bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multiple shooting methods for parabolic optimal control problems with control constraints
Authors: Carraro Thomas , Geiger Michael 
Published: October 2015

AbstractIn the context of ordinary differential equations, shooting techniques are a state‐of‐the‐art solver component, whereas their application in the framework of partial differential equations (PDE) is still at an early stage. We present two multiple shooting approaches for optimal control problems (OCP) governed by parabolic PDE. Direct and indirect shooting for PDE optimal control stem from the same extended problem formulation. Our approach reveals that they are structurally similar but show major differences in their algorithmic realizations. In the presented numerical examples we cover a nonlinear parabolic optimal control problem with additional control constraints. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A priori error estimates for nonstationary optimal control problems with gradient state constraints
Authors: Ludovici Francesco , Neitzel Ira , Wollner Winnifried 
Published: October 2015

AbstractWe are concerned with the discretization of semilinear parabolic optimization problems subject to constraints on the first derivative of the solution of the PDE. Constructing sequences of feasible controls for the dG(0)‐cG(1) discretization of the problem and relying on a quadratric growth condtion, we show convergence orders as temporal and spatial mesh tends to zero. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction
Authors: Peitz Sebastian , Dellnitz Michael 
Published: October 2015

AbstractIn this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dual‐weighted residual adaptivity for phase‐field fracture propagation
Authors: Wick Thomas 
Published: October 2015

AbstractIn this study, we consider phase‐field‐based fracture propagation in solid mechanics. The phase‐field model is based on a thermodynamically‐consistent version proposed by Miehe, Welschinger, Hofacker. The main focus is on goal‐oriented functional evaluations using a partition‐of‐unity dual‐weighted residual estimator for accurate measurement of, for example, point values, stresses, or crack opening displacements. Our developments are substantiated with a numerical test. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Controlled invariance for DAEs
Authors: Berger Thomas 
Published: October 2015

AbstractWe study the concept of locally controlled invariant submanifolds for nonlinear descriptor systems. In contrast to classical approaches, we define controlled invariance as the property of solution trajectories to evolve in a given submanifold whenever they start in it. It is then shown that this concept is equivalent to the existence of a feedback which renders the closed‐loop vector field invariant in the descriptor sense. This result is motivated by a preliminary consideration of the linear case.Local controlled invariance leads to the concept of output zeroing submanifolds. We show that the outcome of the differential‐algebraic version of the zero dynamics algorithm yields a locally maximal output zeroing submanifold. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A counter‐example concerning regularity properties for systems of conservation laws
Authors: Caravenna Laura , Spinolo Laura V. 
Published: October 2015

AbstractWe exhibit an explicit counter‐example which rules the possibility of extending to systems of conservation laws a regularity property of scalar conservation laws known as Schaeffer's Theorem. Loosely speaking, Schaeffer's Regularity Theorem asserts that, for a generic smooth initial datum, the solution of the Cauchy problem can develop at most finitely many discontinuities on compact sets. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coordination of guidance and stabilization tasks for bicycle rider modelling
Authors: Edelmann Johannes , Haudum Martin , Plöchl Manfred 
Published: October 2015

AbstractLearning to ride a bicycle requires practice and endurance fundamental to interpret the dynamics of a bicycle to control it. Modelling a virtual bicycle rider as a controller considering basic human characteristics is a similar demanding task. One approach for a virtual bicycle rider model is presented here, capable to stabilize the bicycle and follow a given course. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Minimal data rates and entropy in digitally networked systems
Authors: Kawan Christoph 
Published: October 2015

AbstractIn digitally networked systems the assumption of classical control theory that information can be transmitted instantaneously, lossless and with arbitrary precision is violated. This raises the question about the smallest data rate above which a control task can be solved. For a single control loop and the problem to make a set Q of states invariant, the minimal data rate can be described by an entropy‐like quantity, the so‐called invariance entropy. Under some controllability and hyperbolicity assumptions, the invariance entropy can be expressed in terms of Lyapunov exponents. Furthermore, one can show that for making Q invariant with a data rate close to the smallest, no strategies more complicated than stabilization at periodic trajectories are necessary. For a network with n subsystems, which can all communicate with each other, there are different ways to formulate the question about the smallest data rate for the invariance problem, but also in this setting entropy‐like quantities yield important information. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear Volume Flow Control of a Variable Displacement Vane Pump
Authors: Köster Marius , Fidlin Alexander 
Published: October 2015

AbstractVariable displacement vane pumps are used for mid‐pressure applications in a variety of systems. Due to their potential for power loss reduction they are most prominently featured in automotive applications. They provide a hydraulic consumer with varying levels of volume flow, depending on the eccentricity of the cam ring of the pump. Eccentricity control is typically achieved by means of hydraulic actuation. In this contribution, a model of a hydraulic aggregate featuring a VDVP with a nonlinear control technique based on input‐output‐linearization for volume flow tracking requirements is presented. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Kalman‐Yakubovich‐Popov Inequality for Descriptor Systems
Authors: Reis Timo , Voigt Matthias 
Published: October 2015

AbstractIn this paper, we consider the Kalman‐Yakubovich‐Popov lemma for descriptor systems. We study the arising linear matrix inequality in more detail. In particular, we give details about stabilizing solutions which play an important role for linear‐quadratic control problems. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reachable Sets of Quasilinear Hyperbolic Control Systems with Applications to Separation Processes
Authors: Zuyev Alexander 
Published: October 2015

AbstractThis paper is devoted to the analysis of reachable sets for quasilinear distributed parameter systems by using smooth finite dimensional controls. The class of systems under consideration includes models of a moving bed chromatographic process. We propose sufficient conditions on the states of such quasilinear systems to be approximately reachable with a family of controls corresponding to their finite dimensional approximations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multivariate generalized sampling type series: estimates of pointwise convergence
Authors: Bardaro Carlo , Mantellini Ilaria 
Published: October 2015

AbstractIn this short note we consider suitable linear combinations of Bochner‐Riesz type multivariate sampling series, which greatly improve the order of pointwise approximation. In particular we state some asymptotic formulae of Voronovskaja type which are of interest in image reconstruction. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Ambiguities in one‐dimensional phase retrieval of structured functions
Authors: Beinert Robert , Plonka Gerlind 
Published: October 2015

AbstractPhase retrieval means that we wish to recover a complex‐valued signal (discrete or continuous) from the magnitudes of its Fourier transform. Here we restrict ourselves to the recovery of structured functions, e.g. linear spline functions with equidistant knots. First, a complete characterization of the occurring ambiguities is presented. Moreover, we investigate additionally given moduli of the signal itself regarding their ability to reduce the set of ambiguities. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multivariate sampling Kantorovich operators: from the theory to the Digital Image Processing algorithm
Authors: Costarelli Danilo , Vinti Gianluca 
Published: October 2015

AbstractIn this note we consider the theory of sampling Kantorovich operators, and we show how it is possible to deduce an algorithm for Digital Image Processing starting from the general theory. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of learning algorithms for colour recognition on underwater images
Authors: Hoth Julian , Kowalczyk Wojciech 
Published: October 2015

AbstractObjects look very different in the underwater environment compared to their appearance in sunlight. High quality images with correct colouring simplify the detection of underwater objects. Hence, image processing is required to obtain images of high quality and correct colouring. Current algorithms focus on the colour reconstruction of scenery at diving depth where a significant part of sunlight is still present and different colours can still be distinguished. At greater depth the filtering is much stronger such that this is not possible. In this study it is investigated whether machine learning can be used to transform image data obtained in a controlled laboratory setup. The images are fed through learning machines with or without pre‐filters. It is shown that k‐nearest neighbour and support vector machines are most suitable for the given task and yield excellent results. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Prony's Method for Multivariate Signals
Authors: Peter Thomas , Plonka Gerlind , Schaback Robert 
Published: October 2015

AbstractThe problem of recovering translates and corresponding amplitudes of sparse sums of Gaussians out of sampling values as well as reconstructing sparse sums of exponentials are nonlinear inverse problems that can be solved for example by Prony's method. Here, we want to demonstrate a new extension to multivariate input data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Digital image processing algorithms for diagnosis in arterial diseases
Authors: Costarelli Danilo , Seracini Marco , Vinti Gianluca 
Published: October 2015

AbstractComputed Tomography images (C.T.) are currently part of the routine procedure in medical diagnostic techniques and can be used for the evaluation of occlusion rate of arterial vessels in presence of many diseases. The correct individuation of the morphology of these arterial anomalies allows specialists to diagnose the risk rate for the health of patients and to decide for surgical stent implants. Multivariate sampling Kantorovich operators are suitable for studying not necessarily continuos signals/images as the ones involved in the medical field. Convergent results for such a family of discrete operators translate into reconstruction and even enhancement of a given signal/image increasing the sampling rate. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A unifying approach for the study of linear sampling type operators in function spaces
Authors: Vinti Gianluca , Zampogni Luca 
Published: October 2015

AbstractSampling series play a crucial role in Signal and Image Processing. In this note, we illustrate a general method to construct Sampling series and to determine their convergence in Orlicz spaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Parallel simulation of large scale multibody systems
Authors: Klöppel Michael , Naumann Andreas , Waurich Volker , Walther Marcus , Wensch Jörg 
Published: October 2015

AbstractVirtual prototyping plays an ever increasing role in the engineering disciplines. Nowadays, engineers can rely on powerful tools like object oriented modeling languages, e.g., Modelica. Models written in this language can be simulated by open source software as well as commercial tools. The advantage of this approach is that the engineers can concentrate themselves on modeling, whereas the numerical intricacies of the simulation are handled by the software. On the other hand the simulations are usually slower than implementations which are parallelized and optimized manually. This can lead to computation times which are infeasible in practice, e.g., when a real time simulation is necessary for a hardware‐in‐the‐loop simulation.In this contribution we are concerned with speeding up such automated simulations by parallelization (on desktop hardware as well as HPC systems). We examine the parallelism across the system approaches. Additionally, the influence of the problem formulation on the simulation time is discussed. The implemented methods are demonstrated on engineering examples. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Qualitative Analysis and the Critical Hypersurfaces of Elliptic and Hyperbolic PDEs
Authors: Nastase Adriana 
Published: October 2015

AbstractMany boundary value problems of PDEs of the applied mathematics lead to the solving of equivalent elliptic and hyperbolic quadratic algebraic equations (QAEs) with variable coefficients. The qualitative analysis of elliptic and hyperbolic QAEs is started here by the determination of their behaviors by systematical variation of their free and linear terms, from −∞ to +∞ and by their visualization. It comes out that, for these variations of their coefficients, the elliptic and hyperbolic QAEs have critical hypersurfaces, which are obtained by cancellation of their great determinant as in [1], [2]. The critical hypersurface can be considered as a limit of existence of real solutions of an elliptic QAE. The hyperbolic QAE degenerates jumps and breaks along its critical hypersurface, which is also its asymptote. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of coupled machine components on long time scales
Authors: Klöppel Michael , Naumann Andreas , Wensch Jörg 
Published: October 2015

AbstractThe accuracy requirements in recent mass production processes demand new compensation techniques and structures of tool machines. To achieve these requirements, one has to know the thermo‐elastic behavior and interaction of the coupled components during the design phase.We discretize the machine components using finite elements. The heat exchange of the components couples the temperature fields, which leads to additional constraints on parallel FEM. The discretization in space leads to a system of coupled ODEs, which are of stiff parabolic type with fast time‐varying source terms. We concentrate on numerical methods to solve those equations on large timescales and reduce the timestep restriction to the fast coupling. This includes averaging techniques, as well as parallel in time methods. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive space‐time finite element methods for dynamic linear thermoelasticity
Authors: Rademacher Andreas 
Published: October 2015

AbstractThis article focuses on goal oriented error control for dynamic linear thermoelastic problems. To this end, we present a space‐time formulation of this problem class. The corresponding space‐time Galerkin discretization is the basis for the derivation of the error estimator using the dual weighted residual (DWR) method. A numerical example substantiates the accuracy and efficiency of the presented approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Enriching the Finite Element Method with meshfree techniques in structural mechanics
Authors: Zanette Andrea , Ferronato Massimiliano , Janna Carlo 
Published: October 2015

AbstractThe automatic generation of meshes for the Finite Element method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the nodes selected in a general domain. However, a thoroughly meshfree technique can be computationally quite expensive. Usually, the most expensive tasks rely on identifying the nodal contacts and computing the Galerkin integrals. In this thesis we advance a novel hybrid technique that blends Finite Elements with the Meshless Local Petrov‐Galerkin method with the aim at exploiting the most attractive properties of each procedure. The idea relies on the use of the Finite Element Method to compute a background solution that is locally improved by enriching the approximating space with the basis functions associated to a few meshless nodes, thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid. Adding the meshless particles only where needed avoids the cost of mesh refining, or even of re‐meshing, without the prohibitive burden of a thoroughly meshfree approach. In particular, two enriching methods are introduced and discussed, with applications in structural mechanics. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Eigenfunction expansions associated with the one‐dimensional Schroedinger operator
Authors: Gilbert Daphne 
Published: October 2015

AbstractWe consider the one‐dimensional Schroedinger operator H on L2(−∞, ∞) associated with

where q(r) : R → R is locally integrable, λ ∈ R is a spectral parameter, and the differential expression is in Weyl's limit point cases at both endpoints. Starting from the well known Weyl‐Kodaira formulation of the eigenfunction expansion associated with H [1], an alternative formulation can be derived in such a way that the principal features contributing to it, namely a scalar spectral density function, the location and multiplicity of the spectrum, and the spectral types of the generalised eigenfunctions, can be explicitly exhibited in the resulting expansion. The proof is based on classical work of Kac [2] and the theory of subordinacy [3], [4]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On a Particular Construction of Skew‐Selfadjoint Operator Matrices
Authors: Picard Rainer , Seidler Stefan , Trostorff Sascha , Waurick Marcus 
Published: October 2015

AbstractWe consider a particular construction for skew‐selfadjoint operator matrices, which are of central importance in initial boundary value problems of mathematical physics. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Exponential stability of a second‐order integro‐differential equation with delay
Authors: Trostorff Sascha 
Published: October 2015

AbstractWe consider a second order integro‐differential equation with time‐delay and show that this equation can be written as an evolutionary equation. Within the framework of evolutionary equations we show the well‐posedness and the exponential stability of the equation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the graphic statics for the analysis of masonry domes
Authors: Cavalagli Nicola , Gusella Vittorio 
Published: October 2015

AbstractThe graphic statics applied to constructions has been characterized by a rapid development between the end of the 19th century and the first decades of the 20th century. In this paper the application of the graphic statics to masonry domes is show. In particular three different methods are applied to a specific case study and the results discussed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Beltrami's continuum mechanics in non‐Euclidean spaces
Authors: Capecchi Danilo , Ruta Giuseppe 
Published: October 2015

AbstractEugenio Beltrami investigated if ambient space, where physical phenomena occur, is Euclidean: such a subject was trendy in the mathematical scientific community at the end of the 19th century. Beltrami, along with Riemann, was interested also on how non‐Euclidean geometry affects elasticity and electro‐magnetism. Beltrami opened new paths for mathematical physics; his pupils Ernesto Cesaro, Ernesto Padova, Carlo Somigliana also studied elasticity in non‐Euclidean spaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The role of virtual work in Levi‐Civita's parallel transport
Authors: Iurato Giuseppe , Ruta Giuseppe 
Published: October 2015

AbstractAccording to current history of science, Levi‐Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi‐Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adjoint Error Estimation for a Pseudo‐Spectral Approach to Stochastic Field‐Circuit Coupled Problems
Authors: Römer Ulrich , Schöps Sebastian 
Published: October 2015

AbstractThis work is concerned with the numerical approximation of random differential‐algebraic equations (DAE), arising from electric field‐circuit coupled problems. Using the adjoint DAE, the stochastic collation error is analyzed. The error can be evaluated using a collocation method of the same polynomial degree for the adjoint DAE. In particular, there is no need for constructing a solution of higher polynomial degree. The accuracy of the estimator is illustrated by a numerical example. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A finite element phase field model for relaxor ferroelectrics
Authors: Xu Bai‐Xiang , Wang Shuai , Yi Min 
Published: October 2015

AbstractA mechanically coupled phase field model is presented for the domain evolution and mesoscopic response of relaxor ferroelectrics. In the model the spontaneous polarization is treated as order parameter. The model is derived from thermodynamic analysis including the material force theory. Random field theory is adopted to take the disorder of relaxor ferroelectrics into account. Results show that the model is capable of reproducing relaxor features, such as domain miniaturization, small remnant polarization and large piezoelectric response. Dependence of these features on the random field strength is discussed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Block triangular preconditioning for time‐dependent Stokes control
Authors: Pearson John W. 
Published: October 2015

AbstractWe consider the numerical solution of time‐dependent Stokes control problems, an important class of flow control problems within the field of PDE‐constrained optimization. The problems we examine lead to large and sparse matrix systems which, with suitable rearrangement, can be written in block tridiagonal form, with the diagonal blocks given by saddle point systems. Using previous results for preconditioning PDE‐constrained optimization and fluid dynamics problems, along with well‐studied saddle point theory, we construct a block triangular preconditioner for the matrix systems. Numerical experiments verify the effectiveness of our solver. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)