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  • Opus-Repositorium ZIB  (347)
  • 1990-1994  (255)
  • 1985-1989  (92)
  • 1915-1919
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  • 101
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    A quasiresonant smoothing algorithm for the fast analysis of selective vibrational excitation. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: One key problem in modern chemistry is the simulation of the dynamical reaction of a molecule subjected to external radiation. This is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in form of a system of ordinary differential equations, whose solutions show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. This idea leads to the construction of a quasiresonant smoothing algorithm (QRS). In QRS, a natural and computationally available splitting parameter $\delta$ controls the smoothing properties. The performance of QRS is demonstrated in two applications treating the selective excitation of vibrational states by picosecond laser pulses. In comparison with standard methods a speedup factor of 60--100 is observed. A closer look to purely physically motivated quasiresonant approximations such as WFQRA shows some additional advantages of the above smoothing idea. Among these the possibility of an adaptive formulation of QRS via the parameter $\delta$ is of particular importance.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 102
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    Combinatorial Optimization. (1993)
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    Publikationsdatum: 2020-11-16
    Beschreibung: This paper will appear as Chapter 28 of the forthcoming "Handbook on Combinatorics" (editors: R. Graham, M. Grötschel, L. Lovasz) to be published in 1994, by North-Holland.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 103
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    Numerical Simulation of Relaxation Oscillations of Waveguide-Lasers. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: An analysis of relaxation oscillations in local Er-doped optically pumped lasers is reported. It is based on a time dependent rate equation model for a quasi-two-level-system with wavelength dependent emission- and absorption cross-sections. For the first time a numerically reliable simulation of the characteristic laser behaviour was possible: the onset and decay of the oscillations, the time-dependent repetition period and the steady state signal output power. The characteristic waveguide parameters, as the erbium-concentration profile, the polarization dependent pump- and signal mode intensity profiles, the scattering losses, the cavity length and the front and rear reflectivities were all taken into account. The basic formulas are general and can also be used for Er-doped fiber lasers. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. The used algorithmic replacement procedure is motivated and discussed in detail. Here, pump- and signal evolution versus time are presented for an planar Er-diffused $\rm Ti$:$\rm LiNbO_{3}$ waveguide laser. The numerically obtained results show a nearly quantitative agreement with experimental investigations. Simultanously they supply knowledge about non-measureable (space-dependent population dynamic of the Er-atoms) and till today not measured data (dynamical response of the laser by a sharp peak in the external pump).
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 104
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    Algebraic Algorithms for Sampling from Conditional Distributions. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 105
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    Monotone Multigrid Methods for Elliptic Variational Inequalities I. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Extending well--known linear concepts of successive subspace correction, we arrive at extended relaxation methods for elliptic variational inequalities. Extended underrelaxations are called monotone multigrid methods, if they are quasioptimal in a certain sense. By construction, all monotone multigrid methods are globally convergent. We take a closer look at two natural variants, which are called symmetric and unsymmetric multigrid methods, respectively. While the asymptotic convergence rates of the symmetric method suffer from insufficient coarse--grid transport, it turns out in our numerical experiments that reasonable application of the unsymmetric multigrid method may lead to the same efficiency as in the linear, unconstrained case.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 106
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    Multilevel Methods for Elliptic Problems on Domains not Resolved by the Coarse Grid. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Elliptic boundary value problems are frequently posed on complicated domains which cannot be covered by a simple coarse initial grid as it is needed for multigrid like iterative methods. In the present article, this problem is resolved for selfadjoint second order problems and Dirichlet boundary conditions. The idea is to construct appropriate subspace decompositions of the corresponding finite element spaces by way of an embedding of the domain under consideration into a simpler domain like a square or a cube. Then the general theory of subspace correction methods can be applied.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 107
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    Zonotopal Tilings and the Bohne-Dress Theorem. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We prove a natural bijection between the polytopal tilings of a zonotope $Z$ by zonotopes, and the one-element-liftings of the oriented matroid ${\cal M}(Z)$ associated with $Z$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 108
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    A package on formal power series. (1993)
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    Publikationsdatum: 2015-06-01
    Beschreibung: Formal Laurent-Puiseux series of the form \[ f(x)=\sum \limits_{k=k_0}^{\infty}a_{k}x^{k/n} \] are important in many branches of mathematics. Whereas {\sc Mathematica} supports the calculation of truncated series with its {\tt Series} command, and the {\sc Mathematica} package {\tt SymbolicSum} that is shipped with {\sc Mathematica} version 2 is able to convert formal series of the type mentioned above in some instances to their corresponding generating functions, in six publications of the author we developed an algorithmic procedure to do these conversions that is implemented by the author, A.\ Rennoch and G.\ Stölting in the {\sc Mathematica} package {\tt PowerSeries}. The implementation enables the user to reproduce most of the results of the extensive bibliography on series of Hansen, E.\ R.: A table of series and products. Prentice-Hall, 1975. Moreover a subalgorithm of its own significance generates differential equations satisfied by the input function.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 109
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    Formal Power Series. (1993)
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    Publikationsdatum: 2015-06-01
    Beschreibung: {\newcommand{\C}{{\rm {\mbox{C{\llap{{\vrule height1.52ex}\kern.4em}}}}}} \newcommand{\Z} {{\rm {\mbox{\protect\makebox[.2em][l]{\sf Z}\sf Z}}}} \newcommand{\Maple}{{\sc Maple}} Formal Laurent-Puiseux series of the form \[ f(x)=\sum\limits_{k=k_0}^{\infty}a_{k}x^{k/n} \label{eq:formalLPS} \] with coefficients $a_{k}\in\C\;(k\in\Z)$ are important in many branches of mathematics. \Maple\ supports the computation of {\em truncated\/} series with its {\tt series} command, and through the {\tt powerseries} package infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients. This is known as {\em lazy evaluation\/}. But these tools fail, if one is interested in an explicit formula for the coefficients $a_k$. In this article we will describe the \Maple\ implementation of an algorithm presented in several papers of the second author which computes an {\em exact\/} formal power series of a given function. This procedure will enable the user to reproduce most of the results of the extensive bibliography on series. We will give an overview of the algorithm and then present some parts of it in more detail. This package is available through the \Maple-share library with the name {\tt FPS}. We flavor this procedure with the following example. %\begin{maple} \begin{verbatim}〉 FormalPowerSeries(sin(x), x=0);\end{verbatim} \begin{samepage} \begin{verbatim} infinity ----- k (2 k + 1) \ (-1) x ) ---------------- / (2 k + 1)! ----- k = 0 \end{verbatim} \end{samepage} }
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 110
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    Packing Paths and Steiner Trees: Routing of Electronic Circuits. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: One of the challenging problems in the design of electronic circuits is the so-called routing problem. Roughly speaking, the task is to connect so-called terminal sets via wires on a predefined area. In addition, certain design rules are to be taken into account and an objective function such as the wiring length must be minimized. The routing problem in general is too complex to be solved in one step. Depending on the user's choice of decomposing the chip design problem into a hierarchy of stages, on the underlying technology, and on the given design rules, various subproblems arise. We discuss several variants of practically relevant routing problems and give a short overview on the underlying technologies and design rules. Many of the routing problems that come up this way can be formulated as the problem of packing so-called Steiner trees in certain graphs. We consider the Steiner tree packing problem from a polyhedral point of view and present three possibilities to define an appropriate polyhedron. Weighing their pros and cons we decide for one of these polytopes and sketch some of our investigations.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 111
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    Monotone Multigrid Methods for Elliptic Variational Inequalities II. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We derive fast solvers for discrete elliptic variational inequalities of the second kind as resulting from the approximation by piecewise linear finite elements. Following the first part of this paper, monotone multigrid methods are considered as extended underrelaxations. Again, the coarse grid corrections are localized by suitable constraints, which in this case are fixed by fine grid smoothing. We consider the standard monotone multigrid method induced by the multilevel nodal basis and a truncated version. Global convergence results and asymptotic estimates for the convergence rates are given. The numerical results indicate a significant improvement in efficiency compared with previous multigrid approaches.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 112
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    A Polyhedral Approach to Multicommodity Survivable Network Design. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The design of cost-efficient networks satisfying certain survivability constraints is of major concern to the telecommunications industry. In this paper we study a problem of extending the capacity of a network by discrete steps as cheaply as possible, such that the given traffic demand can be accommodated even when a single edge or node in the network fails. We derive valid and non-redundant inequalities for the polyhedron of capacity design variables, by exploiting its relationship to connectivity network design and knapsack-like subproblems. Computational work using this model and the additional inequalities is in progress.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 113
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    Adaptive Discrete Galerkin-Methods for Macromolecular Processes. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper, a rather recent algorithmic approac to the numerical simulation of macromolecula processes is surveyed. It avoids the numerical stiff integration o thousands up to millions of ODE's by constructing a scale of discret Hilbert spaces, especially weighted sequence spaces, and establishing corresponding Galerkin method. Examples including polyreactions o industrial relevance and ecological waste management by biochemica recycling illustrate the importance and efficiency of the algorithm.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 114
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    Optimum Path Packing on Wheels: The Noncrossing Case. (1993)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that no two terminal pairs cross, then a path packing, i.~e.,a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 115
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    Jahresbericht 1993 (1993)
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    Publikationsdatum: 2019-10-24
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: annualzib , doc-type:report
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  • 116
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    Jahresbericht 1992 (1993)
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    Publikationsdatum: 2019-10-24
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: annualzib , doc-type:report
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  • 117
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    Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation. (1993)
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    Publikationsdatum: 2022-07-07
    Beschreibung: The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrödinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 118
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    An Adaptive Approach to the Numerical Solution of Fresnel’s Wave Equation. (1993)
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    Publikationsdatum: 2022-07-07
    Sprache: Englisch
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  • 119
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    On the Impact of Communication Latencies on Distributed Sparse LU Factorization. (1993)
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    Publikationsdatum: 2022-07-19
    Beschreibung: Sparse LU factorization offers some potential for parallelism, but at a level of very fine granularity. However, most current distributed memory MIMD architectures have too high communication latencies for exploiting all parallelism available. To cope with this, latencies must be avoided by coarsening the granularity and by message fusion. However, both techniques limit the concurrency, thereby reducing the scalability. In this paper, an implementation of a parallel LU decomposition algorithm for linear programming bases is presented for distributed memory parallel computers with noticable communication latencies. Several design decisions due to latencies, including data distribution and load balancing techniques, are discussed. An approximate performance model is set up for the algorithm, which allows to quantify the impact of latencies on its performance. Finally, experimental results for an Intel iPSC/860 parallel computer are reported and discussed.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 120
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    Monte Carlo Renormalization Study at Large beta in the Confinement Region (1993)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 121
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    Study of Spatial Size Effects in Quenched Wilson Hadron Spectroscopy at beta = 6.3 (1993)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 122
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    QCD on the Massively Parallel Computer AP 1000 (1993)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 123
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    Autocorrelation in Updating Pure SU(3) Lattice Gauge Theory by the Use of Overrelaxed Algorithms (1993)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 124
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    A Quasiresonant Smoothing Algorithm for the Fast Analysis of Selective Vibrational Excitation (1993)
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    Publikationsdatum: 2023-08-14
    Sprache: Englisch
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  • 125
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    Discrete Mathematics in Manufacturing. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Manufacturing is a topic that provides rich opportunities for important mathematical contributions to real-world problems. The purpose of this paper is to show, by means of several examples, where and how mathematical problems of a discrete nature arise in manufacturing and to demonstrate the savings and improvements that can be achieved by employing the techniques of combinatorial optimization. The topics covered range from the design phase of a product (e. g.,routing, placement and via minimization in VLSI design), the control of CNC machines (e. g., drilling and plotting), to the management of assembly lines, storage systems and whole factories. We also point out difficulties in the modelling of complex situations and outline the algorithmic methods that are used for the solution of the mathematical problems arising in manufacturing. {\bf Key words:} discrete mathematics , combinatorial optimization, applications to manufacturing.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 126
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    A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Large scale combustion simulations show the need for adaptive methods. First, to save computation time and mainly to resolve local and instationary phenomena. In contrast to the widespread method of lines, we look at the reaction- diffusion equations as an abstract Cauchy problem in an appropriate Hilbert space. This means, we first discretize in time, assuming the space problems solved up to a prescribed tolerance. So, we are able to control the space and time error separately in an adaptive approach. The time discretization is done by several adaptive Runge-Kutta methods whereas for the space discretization a finite element method is used. The different behaviour of the proposed approaches are demonstrated on many fundamental examples from ecology, flame propagation, electrodynamics and combustion theory. {\bf Keywords:} initial boundary value problem, Rothe- method, adaptive Runge-Kutta method, finite elements, mesh refinement. {\bf AMS CLASSIFICATION:} 65J15, 65M30, 65M50.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 127
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    Packing Steiners Trees: A Cutting Plane Algorithm and Computational Results. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSI-design and report on our computational experience. This includes a brief discussion of separation algorithms, a new LP-based primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree packing polyhedron developed in our companion paper SC 92-8 and meant to turn this theory into an algorithmic tool for the solution of practical problems.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 128
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    Packing Steiner Trees: Polyhedral Investigations. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Let $G=(V,E)$ be a graph and $T\subseteq V$ be a node set. We call an edge set $S$ a Steiner tree with respect to $T$ if $S$ connects all pairs of nodes in $T$. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph $G=(V,E)$ with edge weights $w_e$, edge capacities $c_e, e \in E,$ and node sets $T_1,\ldots,T_N$, find edge sets $S_1,\ldots,S_N$ such that each $S_k$ is a Steiner tree with respect to $T_k$, at most $c_e$ of these edge sets use edge $e$ for each $e\in E$, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the Steiner tree packing Problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet-defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper SC 92-09.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 129
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    Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits. (1992)
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    Publikationsdatum: 2020-10-05
    Beschreibung: The placement in the layout design of electronic circiuts consists of finding a non- overlapping assignment of rectangular cells to positions on the chip so what wireability is guaranteed and certain technical constraints are met.This problem can be modelled as a quadratic 0/1- program subject to linear constraints. We will present a decomposition approach to the placement problem and give results about $NP$-hardness and the existence of $\varepsilon$-approximative algorithms for the involved optimization problems. A graphtheoretic formulation of these problems will enable us to develop approximative algorithms. Finally we will present details of the implementation of our approach and compare it to industrial state of the art placement routines. {\bf Keywords:} Quadratic 0/1 optimization, Computational Complexity, VLSI-Design.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 130
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    Das Implementieren des Simplex- Verfahrens: Die Startbasis. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Dieses Paper enthält die ersten beiden Teile einer geplanten Serie von Aufsätzen über die $CPLEX^2$-Implementierung des Simplex- Verfahrens. Der erste Teil ist eine Einführung: er liefert eine kurze Beschreibung des Verfahrens für Probleme mit beschränkten Variablen, zusammen mit einer relativ ausführlichen Diskussion der numerischen Eigenschaften der Netlib-Probleme. Diese Probleme bilden auch das Fundament der rechnerischen Untersuchungen in den folgenden Teilen. Der zweite Teil enthält die Hauptergebnisse dieses Papers, eine Beschreibung der Methode, die von CPLEX verwendet wird, um eine Startbasis zu konstruieren.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 131
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    Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of RamanSpectroscopy. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Models for occupation dynamics in discrete quantum systems lead to large or even infinite systems of ordinary differential equations. Some new mathematical techniques, developed for the simulation of chemical processes, make a numerical solution of countable systems of ordinary differential equations possible. Both, a basic physical concept for the construction of such systems and the structure of the numerical tools for solving them are presented. These conceptual aspects are illustrated by a simulation of an occupation process from spectroscopy. In this example the structures of rotation spectra observed in infrared spectroscopy are explained and some possibilities for an extension of the model are shown.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 132
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    A Polyhedral Approach to Network Connectivity Problems (Extended Abstract). (1992)
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    Publikationsdatum: 2020-12-14
    Beschreibung: We present a polyhedral approach for the general problem of designing a minimum-cost network with specified connectivity requir
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 133
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    Group Theoretical Mode Interactions with Different Symmetries. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the innerconnectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.
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    Sprache: Englisch
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  • 134
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    Packing Steiner Trees: Separation Algorithms. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.~g., in VLSI routing. The separation problem for Steiner partition inequalities is ${\cal N}\hskip-2pt{\cal P}$-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point $y$, a lower bound for the gap $\alpha-a^Ty$ over all alternating cycle inequalities $a^Tx\ge\alpha$. This gives rise to a very effective separation heuristic. A by-product of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the ``length'' of a path is its usual length minus the length of its longest edge.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 135
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    Packen von Steinerbäumen: Polyedrische Studien und Anwendung. (1992)
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    Publikationsdatum: 2014-02-27
    Beschreibung: Gegeben sei ein Graph $G=(V,E)$ mit positiven Kantenkapazitäten $c_e$ und Knotenmengen $T_1,\ldots,T_N$. Das Steinerbaumpackungs-Problem besteht darin, Kantenmengen $S_1,\ldots,S_N$ zu finden, so da\ss\ jedes $S_k$ die Knoten aus $T_k$ verbindet und jede Kante $e$ in höchstens $c_e$ Kantenmengen aus $S_1,\ldots,S_N$ vorkommt. Eine zulässige Lösung dieses Problems nennen wir eine Steinerbaumpackung. Ist zusätzlich eine Gewichtung der Kanten gegeben und nach einer bezüglich dieser Gewichtung minimalen Steinerbaumpackung gesucht, so sprechen wir vom gewichteten Steinerbaumpackungs-Problem. Die Motivation zum Studium dieses Problems kommt aus dem Entwurf elektronischer Schaltungen. Ein dort auftretendes Teilproblem ist das sogenannte Verdrahtungsproblem, das im wesentlichen darin besteht, gegebene Punktmengen unter bestimmten Nebenbedingungen und Optimalitätskriterien auf einer Grundfläche zu verbinden. Wir studieren das Steinerbaumpackungs-Problem aus polyedrischer Sicht und definieren ein Polyeder, dessen Ecken genau den Steinerbaumpackungen entsprechen. Anschlie\ss end versuchen wir, dieses Polyeder durch gute'' beziehungsweise facetten-definierenden Ungleichungen zu beschreiben. Basierend auf diesen Ungleichungen entwickeln wir ein Schnittebenenverfahren. Die Lösung des Schnittebenenverfahrens liefert eine untere Schranke für die Optimallösung und dient als Grundlage für die Entwicklung guter Primalheuristiken. Wir haben das von uns implementierte Schnittebenenverfahren an einem Spezialfall des Verdrahtungsproblems, dem sogenannten Switchbox-Verdrahtungsproblem, getestet und vielversprechende Ergebnisse erzielt.
    Schlagwort(e): ddc:000
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  • 136
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    Stochastic Versus Deterministic Numerical ODE Integration (1992)
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    Publikationsdatum: 2020-03-06
    Sprache: Englisch
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  • 137
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    Asymptotic Mesh Independence for Newton-Galerkin Methods via a Refined Mysovskii Theorem (1992)
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    Publikationsdatum: 2020-12-15
    Sprache: Englisch
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  • 138
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    Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions (1992)
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    Publikationsdatum: 2020-03-20
    Sprache: Englisch
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  • 139
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    Theoretical and practical aspects of combinatorial problem solving (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 140
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    Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 141
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    Clique-Web Facets for Multicut Polytopes (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 142
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    Facets for polyhedra arising in the design of communication networks with low-connectivity constraints (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 143
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    A cutting plane algorithm for the windy postman problem (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 144
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    Computation of Bifurcation Graphs. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The numerical treatment of Equivariant parameter-dependent onlinear equation systems, and even more its automation requires the intensive use of group theory. This paper illustrates the group theoretic computations which are done in the preparation of the numerical computations. The bifurcation graph which gives the bifurcation subgroups is determined from the interrelationship of the irreducible representations of a group and its subgroups. The Jacobian is transformed to block diagonal structure using a modification of the transformation which transforms to block diagonal structure with respect to a supergroup. The principle of conjugacy is used everywhere to make symbolic and numerical computations even more efficient. Finally, when the symmetry reduced problems and blocks of Jacobian matrices are evaluated numerically, the fact that the given representation is a quasi-permutation representation is exploited automatically.
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    Sprache: Englisch
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  • 145
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    Routing in Grid Graphs by Cutting Planes. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: {\def\N{{\cal N}} \def\R{\hbox{\rm I\kern-2pt R}} \def\MN{{\rm I\kern-2pt N}} In this paper we study the following problem, which we call the weighted routing problem. Let be given a graph $G=(V,E)$ with non-negative edge weights $w_e\in\R_+$ and integer edge capacities $c_e\in\MN$ and let $\N=\{T_1,\ldots,T_N\}$, $N\ge 1$, be a list of node sets. The weighted routing problem consists in finding edge sets $S_1,\ldots,S_N$ such that, for each $k\in\{1,\ldots,N\}$, the subgraph $(V(S_k),S_k)$ contains an $[s,t]$-path for all $s,t\in T_k$, at most $c_e$ of these edge sets use edge $e$ for each $e\in E$, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We briefly sketch our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances.}
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 146
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    An Adaptive Continuation Method for Implicitly Defined Surfaces. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A new method for the numerical aproximation of an implicitly defined surface is presented. It is a generalization of the Euler- Gauss-Newton method for implicitly defined (one- parameter) curves to the case of (two-parameter) surfaces. The basic task in the more general case is an efficient combination of modern CAGD techniques (such as triangular Bernstein-Bzier patches and the nine parameter Hermite interpolant) and the rank deficient Gauss-Newton method.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 147
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    Discretization and Iterative Solution of Convection Diffusion Equations. (1992)
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    Publikationsdatum: 2021-03-16
    Beschreibung: We propose an extended box method which turns out to be a variant of standard finite element methods in the case of pure diffusion and an extension of backward differencing to irregular grids if only convective transport is present. Together with the adaptive orientation proposed in a recent paper and a streamline ordering of the unknowns, this discretization leads to a highly efficient adaptive method for the approximation of internal layers in the case of large local Peclet numbers.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 148
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    Dynamic Sparsing in Stiff Extrapolation Methods. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Based on a simple stability analysis for the semi--implicit Euler discretization a new dynamic sparsing procedure is derived. This procedure automatically eliminates ``small'' elements of the Jacobian matrix. As a consequence, the amount of work needed to handle the linear algebra within a semi--implicit extrapolation integrator can be reduced drastically. Within the course of integration the sparsing criterion, which decides what ``small'' means, is dynamically adapted to ensure stability of the discretization scheme. Thus, stepsize restrictions due to instability can be avoided. Numerical experiments for quite different problems show robustness and efficiency of this dynamic sparsing technique. The techniques developed here in the context of stiff extrapolation integrators can, in principle, be applied to W--methods, where exact Jacobians may be replaced by ``sufficiently good'' approximations. {\bf Keywords:} Large scale integration, extrapolation methods, stiff ODEs, W--methods, sparse matrix techniques.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 149
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    Packing Steiner Trees: Further Facets. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we continue the investigations in [GMW92a] for the \def\sbppo{Steiner tree packing polyhedron} \sbppo. We present several new classes of valid inequalities and give sufficient (and necessary) conditions for these inequalities to be facet-defining. It is intended to incorporate these inequalities into an existing cutting plane algorithm that is applicable to practical problems arising in the design of electronic circuits.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 150
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    A Basic Norm Equivalence for the Theory of Multilevel Methods. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Subspace decompositions of finite element spaces based on $L2$-like orthogonal projections play an important role for the construction and analysis of multigrid like iterative methods. Recently several authors proved the equivalence of the associated discrete norms with the $H^1$-norm. The present report gives an elementary, self-contained derivation of this result which is based on the use of $ K$-functionals known from the theory of interpolation spaces. {\bf Keywords:} multilevel methods, nonuniform meshes, optimal convergence rates. {\bf AMS(MOS) Subject classifications:} 65N55, 65N30, 65N50.
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    Sprache: Englisch
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  • 151
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    Combinatorics in Statistical Physics (1992)
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    Publikationsdatum: 2014-02-26
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 152
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    Radius of Convergence of the 1/Z-Expansion for Diatomic Molecules: The Ground State of the Isoelectronic H2Sequence. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Using the perturbational-variational Rayleigh-Ritz matrix formalism, the 1/Z-expansion for the ground state of the isoelectronic $H_2$ sequence in the range of the internuclear distance $0.2\le R \le 9.0$ is calculated. Also lower bounds of the radius of convergence, based on Kato's theory of linear operators, are given. The numerical results of the 1/Z-expansion can be compared with the exact results and do not converge in the whole R-range. This behavior is in qualitative agreement with the lower bounds for the radius of convergence and enlights some still open properties of 1/Z- expansions for this sequence in the literature. {\bf PACS:} 31.15 + q; 31.20 Di; 31.20 Tz.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 153
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    Jahresbericht 1991 (1992)
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    Publikationsdatum: 2019-10-24
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: annualzib , doc-type:report
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  • 154
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    Medians of Binary Relations: Computational Complexity. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Let $\Re$ be the set of all binary relations on a finite set $N$ and $d$ be the symmetric difference distance defined on $\Re$. For a given profile $\Pi = (R_1,...,R_m) \in R^m$, a relation $R* \in \Re $ that minimizes the function $\sum^m_{k=1} d(R_k,R) $ is called a median relation of $\Pi$. A number of problems occuring in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile $\Pi$ represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of $\Pi$ with some special feature (representing e. g., consensus of preferences, clustering of similar objects, ranking of teams, etc.). In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexitivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is $NP$-hard. In some cases we prove that they remain $NP$-hard when the profile $\Pi$ has a fixed number of binary relations.
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    Sprache: Englisch
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  • 155
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    MEXX - Numerical Software for the Integration of Constrained Mechanical Systems. (1992)
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    Publikationsdatum: 2020-11-16
    Beschreibung: MEXX (short for MEXanical systems eXtrapolation integrator) is a Fortran code for time integration of constrained mechanical systems. MEXX is suited for direct integration of the equations of motion in descriptor form. It is based on extrapolation of a time stepping method that is explicit in the differential equations and linearly implicit in the nonlinear constraints. It only requires the solution of well--structured systems of linear equations which can be solved with a computational work growing linearly with the number of bodies, in the case of multibody systems with few closed kinematic loops. Position and velocity constraints are enforced throughout the integration interval, whereas acceleration constraints need not be formulated. MEXX has options for time--continuous solution representation (useful for graphics) and for the location of events such as impacts. The present article describes MEXX and its underlying concepts.
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    Sprache: Englisch
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  • 156
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    Adaptive Multilevel-Methods in 3-Space Dimensions. (1992)
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    Publikationsdatum: 2019-05-10
    Beschreibung: We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. as the performance of hierarchical bases preconditioners deteriorate in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a-posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.
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    Sprache: Englisch
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  • 157
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    The Numerical Solution of Constrained Hamiltonian Systems. (1992)
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    Publikationsdatum: 2021-01-21
    Beschreibung: A Hamiltonian system subject to smooth constraints can typically be viewed as a Hamiltonian system on a manifold. Numerical computations, however, must be performed in $ R^n$. In this paper, canonical transformations from ``Hamiltonian differential--algebraic equations'' to ODEs in Euclidean space are considered. In \S2, canonical parameterizations or local charts are developed and it is shown how these can be computed in a practical framework. In \S3 we consider the construction of unconstrained Hamiltonian ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an integral invariant and whose flow reduces to the flow of the constrained system along the manifold. It is shown that certain of these unconstrained Hamiltonian systems force Lyapunov stability of the constraint--invariants, while others lead to an unstable invariant. In \S4, we compare various projection techniques which might be incorporated to better insure preservation of the constraint--invariants in the context of numerical discretization. Numerical experiments illustrate the degree to which the constraint and symplectic invariants are maintained under discretization of various formulations. {\bf Keywords:} differential--algebraic equations, Hamiltonian systems, canonical discretization schemes. {\bf AMS(MOS):} subject classification 65L05.
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    Sprache: Englisch
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  • 158
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    MmB schemes on regular triangular meshes for 2-D conservation laws. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper, two classes of second order accurate high resolution schemes are presented on regular triangular meshes for initial value problem of two dimensional conservation laws. The first class are called Runge-Kutta-FVM MmB (locally Maximum- minimum Bounds preserving) schemes, which are first discretized by (FVM) finite volume method in space direction and modifying numerical fluxes, and then by Runge-Kutta methods in time direction; The second class, constructed by Taylor expansion in time, and then by FVM methods and making modifications to fluxes, are called Taylor- FVM MmB schemes. MmB properties of both schemes are proved for 2-D scalar conservation law. Numerical results are given for Riemann problems of 2-D scalar conservation law and 2-D gas dynamics systems and some comparisons are made between the two classes of the schemes. Key words and phrases: MmB schemes, 2-D, conservation laws, gas dynamics systems, Runge-Kutta-FVM, Taylor-FVM.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 159
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    On decomposing systems of polynomial equations with finitely many solutions. (1992)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: This paper deals with systems of $m$ polynomial equations in $n$ unknown, which have only finitely many solutions. A method is presented which decomposes the solution set into finitely many subsets, each of them given by a system of type \begin{displaymath} f_1(x_1)=0, f_2(x_1,x_2)=0,...,f_n(x_1,...,x_n)=0. \end{displaymath} The main tools for the decomposition are from ideal theory and use symbolical manipulations. For the ideal generated by the polynomials which describe the solution set, a lexicographical Gröbner basis is required. A particular element of this basis allows the decomposition of the solution set. A recursive application of these decomposition techniques gives finally the triangular subsystems. The algorithm gives even for non-finite solution sets often also usable decompositions. {\bf Keywords:} Algebraic variety decomposition, Gröbner bases, systems of nonlinear equations.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 160
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    Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A new adaptive approach for one-dimensional scalar conservation laws with convex flux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to LAX. For arbitrary times, the solutions is represented by an adaptive monotone spline interpolation. The spatial approximation is controlled by local $L^1$-error estimated. As a distinctive feature of the approach, there is no discretization in time. The method is monotone on fixed grids. Numerical examples are included, to demonstrate the predicted behavior. {\bf Key words.} method of characteristics, adaptive grids, monotone interpolation, $L^1$-error estimates {\bf AMS(MOS) subject classification.} 65M15, 65M25, 65M50.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 161
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    Shellability of Chessboard Complexes. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description as chessboard complexes: the complexes of all non-taking rook positions on chessboards of various shapes. In this paper we construct `certificate $k$-shapes' $\Sigma(m,n,k)$ such that if the shape $A$ contains some $\Sigma(m,n,k)$, then the $(k{-}1)$-skeleton of the chessboard complex $\Delta(A)$ is vertex decomposable in the sense of Provan & Billera. This covers, in particular, the case of rectangular chessboards $A=[m]{\times}[n]$, for which $\Delta(A)$ is vertex decomposable if $n\ge 2m{-}1$, and the $(\lfloor{m+n+1\over3}\rfloor{-}1)$-skeleton is vertex decomposable in general. The notion of vertex decomposability is a very convenient tool to prove shellability of such combinatorially defined simplicial complexes. We establish a relation between vertex decomposability and the CL-shellability technique (for posets) of Björner & Wachs.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 162
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    Numerical Riemann solutions in multi-pieces for 2-D gas dynamics systems I. Contact discontinuities. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The numerical solutions of Riemann problems in three, four, five and six pieces, which only contain contact discontinuities, are presented by using Taylor FVM MmB schemes on regular triangular meshes for 2-D gas dynamics systems. The 2-D Riemann initial data are as defined in [1], under the assumption that each jump in initial data outside of the origin projects exactly one planar wave of shocks, centered rarefaction waves , or contact discontinuities. The main ends of the paper are that spirals will be shown for some configurations and the relations of the solutions between different distibutions of Riemann initial data are explained by the numerical solutions of modified Riemann problems. Key words and phrases: Riemann problem, gas dynamics systems, spiral, MmB schemes.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 163
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    An Algorithm for Optimizing a Linear Function over the Integer Efficient Set. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Whereas optimization of a linear function over an efficient set is a favourite topic for theoretical studies, the problem ($P^I$) of finding a maximal value of a linear function $dx$ over an integer efficient set is still open. The problem ($P^I$) is NP-hard and it is very unlikely that the maximal objective value of the integer problem ($P^I$) in many cases is greater than the maximal objective value of it's corresponding continuous problem ($P$). In this paper we pay atention to the study of the problem ($P^I$) and some related properties of the problem ($P$). In particular, we establish conditions determining whether or not an optimal solution to the problem ($P$) is an optimal solution to the it's corresponding linear program. For the problem ($P^I$) we find an upper bound for it's optimal objective value and present an algorithm which gives a global optimal solution after a finite number of steps. We also study two particular classes of problems ($P^I$) : the bicriteria case and the case when $d$ is a nonnegative linear combination of the vectors-criteria defining the efficient set. Key words: Multiple objective linear programming, integer efficient set, efficient cone, cutting plane.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 164
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    Ab initio Quantum Chemical Calculations with GAMESS-UK and GAUSSIAN90 Program Packeges - A Comparison -. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Two commercially available molecular electronic structure software packages GAUSSIAN90 and GAMESS-UK are compared. Basis for this comparison is a benchmark suite which is designed to highlight the typical range of calculations commonly performed by the ab initio computational chemist.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 165
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    Computational Chemistry Software at ZIB. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The following report intends to provide a survey over the computational chemistry molecular structure software installed on the supercomputers CRAY X-MP/216 and CRAY Y-MP2E/164 at ZIB. It shows what kind of problems can be tackled with the existing chemistry software, which covers a wide range of ab initio, semiempirical, molecular mechanics, and dynamics applications.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 166
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    Plazieren von Zellen: Theorie und Lösung eines quadratischen 0/1- Optimierungsproblems. (1992)
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    Publikationsdatum: 2014-02-27
    Beschreibung: Die vorliegende Arbeit beschäftigt sich mit dem Plazierungsproblem, welches beim Entwurf elektronischer Schaltungen auftritt. Das Plazierungsproblem modellieren wir als ein quadratisches 0/1 Optimierungsproblem unter linearen Nebenbedingungen und untersuchen das Modell komplexitätstheoretisch. Der zweite Aspekt der Arbeit bezieht sich auf die Lösung praktischer Problembeispiele im sogenannten Sea of cells"-Entwurfsstil. Zur Lösung dieser Beispiele wurde ein Prototyp implementiert und mit state of the art"-Plazierungsverfahren verglichen. Schlie\ss lich werden wir uns mit dem Clusteringproblem, das eine Variante des Mehrfachschnitt-Problems darstellt, beschäftigen. Dabei steht einerseits im Vordergrund, wie diese Probleme heuristisch gelöst werden können und wie die Integration des Ansatzes in das Plazierungsprogramm erfolgt. Andererseits soll das Clusteringproblem polyedrisch untersucht werden.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 167
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    A Family of Newton Codes for Systems of Highly Nonlinear Equations. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: This report presents new codes for the numerical solution of highly nonlinear systems. They realize the most recent variants of affine invariant Newton Techniques due to Deuflhard. The standard method is implemented in the code NLEQ1, whereas the code NLEQ2 contains a rank reduction device additionally. The code NLEQ1S is the sparse version of NLEQ1, i.e. the arising linear systems are solved with sparse matrix techniques. Within the new implementations a common design of the software in view of user interface and internal modularization is realized. Numerical experiments for some rather challenging examples illustrate robustness and efficiency of algorithm and software.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 168
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    Modular Design of Extrapolation Codes. (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we describe a modular implementation of the well-established extrapolation codes EULEX, EULSIM and DIFEX for initial value problems of ordinary differential equations. The basic module embodies an abstract extrapolation method with order and stepsize control. Based on this module the particular integration codes only have to provide the underlying discretization schemes.
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    Sprache: Englisch
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  • 169
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    Handbuch zur Visualisierung am ZIB (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Scientists intending to employ scientific visualization techniques are confronted with the unpleasant task of choosing visualization software that meets their specific needs. A good choice requires consideration of several aspects. Most important are functionality, i.e. the set of supported visual representations, and restrictions due to the user's production environment (i.e. available hardware and software platforms, software compatibility constraints, need of specific input and output formats, network distribution requirements). Crucial are quality demands, ranging from simple graphics for interactive control of simulations, to images of highest quality (glossy prints, slides or video movies) for presentation purposes. Further aspects of consideration are: ease of use, level on which the user is willing to program, portability, conformity to prevalent standards, availability in the world-wide user community, future dissemination, as well as emerging trends in computer graphics and scientific visualization. The aim of this manual is to give a survey on the graphics and visualization software that is currently being provided at ZIB (mainly for internal use). The whole range of computer graphics software relevant in mathematical, natural and technical sciences is covered: image synthesis (basic and higher graphics libraries, plot programs, visualization environments, combined text and drawing programs, renderers), image processing and storage (raster and vector formats, page description languages, raster toolkits for image processing and format conversion), capturing of images as well as printing on paper and recording on photographic film or video tape. This information together with a glossary and recommendations for further reading should help prospective users in getting started and assist them in making good choices of graphics and visualization software.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 170
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    Elektronische Fachinformation im Bereich der Mathematik an Hochschulen und Statusbericht zum DMV-Projekt. "Fachinformation". (1992)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Im Bereich der Mathematik entwickelte sich in Deutschland die elektronische Fachinformation in Form der Online-Datenbank MATH und der CD-ROM CompactMATH auf der Grundlage der Arbeiten des Referateorgans "Zentralblatt für Mathematik und Ihre Grenzgebiete". Das "Zentralblatt" fand weithin Anerkennung und Verbreitung. Die Rezeption elektronischer Fachinformation ging jedoch - nicht nur im Bereich der Mathematik - nur zögerlich vonstatten. Die Gründe dafür werden in einer vom Bundesminister für Forschung und Technologie (BMFT) initiierten Studie analysiert. Ein kürzlich von der Deutschen Mathematiker - Vereinigung begonnenes und vom BMFT gefördertes Vorhaben hat die "Verbesserung des benutzerorientierten Zugriffs auf fachspezifische Online-Datenbanken und CD-ROM für Mathematische Institute in der Bundesrepublik Deutschland" zum Ziel. Insgesamt 51 mathematische Fachbereiche und Institute nehmen daran teil. Elektronische Fachinformation soll zu einem festen Bestandteil des methodischen Instrumentariums der wissenschaftlichen Arbeit werden. Diese Schrift soll die Ausgangslage in den Fachbereichen darstellen und die organisatorischen und technischen Infrastrukturmaßnahmen erläutern, mit denen den spezifischen Nutzungshemmnissen begegnet werden soll.
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    Sprache: Deutsch
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  • 171
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    Adaptive Multilevel Beam Propagation Method (1992)
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    Publikationsdatum: 2022-07-07
    Sprache: Englisch
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  • 172
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    An Adaptive Approach to a Beam Propagation Method (1992)
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    Publikationsdatum: 2022-07-07
    Sprache: Englisch
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  • 173
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    Improved Method of Mode Determination in Planar Optical Waveguides Using Line Transmission Approach (1992)
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    Publikationsdatum: 2022-07-07
    Sprache: Englisch
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  • 174
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    Hadron Spectroscopy on a 32^3 * 48 Lattice (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 175
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    AGIL - the Adaptable Graphical Interface Layer, Programmierer-Handbuch (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
    Materialart: other , doc-type:Other
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  • 176
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    SU(3) Renormalization Group Study on Parallel Computer AP 1000 (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 177
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    Conference Report: Parallel Computing 91 (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 178
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    QCD on the Highly Parallel Computer AP 1000 (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 179
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    Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of Raman Spectroscopy. (1992)
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    Publikationsdatum: 2023-08-14
    Sprache: Englisch
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  • 180
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    A Refined Gauss-Newton- Mysovskii Theorem. (1991)
    Details
    Publikationsdatum: 2020-12-15
    Beschreibung: The present paper contains a generalization of a refinement of the Newton- Mysovskii theorem, recently obtained by the authors, to the case of Gauss-Newton procedures for solving nonlinear least-squares problems with full Jacobians. Invariant sufficient conditions are given that ensure the convergence of the Gauss-Newton iterates towards a solution of the problem, as well as the uniqueness of that solution in an explicitely defined neighborhood. It is shown by a counter- example that the results do not carry over to the rank deficient case.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 181
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    Self Adaptive Computation of the Breakdown Voltage of Planar pn-Junctions with Multistep Field Plates. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The breakdown voltage highly depends on the electric field in the depletion area whose computation is the most time consuming part of the simulation. We present a self adaptive Finite Element Method which reduces dramatically the required computation time compared to usual Finite Difference Methods. A numerical example illustrates the efficiency and reliability of the algorithm.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 182
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    An Adaptive Multilevel Approach to Parabolic Equations III. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Part III of the paper is devoted to the construction of an adaptive FEM solver in two spatial dimensions, which is able to handle the singularly perturbed elliptic problems arising from discretization in time. The problems of error estimation and multilevel iterative solution of the linear systems - both uniformly well behaved with respect to the time step - can be solved simultaneously within the framework of preconditioning. A multilevel nodal basis preconditioner able to handle highly nonuniform meshes is derived. As a numerical example an application of the method to the bioheat-transfer equation is included. {\bf AMS CLASSIFICATION:} 65F10, 65F35, 65M50, 65M60, 65N30.
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    Sprache: Englisch
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  • 183
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    Sequential Evaluation of Adjoints and Higher Derivative Vectors by Overloading and Reverse Accumulation. (1991)
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    Publikationsdatum: 2020-09-24
    Beschreibung: Most nonlinear computations require the evaluation of first and higher derivatives of vector functions defined by computer programs. It is shown here how vectors of such partial derivatives can be obtained automatically and efficiently if the computer language allows overloading (as is or will be the case for C++, PASCAL-XSC, FORTRAN90, and other modern languages). Here, overloading facilitates the extension of arithmetic operations and univariate functions from real or complex arguments to truncated Taylor-series (or other user- defined types), and it generates instructions for the subsequent evaluation of adjoints. Similar effects can be achieved by precompilation of FORTRAN77 programs. The proposed differentiation algorithm yields gradients and higher derivatives at a small multiple of the run-time and RAM requirement of the original function evaluation program. {\bf Keywords:} Automatic Differentiation, Chain Rule, Overloading, Taylor Coefficients, Gradients, Hessians, Reverse Accumulation, Adjoint Equations. {\bf Abbreviated title:} Automatic Differentiation by Overloading.
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    Sprache: Englisch
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  • 184
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    The Treatment of Macromolecular Processes with Chain-Length-Dependent Reaction Coefficients - An Examplefrom Soot Formation. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The description of chain length distributions in macromolecular reaction kinetics leads to so-called countable systems of differential equations. In particular, when the appearing reaction rate coefficients depend on the chain length of the reacting macromolecules itself, an efficient numerical treatment of these systems is very difficult. Then even the evaluation of the right-hand side of the system can become prohibitively expensive with respect to computing time. In this paper we show how the discrete Galerkin method can be applied to such problems. The existing algorithm CODEX is improved by use of a multiplicative error correction scheme for time discretization and a new type of numerical preprocessing by means of a Gauss summation. Both ideas are exemplary for a wide class of approximation types and are described very briefly here. The new numerical techniques are tested on an example from soot formation, where the coagulation of molecules is modeled in terms of reaction coefficients depending on the surface of the particles and their collision frequency.
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    Sprache: Englisch
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  • 185
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    OCCAL: A mixed symbolic- numeric Optimal Control CALculator. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The numerical solution of optimal control problems by indirect methods (such as multiple shooting or collocation) requires a considerable amount of analytic calculation to establish a numerically tractable system. These analytic calculations, though being rather tedious in realistic examples, are nowadays mostly still done by hand-and thus prone to calculation errors. The paper aims at automating this analytic processing to a reasonable extent by means of a modern symbolic manipulation language (here: REDUCE). In its present stage of development the package OCCAL (mnemotechnically for \underline{O}ptimal \underline{C}ontrol \underline{CAL}culator) permits an interactive use, covering tasks like automatic determination of control and, in case of a singular control, of its order. In simpler problems, the present version of OCCAL automatically produces the full subroutine input for a MULtiple shooting code (MULCON) with adaptive numerical CONtinuation. In more complicate problems where singular sub-arcs may occur or where the sequence of sub-arcs of the optimal trajectory is unclear OCCAL is a significant help in reducing analytic pre-processing. Numerical examples illustrate the performance of OCCAL/MULCON.
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    Sprache: Englisch
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  • 186
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    On the Difference Between Real and Complex Arrangements. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: If $B$ is an arrangement of linear complex Hyperplanes in $C^d$, then the following can be constructed from knowledge of its intersection lattice: (a) the cohomology groups of the complement [Br], (b) the cohomology algebra of the complement [OS], (c) the fundamental group of the complement, if $d\le2$, (d) the singularity link up to homeomorphism, if $d\le3$, (e) the singularity link up to homotopy type [ZZ]. If $B'$ is, more generally, a 2-arrangement in $ R^{2d}$ (an arrangement of real subspaces of codimension 2 with even-dimensional intersections), then the intersection lattice still determines (a) the cohomology groups of the complement [GM] and (e) the homotopy type of the singularity link [ZZ]. We show, however, that for 2-arrangements the data (b), (c) and (d) are not determined by the intersection lattice. They require the knowledge of extra information on sign patterns, which can be computed as determinants of linear relations, or (equivalently) as linking coefficients in the sense of knot theory.
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    Sprache: Englisch
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  • 187
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    Homotopy Types of Subspace Arrangements via Diagrams of Spaces. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We prove combinatorial formulas for the homotopy type of the union of the subspaces in an (affine, compactified affine, spherical or projective) subspace arrangement. From these formulas we derive results of Goresky & MacPherson on the homology of the arrangement and the cohomology of its complement. The union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset. A closely related space is obtained by taking the homotopy direct limit of this diagram. Our method consists in constructing a combinatorial model diagram over the same poset, whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 188
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    An Adaptive Multilevel Approach to Parabolic Equations in Two Space Dimensions. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A new adaptive multilevel approach for linear partial differential equations is presented, which is able to handle complicated space geometries, discontinuous coefficients, inconsistent initial data. Discretization in time first (Rothe's method) with order and stepsize control is perturbed by an adaptive finite element discretization of the elliptic subproblems, whose errors are controlled independently. Thus the high standards of solving adaptively ordinary differential equations and elliptic boundary value problems are combined. A theory of time discretization in Hilbert space is developed which yields to an optimal variable order method based on a multiplicative error correction. The problem of an efficient solution of the singularly perturbed elliptic subproblems and the problem of error estimation for them can be uniquely solved within the framework of preconditioning. A Multilevel nodal basis preconditioner is derived, which allows the use of highly nonuniform triangulations. Implementation issues are discussed in detail. Numerous numerical examples in one and two space dimensions clearly show the significant perspectives opened by the new algorithmic approach. Finally an application of the method is given in the area of hyperthermia, a recent clinical method for cancer therapy.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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    Tagung NUMSIM '91 5.-08. Mai 1991. Collected Abstracts and Papers. (1991)
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    Publikationsdatum: 2020-03-06
    Beschreibung: NUMSIM 91 fand vom 6.-08. Mai 1991 im Wissenschaftlichen Kommunikations- & Konferenz- Zentrum der Humboldt-Universität in Gosen bei Berlin statt. Im Mittelpunkt dieses Seminars standen Probleme der numerischen Simulation von Ladungstransport- und Technologieprozessen der Mikro- und Optoelektronik. Es führte Spezialisten der physikalischen Modellierung, der numerischen Mathematik und mathematischen Analysis sowie Nutzer von Simulationsprogrammen aus dem deutschsprachigen Raum zusammen. Ziel war die Vermittlung und der Austausch von Erfahrungen, die Diskussion gemeinsamer Aufgabenstellungen und Projekte und - in Anbetracht der deutschen Vereinigung nicht zuletzt - das gegenseitige Kennen- und Verstehenlernen.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 190
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    Die Ausbreitung von HIV/AIDS in Ballungsgebieten. (1991)
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    Publikationsdatum: 2014-03-06
    Beschreibung: The rapidly increasing number of AIDS cases requires a realistic estimation of the future development of the HIV/AIDS disease. For that purpose we develop a large system of coupled nonlinear differential equations describing simultaneously the dynamics of the development of the disease, the population size, the gender and age structure. A set of 1650 coupled equations are linked by balanced parameters. The balancing procedure is described by a set of (formally) 2,178,000 additional algebraic conditions. As the considered system is stiff, it requires new special extrapolation methods combined with techniquees of dynamical sparsing for the solution of sparsely filled systems. According to our simulations we expect 19,0,000 deaths caused by AIDS in the Federal Republic of Germany (former territories) in the year 2000. Such an epidemical spread would tie up about 4-7 percent of the actual health care workers.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: reportzib , doc-type:preprint
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  • 191
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    Global inexact Newton methods for very large scale nonlinear problems (1991)
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    Publikationsdatum: 2020-03-06
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 192
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    Numerische Mathematik I. Eine algorithmisch orientierte Einführung (1991)
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    Publikationsdatum: 2020-10-02
    Sprache: Englisch
    Materialart: book , doc-type:book
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  • 193
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    Strategies for optimized application of annular-phased-array systems in clinical hyperthermia (1991)
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    Publikationsdatum: 2021-03-16
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 194
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    Mengenpartitionen und ihre Anwendung auf ein Maschinenbelegungsproblem (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: masterthesis , doc-type:masterThesis
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  • 195
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    Complete descriptions of small multicut polytopes (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: bookpart , doc-type:bookPart
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  • 196
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    Discrete Mathematics in Manufacturing (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 197
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    Optimal Control of Plotting and Drilling Machines (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 198
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    Solution of large-scale symmetric travelling salesman problems (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
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  • 199
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    Polyhedral Approaches to Network Survivability (1991)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 200
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    An Adaptive Discontinuous Finite Element Method for the Transport Equation. (1991)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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