bluuebunny/crossref_metadata_2025_split huggingface dataset:
About the concept of measure‐valued solutions to distributed parameter systems
Authors: Roubíček Tomáš , Hoffmann Karl‐Heinz 
Published: November 2005

AbstractThe measure‐valued (mv) solutions are commonly defined in the literature simply by putting Young measures into the respective partial differential equations. Here a few examples of mv‐solutions to evolution problems (conservation laws, fluid dynamics and a so‐called backward‐forward heat problem) are re‐investigated to show that such definitions are not satisfactorily selective, i.e. they admit (sometimes surprisingly) many mv‐solutions apparently without any physical sense. Then an attempt for a selective definition in the case of the backward‐forward heat problem is made, resulting to a certain evolution variational inequality.
On a kinetic model for shallow water waves
Authors: Struckmeier Jens 
Published: November 2005

AbstractThe system of shallow water waves is one of the classical examples for non‐linear, two‐dimensional conservation laws. The paper investigates a simple kinetic equation depending on a parameter ϵ which leads for ϵ → 0 to the system of shallow water waves. The corresponding ‘equilibrium’ distribution function has a compact support which depends on the eigenvalues of the hyperbolic system. It is shown that this kind of kinetic approach is restricted to a special class of non‐linear conservation laws. The kinetic model is used to develop a simple particle method for the numerical solution of shallow water waves. The particle method can be implemented in a straightforward way and produces in test examples sufficiently accurate results.
A new system of boundary integral equations for plates with free edges
Authors: Giroire Jean , Nédélec Jean‐Claude 
Published: November 2005

AbstractWe present a new system of boundary integral equations for the free‐edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free‐edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.
Characterization of proteoglycan depletion in articular cartilage using two‐dimensional time domain nuclear magnetic resonance
Authors: Lattanzio Pierre‐Jean , Marshall K. Wayne , Damyanovich Andrei Z. , Peemoeller Hartwig 
Published: November 2005

AbstractIn vitro proteoglycan (PG) depletion in the 20–40% range (enzymatic PG depletion of normal cartilage in the early osteoarthritis (OA) PG depletion range) was investigated in articular cartilage using 2D time domain NMR relaxation techniques. Spin–lattice relaxation times were measured at low fields (T1ρ) and at high fields (T1) using nonselective and selective excitation pulse sequences. The short relaxation time magnetization components in T1ρ (∼8% signal) and nonselective T1 (∼5% signal) experiments were significantly altered with PG degradation. In addition, a magnetization component (∼5% signal) with a “fast ” T1 ∼ 7 ms was observed in the T1 experiment involving selective excitation. This fast T1 was at least 10 times shorter than the short T1 in the nonselective experiment and was associated with a strong magnetization exchange mechanism between collagen and PG. The results suggest that T1ρ and T1 (nonselective and selective) relaxation based MRI techniques, which focus on the short relaxation time magnetization components, have the potential of detecting molecular abnormalities associated with early OA earlier than single, long relaxation time component approaches. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Inducing coordination in supply chains through linear reward schemes
Authors: Golany Boaz , Rothblum Uriel G. 
Published: November 2005

AbstractDecentralized decision‐making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision‐making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi‐agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006
Numerical calculation of invariant manifolds for maps
Authors: Fuming Ma , Küpper Tassilo 
Published: November 2005

AbstractMany processes in the sciences and in engineering are modelled by dynamical systems and—in discretized version—by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.
On the use of periodicity properties for the efficient numerical solution of certain Markov chains
Authors: Bonhoure François , Dallery Yves , Stewart William J. 
Published: November 2005

AbstractMarkov chains with periodic graphs arise frequently in a wide range of modelling experiments. Application areas range from flexible manufacturing systems in which pallets are treated in a cyclic manner to computer communication networks. The primary goal of this paper is to show how advantage may be taken of this property to reduce the amount of computer memory and computation time needed to compute stationary probability vectors of periodic Markov chains. After reviewing some basic properties of Markov chains whose associated graph is periodic, we introduce a ‘reduced scheme’ in which only a subset of the probability vector need be computed. We consider the effect of the application of both direct and iterative methods to the original Markov chain (permuted to normal periodic form) as well as to the reduced system. We show how the periodicity of the Markov chain may be efficiently computed as the chain itself is being generated. Finally, some numerical experiments to illustrate the theory, are presented.
Improved SSOR and incomplete Cholesky solution of linear equations on shared memory and distributed memory parallel computers
Authors: Joubert Wayne , Oppe Thomas 
Published: November 2005

AbstractIn this paper two new implementations of SSOR and incomplete factorization preconditioners are given, for shared memory and distributed memory parallel computers respectively. These new implementations give increased solution speeds for matrix problems such as those arising from discretized partial differential equations with natural ordering of the grid points, for which it is well‐known that the standard implementation of these preconditioners is difficult to parallelize effectively. For shared memory machines, a new technique is presented here which decreases the number of synchronization points in each preconditioning step and thus allows better parallel speedups. For distributed memory machines, an implementation based on block cyclic reduction is given which circumvents the problem of idle processors during the preconditioning phase. Descriptions of the implementations are given, and numerical comparisons are given for a model diffusion problem on the Cray Y‐MP and the CM‐2 Connection Machine.
ILUT: A dual threshold incomplete LU factorization
Authors: Saad Yousef 
Published: November 2005

AbstractIn this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill‐in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill‐in element using only the graph of the matrix. Then each fill‐in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill‐ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.
On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems
Authors: Joubert Wayne 
Published: November 2005

AbstractThe solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s>0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.
A parallel version of the preconditioned conjugate gradient method for boundary element equations
Authors: Pester Matthias , Rjasanow Sergej 
Published: November 2005

AbstractThe parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two‐dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE‐2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.
On the stability of the incomplete Cholesky decomposition for a singular perturbed problem, where the coefficient matrix is not an M‐matrix
Authors: Sauter Stefan A. 
Published: November 2005

AbstractThe incomplete Cholesky decomposition is known as an excellent smoother in a multigrid iteration and as a preconditioner for the conjugate gradient method. However, the existence of the decomposition is only ensured if the system matrix is an M‐matrix. It is well‐known that finite element methods usually do not lead to M‐matrices. In contrast to this restricting fact, numerical experiments show that, even in cases where the system matrix is not an M‐matrix the behaviour of the incomplete Cholesky decomposition apparently does not depend on the structure of the grid. In this paper the behaviour of the method is investigated theoretically for a model problem, where the M‐matrix condition is violated systematically by a suitable perturbation. It is shown that in this example the stability of the incomplete Cholesky decomposition is independent of the perturbation and that the analysis of the smoothing property can be carried through. This can be considered as a generalization of the results for the so called square‐grid triangulation, as has been established by Wittum in [12] and [11].
Matrix shapes invariant under the symmetric QR algorithm
Authors: Arbenz Peter , Golub Gene H. 
Published: November 2005

AbstractThe QR algorithm is a basic algorithm for computing the eigenvalues of dense matrices. For efficiency reasons it is prerequisite that the algorithm is applied only after the original matrix has been reduced to a matrix of a particular shape, most notably Hessenberg and tridiagonal, which is preserved during the iterative process. In certain circumstances a reduction to another matrix shape may be advantageous. In this paper, we identify which zero patterns of symmetric matrices are preserved under the QR algorithm.
Approximate solutions and eigenvalue bounds from Krylov subspaces
Authors: Paige Chris C. , Parlett Beresford N. , van der Vorst Henk A. 
Published: November 2005

AbstractApproximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.
Trust regions based on conic functions in linear and nonlinear programming
Authors: Nazareth J. L. 
Published: November 2005

AbstractAn optimization method is developed based on ellipsoidal trust regions that are defined by conic functions. It provides a powerful unifying theory from which can be derived a variety of interesting and potentially useful optimization algorithms, in particular, conjugate‐gradient‐like algorithms for nonlinear minimization and Karmarkar‐like interior‐point algorithms for linear programming.
Dynamical analysis of numerical systems
Authors: Batterson Steve 
Published: November 2005

AbstractFor many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational problems. In particular the question of global convergence of various QR algorithms can be reduced to the study of certain vector iterations derived from Schur forms of matrices. The technique is illustrated in determining the convergence behavior of normal Hessenberg matrices under the Francis and multishift QR iterations.
A comparison result for multisplittings and waveform relaxation methods
Authors: Frommer Andreas , Pohl Bert 
Published: November 2005

AbstractWe show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M‐matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.
The RSCG algorithm on distributed memory architectures
Authors: Freitag Lori , Ortega James 
Published: November 2005

AbstractIn this paper, we demonstrate the scalability of the Reduced System Conjugate Gradient (RSCG) algorithm on distributed memory architectures. We present speed‐up results obtained on the Intel iPSC/860 that compare one‐, two‐, and three‐dimensional decompositions of the domain for both positive definite and positive semidefinite test problems. We develop a model for the RSCG algorithm to analyze computational and communication costs. The model is validated using experimental data and then used to examine and predict behavior of the RSCG algorithm as a function of architecture parameters including communication latency and transmission times and memory access costs.
Some remarks on the Barrier Lemma and 𝒦‐monotonicity
Authors: Marek I. 
Published: November 2005

AbstractAn abstract version of the well known Barrier Lemma is presented and some of its generalizations are shown for bounded linear and some unbounded densely defined linear monotone operators in some partially ordered Banach spaces. 𝒦‐monotonicity of generally unbounded operators is characterized. Some applications of constructing error bounds for approximately solving equations governed by bounded linear operators are established.
Implicit Cholesky algorithms for singular values and vectors of triangular matrices
Authors: Vince Fernando K. , Parlett Beresford N. 
Published: November 2005

AbstractThe implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.
Finite element analysis of mixing phenomena in tangential twin‐screw extruders for non‐Newtonian fluids
Authors: Sastrohartono T. , Kwon T. H. 
Published: November 2005

AbstractA flow analysis of non‐Newtonian fluids inside co‐rotating tangential twin‐screw extruders is presented with the emphasis on mixing phenomena. A new simplified approach was proposed in modelling the flow, i.e. the flow in twin‐screw extruders was considered as a sequence of flows in two regions: (i) the translation region (T‐region), similar to a single‐screw extruder; and (ii) the mixing region (M‐region), representing the central part of twin‐screw extruders. The flow has been assumed to be isothermal, steady‐state and creeping. Furthermore, it was assumed that the velocity field does not change significantly in one co‐ordinate (i.e. the down‐channel direction in the case of the T‐region and the axial direction in the case of the M‐region) as compared with the other co‐ordinate directions. Accordingly, a quasi‐three‐dimensional finite element method has been developed to analyse the flows in both regions. The mixing mechanisms inside the T ‐ and M‐regions were analysed and the inter‐channel mixing in the M‐region was quantified. The residence time distribution and performance characteristic of a single screw with a self‐wiping profile were also calculated.
Progress in mixed Eulerian‐Lagrangian finite element simulation of forming processes
Authors: Huétink J. , Vreede P. T. , van der Lugt J. 
Published: November 2005

AbstractA review is given of a mixed Eulerian‐Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap openning and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process.
A method of finite element tearing and interconnecting and its parallel solution algorithm
Authors: Farhat Charbel , Roux Francois‐Xavier 
Published: November 2005

AbstractA novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.
Parallel/vector improvements of the frontal method
Authors: Lesoinne M. , Farhat C. , Geradin M. 
Published: November 2005

AbstractWe present, discuss, and report on the performance of two combined parallel/vector frontal algorithms which have been incorporated in a production finite element code. Two parallelization strategies are described. The first approach is algebra driven and is recommended for the solution of problems with a large bandwidth on a coarse grain configuration. The second strategy is targeted for finer grain systems; it blends the first one with a substructuring technique that is based on a careful partitioning of the finite element mesh into a series of subdomains. Using only 4 IBM 3090/VF processors, the proposed algorithms are shown to deliver speed‐ups as high as 17 with respect to a serial non‐vectorized frontal solver.
Solution of large displacement contact problems with friction using Newton's method for generalized equations
Authors: Klarbring Anders , Bjöourkman Gunnar 
Published: November 2005

AbstractThis work is concerned with the formulation and numerical realization of large displacement contact problems with friction. A restricted class of contact problems is treated, where the deformation of one of the contacting bodies is prescribed. The formulation utilizes a particular convected co‐ordinate chart to define, firstly, tangential components for all potential contact points and, secondly, the notion of incremental tangential displacement. By writing the discretized problem as a generalized equation in the sense of Robinson it is made clear how Newton's method may be extended to this kind of non‐differentiable problems. The proposed algorithm is verified by several numerical examples.
Cellular automata simulation of flow around chains of cylinders
Authors: Eissler Werner , Drtina Peter , Frohn Arnold 
Published: November 2005

AbstractThe simulation of flows around single cylinders, tandem cylinders and infinite chains of cylinders with the lattice gas method is presented. The effects of the ratio of the cylinder diameter to channel width and different outflow boundary conditions are discussed. Results obtained applying different lattice gas models are given. Drag coefficient, wake length and Strouhal number are compared with experimental data. The agreement between numerical and experimental results is satisfactory.