J.G.F. Bohnenberger (1765‐1831), who called the device simply Machine. At that time, Bohnenberger was professor for mathematics, physics, and astronomy at the University of Tübingen as well as the scientific head of the historic Württemberg land surveying. The discovery made aware that the historical background of the Machine of Bohnenberger was mainly unexplained. This is remarkable as the instrument was the basis for Foucault's famous work on gyros and as it paved the way to important mechanical navigation instruments like the directional gyro, the artificial horizon, and finally inertial platforms. Therefore, the finding in Tübingen prompted the authors to search for additional historical documents sheding light on Bohnenberger's invention. Meanwhile, several original specimen manufactured by Bohnenberger's instrument maker J.W.G. Buzengeiger (1778‐1836) could be identified, and it was possible to narrow the invention down to the year 1810. The paper outlines the historical background of the Machine of Bohnenberger currently known and sketches the biography of its inventor. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
L1‐regularisation for ill‐posed problems in variational data assimilation
Authors: Freitag Melina A. , Nichols Nancy K. , Budd Chris J. 
Published: November 2010

AbstractWe consider four‐dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2‐regularisation, a widely used method for solving ill‐posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1‐norm regularisation, recovers sharp edges better than L2‐norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1‐norm regularisation performs much better than the standard L2‐norm regularisation in 4DVar. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)