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  • Opus-Repositorium ZIB  (93)
  • 1990-1994  (93)
  • 1992  (55)
  • 1990  (38)
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  • 1990-1994  (93)
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  • 1
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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
    Materialart: reportzib , doc-type:preprint
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  • 2
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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
    Materialart: reportzib , doc-type:preprint
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  • 3
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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
    Materialart: reportzib , doc-type:preprint
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  • 4
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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
    Materialart: reportzib , doc-type:preprint
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  • 5
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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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  • 6
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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
    Materialart: reportzib , doc-type:preprint
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  • 7
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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
    Materialart: reportzib , doc-type:preprint
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  • 8
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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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  • 9
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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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 10
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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
    Materialart: reportzib , doc-type:preprint
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  • 11
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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
    Sprache: Deutsch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 12
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    Stochastic Versus Deterministic Numerical ODE Integration (1992)
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    Publikationsdatum: 2020-03-06
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 13
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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
    Materialart: article , doc-type:article
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  • 14
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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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  • 15
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    Theoretical and practical aspects of combinatorial problem solving (1992)
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    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 16
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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
    Materialart: article , doc-type:article
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  • 17
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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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  • 18
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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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  • 19
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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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  • 20
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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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 21
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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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  • 22
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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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  • 23
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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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  • 24
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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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  • 25
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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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  • 26
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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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 27
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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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  • 28
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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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  • 29
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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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  • 30
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    Medians of Binary Relations: Computational Complexity. (1992)
    Details
    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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 31
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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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 32
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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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 33
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    The Numerical Solution of Constrained Hamiltonian Systems. (1992)
    Details
    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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 34
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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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  • 35
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    On decomposing systems of polynomial equations with finitely many solutions. (1992)
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    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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  • 36
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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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  • 37
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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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  • 38
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    Numerical Riemann solutions in multi-pieces for 2-D gas dynamics systems I. Contact discontinuities. (1992)
    Details
    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
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  • 39
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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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  • 40
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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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  • 41
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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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  • 42
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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.
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    Sprache: Deutsch
    Materialart: doctoralthesis , doc-type:doctoralThesis
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  • 43
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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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  • 44
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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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  • 45
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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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  • 46
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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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  • 47
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    Adaptive Multilevel Beam Propagation Method (1992)
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    Publikationsdatum: 2022-07-07
    Sprache: Englisch
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  • 48
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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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  • 49
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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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  • 50
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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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  • 51
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    AGIL - the Adaptable Graphical Interface Layer, Programmierer-Handbuch (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 52
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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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  • 53
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    Conference Report: Parallel Computing 91 (1992)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
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  • 54
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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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  • 55
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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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  • 56
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    Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non- Hermitian linear systems. As it turns out, both Broydens "good" and "bad" update techniques play a special role - but should be associated with two different line search principles. For Broydens "bad" update technique, a minimum residual principle is natural - thus making it theorectically comparable with a series of well-known algorithms like GMRES. Broydens "good" update technique, however, is shown to be naturally linked with a minimum "next correction" principle - which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized PDE's of convection diffusion type in 2-D with internal layers give a first impression of the possible power of the derived "good" Broyden variant. {\bf Key Words:} nonsymmetric linear system, secant method, rank-1 update, Broydens method, line search, GMRES. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20.
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    Sprache: Englisch
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  • 57
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    An Adaptive Multilevel Approach to Parabolic Equations I. General Theory & 1D-Implementation. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A new adaptive multilevel approach for parabolic PDE's is presented. Full adaptivity of the algorithm is realized by combining multilevel time discretization, better known as extrapolation methods, and multilevel finite element space discretization. In the theoretical part of the paper the existence of asymptotic expansions in terms of time-steps for single-step methods in Hilbert space is established. Finite element approximation then leads to perturbed expansions, whose perturbations, however, can be pushed below a necessary level by means of an adaptive grid control. The theoretical presentation is independent of space dimension. In this part I of the paper details of the algorithm and numerical examples are given for the 1D case only. The numerical results clearly show the significant perspectives opened by the new algorithmic approach.
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    Sprache: Englisch
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  • 58
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    Symplectic Difference Schemes for Perturbed Hamiltonian Systems. (1990)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: In this paper we consider symplectic difference schemes for perturbed Hamiltonian systems of integrable ones, which can cover many important problems. Symplectic difference schemes for general Hamiltonian systems can also be used to these problems. But the perturbation property has not been paid proper attention to, which is important in the method proposed here. Numerical simulation shows that, for this method the time step size can be taken quite large and the qualitative property , such as preserving invariant tori, is also better than usual symplectic difference schemes.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 59
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    Gruppentheoretische Konstruktion von symmetrischen Kubaturformeln. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: $G$-invariant cubature formulas for numerical integration over n-dimensional, $G$- invariant integration regions are computed symbolically. The nodes are the common zeros of some $d$-orthogonal polynomials which build an $H$-basis of an ideal. Approaches for these polynomials depending on parameters are made with the help of the theory of linear representations of a group $G$. This theory is also used for the effective computation of necessary conditions which determines the parameters. Another approach uses invariant theory and gröbner bases.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 60
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    Datenabhängigkeitsanalyse und Programmtransformationen auf CRAY-Rechnern mit dem Fortran-Präprozessor fpp (1990)
    Details
    Publikationsdatum: 2020-03-09
    Beschreibung: The FORTRAN preprocessor fpp in the newly introduced Autotasking System of CRAY Research allows automatic vectorization and parallelization on basis of a data dependence analysis. An introduction into data dependence analysis is given, showing how data dependence graphs unveil opportunities for program transformations like vectorization and concurrentization. The report contains a complete description of the preprocessors functionality, its options and directives for increasing the effectiveness of the dependence analyzer and steering the code transformations. Finally, some advice is given for the practical use of fpp on CRAY computers.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 61
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    Numerical Treatment of Countable Systems of Ordinary Differential Equations. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a full adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerkin approach as discretization of the stationary subproblems. The Galerkin method is based on orthogonal functions of a discrete variable , which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations can be assembled either by use of analytical properties of the orthogonal functions or numerically by a multilevel summation algorithm. The resulting algorithm CODEX is applied to many examples of technological interest, in particular from polymer chemistry.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 62
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    Uniqueness Theorems for Stiff ODE Initial Value Problems (1990)
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    Publikationsdatum: 2020-03-06
    Sprache: Englisch
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  • 63
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    Fast secant methods for the iterative solution of large nonsymmetric linear systems (1990)
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    Publikationsdatum: 2021-03-16
    Sprache: Englisch
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  • 64
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    Recent Developments in Chemical Computing (1990)
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    Publikationsdatum: 2020-12-14
    Sprache: Englisch
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  • 65
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    On Identifying in Polynomial Time Violated Subtour Elimination and Precedence Forcing Constraints for the Sequential Ordering Problem (1990)
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    Publikationsdatum: 2014-02-24
    Sprache: Englisch
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  • 66
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    Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints (1990)
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    Publikationsdatum: 2014-02-24
    Sprache: Englisch
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  • 67
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    Composition of facets of the clique partitioning polytope (1990)
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    Publikationsdatum: 2014-02-24
    Sprache: Englisch
    Materialart: bookpart , doc-type:bookPart
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  • 68
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    Facets of the clique partitioning polytope (1990)
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    Publikationsdatum: 2014-02-24
    Sprache: Englisch
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  • 69
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    Symbolic Exploitation of Symmetry in Numerical Path-following. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations. In the symbolic part of the algorithm the complete analysis of the symmetry occurs, and it is here where symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed. Given a particular problem, the symbolic algorithm can create and compute through the list of possible bifurcations thereby forming a so-called tree of decisions correlated to the different types of symmetry breaking bifurcation points. The remaining part of the algorithm deals with the numerical pathfollowing based on the implicit reparametrisation as suggested and worked out by Deuflhard/Fiedler/Kunkel. The symmetry preserving bifurcation points are computed using recently developed augmented systems incorporating the use of symmetry. {\bf Keywords:} pathfollowing, mixed symbolic-numeric algorithm, parameter-dependent, nonlinear systems, linear representations.
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    Sprache: Englisch
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  • 70
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    Symbolic solution of polynomial equation systems with symmetry. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Systems of polynomial equations often have symmetry. The Buchberger algorithm which may be used for the solution ignores this symmetry. It is restricted to moderate problems unless factorizing polynomials are found leading to several smaller systems. Therefore two methods are presented which use the symmetry to find factorizing polynomials, decompose the ideal and thus decrease the complexitiy of the system a lot. In a first approach projections determine factorizing polynomials as input for the solution process, if the group contains reflections with respect to a hyperplane. Two different ways are described for the symmetric group Sm and the dihedral group Dm. While for Sm subsystems are ignored if they have the same zeros modulo G as another subsystem, for the dihedral group Dm polynomials with more than two factors are generated with the help of the theory of linear representations and restrictions are used as well. These decomposition algorithms are independent of the finally used solution technique. We used the REDUCE package Groebner to solve examples from CAPRASSE, DEMARET and NOONBURG which illustrate the efficiency of our REDUCE program. A short introduction to the theory of linear representations is given. In a second approach problems of another class are transformed such that more factors are found during the computation; these transformations are based on the theory of linear representations. Examples illustrate these approaches. The range of solvable problems is enlarged significantly.
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    Sprache: Englisch
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  • 71
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    On Symplectic Difference Schemes for Hamiltonian Systems. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Symplectic difference schemes have been shown to be a right formalism for numerical computation of Hamiltonian systems. They are suitable to long time computation and of good qualitative properties. These properties are ensured by the fact that a symplectic difference scheme approximating to a time-independent Hamiltonian system can be regarded as a perturbed time-dependent Hamiltonian system of the original one. That is, a solution of a symplectic difference scheme is a solution of a certain perturbed time dependent Hamiltonian system evaluated at discrete (time) points. This is the main result of the paper. Moreover, linear symplectic difference schemes approximating to a linear time-independent Hamiltonian system can be regarded as a perturbed time-independent Hamiltonian system. So it has all properties that a linear Hamiltonian system has. Based on these results, stochastic webs and chaos in symplectic difference schemes are also discussed. They will appear in numerical simulation for Hamiltonian systems, even with one degree of freedom.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 72
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    Self Adaptive FEM Simulation of Reverse Biased pn-Junctions. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The potential distribution of reverse biased pn-junctions can be described by a double obstacle problem for the Laplacian. This problem is solved by a self adaptive Finite Element Method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse biased pn- junction with multi-step field plate and stop- electrode to illustrate its efficiency and reliability.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 73
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    Asymptotic Mesh Independence of Newton-Galerkin Methods via a Refined Mysovskii Theorem. (1990)
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    Publikationsdatum: 2020-12-15
    Beschreibung: The paper presents a theoretical characterization of the often observed asymptotic mesh independence of Newton's method, which means that Newton's method applied to discretized operator equations behaves essentially the same for all sufficiently fine discretizations. The theory does not need any uniform Lipschitz assumptions that were necessary in comparable earlier treatments. The refined Newton-Mysovskii theorem, which will be of interest in a wider context, gives both existence and uniqueness of the solution and quadratic convergence for sufficiently good starting points. Attention is restricted to Galerkin approximations even though similar results should hold for finite difference methods - but corresponding proofs would certainly be more technical. As an illustrative example, adaptive 1-D collocation methods are discussed.
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    Sprache: Englisch
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  • 74
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    Automatic Generation of Reaction Mechanisms for Description of Oxidation of Higher Hydrocarbons. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Oxidation mechanisms even for rather simple hydrocarbons like heptane consist due to the occurrence of many isomeric structures of thousands of reactions of hundreds of species. The automatic generation of these reaction mechanisms using artificial intelligence means is described. Results are presented for n-heptane-air mixtures, where a hand-written reaction mechanism tested against experimental data is available.
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    Sprache: Englisch
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  • 75
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    Recent Developments in Chemical Computing. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The paper surveys three aspects of chemical computing, which seem to play a role in recent developments. First, extrapolation methods for the numerical treatment of differential- algebraic equations are introduced. The associated extrapolation code LIMEX has reached a certain level of sophistication, which makes it a real competitor to the elsewhere widely used multi-step code DASSL of Petzold. Second, adaptive methods of lines for partial differential equations such as those arising in combustion problems are treated. Both static and dynamic regridding techniques are discussed in some detail. Finally, some new ideas about the treatment of the kinetic equations arising from polymer reactions are presented. The new feature of the suggested approach is the application of a Galerkin procedure using sets of orthogonal polynomials over a discrete variable (which, of course, in the case of polymer reactions is the polymer degree). The new approach may open the door to a new reliable low dimensional treatment of complex polymer reactions.
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    Sprache: Englisch
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  • 76
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    Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.
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    Sprache: Englisch
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  • 77
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    Global Inexact Newton Methods for Very Large Scale Nonlinear Problems. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Newton methods for nonlinear problems are known to require the solution of a sequence of linear problems of the same type. For very large scale problems, as understood herein, the arising linear systems can only be solved by iterative methods. Then Newtons iteration appears as outer iteration. The question of interest will be to control the accuracy of the inner iteration such that the convergence speed of Newtons method is preserved. The purpose of the paper is to combine the concept of inexact Newton methods with the concept of the affine invariant exact Newton methods - which is important for problems with ill- conditioned Jacobian matrices (such as typical 2-D or 3-D discretized partial differential equations).
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    Sprache: Englisch
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  • 78
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    Sparse Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems $ Ax = b $ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate $ A ^{-1} $ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization $ LU $ of $ A $ is the starting point and we tried to improve this easy invertible approximation of $ A $. The update is constructed in such a way that the sparsity structure of $ L $ and $ U $ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization.
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    Sprache: Englisch
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  • 79
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    Numerical Treatment of Polyreactions - Recent Developments. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: The mathematical modeling of macromolecular reactions leads to countable (possibly infinite) systems of ordinary differential equations (CODE's). This paper reviews two recent developments of the so-called discrete Galerkin method, which has been developed for the numerical treatment of countable systems, which arise e.g. in polymer chemistry. The first approach can be considered as a method of lines with moving basis functions and has been implemented recently in the program package MACRON. The second type of the Galerkin method is characterized by a so-called outer time discretization of the complete problem and an appropriate and efficient solution of the arising subproblems. This method is realized in the research code CODEX.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 80
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    An Adaptive Multilevel Approach to Parabolic Equations II. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In continuation of part I this paper develops a variable-order time discretization in Hilbert space based on a multiplicative error correction. Matching of time and space errors as explained in part I allows to construct an adaptive multilevel discretization of the parabolic problem. In contrast to the extrapolation method in time, which has been used in part I, the new time discretization allows to separate space and time errors and further to solve fewer elliptic subproblems with less effort, which is essential in view of the application to space dimension greater than one. Numerical examples for space dimension one are included which clearly indicate the improvement.
    Schlagwort(e): ddc:000
    Sprache: Englisch
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  • 81
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    Improvement of Incomplete Factorizations by a Sparse Secant Method. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: In the present paper, the improvement of an incomplete factorization of a non-symmetric matrix A is discussed. Starting from the ideas of sparsity preserving quasi-Newton methods, an algorithm is developed which improves the approximation of A by the incomplete factorization maintaining the sparsity structure of the matrices. No renumbering of the unknowns or the admittance of additional fill-in is necessary. The linear convergence of the algorithm is proved under the assumption, that $ L $ and $ U $* have the same sparsity structure and an incomplete factorization with some reasonable approximation property exits. In combination with this algorithm, the method of incomplete factorization and its several modifications are applicable to a wider class of problems with improved convergence qualities. This is shown by a numerical example. {\bf Key Words:} non-symmetric linear system, sparse secant method, incomplete factorization. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20, 65N30.
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    Sprache: Englisch
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  • 82
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    CRAY-Handbuch. Einführung in die Benutzung der CRAY X-MP unter UNICOS 5.1 (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Das CRAY-Handbuch des ZIB beschreibt nach einer grundlegenden bersicht detailliert die Handhabung von UNICOS-Dateien, die Verwendung von UNICOS-Kommandos und schließlich die (für Benutzer allein zugelassene) Ausführung von Batchjobs auf der CRAY. Neben der Erreichbarkeit der CRAY über das TCP/IP-Netz werden die Compiler FORTRAN, PASCAL und C beschrieben und schließlich auf die Optimierung der Rechenzeit ebenso wie auf die Fehlersuche eingegangen. Ein umfangreicher Anhang führt bereitgestellte Programmpakete, weiterführende Literatur, Zahlenbereiche und Zeichendarstellung an der CRAY auf.
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    Sprache: Deutsch
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  • 83
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    Einführung in die Numerische Mathematik. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Diese Vorlesung ist eine Einführung in die Numerische Mathematik als einem der drei Bereiche (neben den Naturwissenschaften und der Informatik) des am besten mit dem Begriff Scientific Computing charakterisierten Forschungsgebietes. Aufgabe dieser relativ jungen Wissenschaft ist die Entwicklung von Rechenverfahren für Probleme aus den Naturwissenschaften mit Hilfe mathematischer Methoden.
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    Sprache: Deutsch
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  • 84
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    Konrad Zuses Plankalkül als Vorläufer moderner Programmier-modelle. (Vortrag) (1990)
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    Publikationsdatum: 2014-02-26
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 85
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    MACRON - A Program Package for Macromalecular Reaction Kinetics. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: This paper presents the new program package MACRON for the simulation of macromolecular kinetics including standard chemical reactions. Such problems lead to countable (possibly) infinite systems of ordinary differential equations (CODE's), which are numerically treated by the so-called discrete Galerkin method here. By a chemical compiler the required analytical preprocessing is performed, such that the complete reaction system, standard kinetics as well as macromolecular reactions, can be entered in the chemical formalism. Typical macromolecular reaction steps are chain addition, termination, chain transfer and degradation (cracking). In order to ensure efficiency and reliability, high sophisticated numerical routines are built within the package. MACRON can be used without a detailed knowledge of the used numerical methods. As an illustration the application of MACRON to some realistic problems is presented.
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    Sprache: Englisch
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  • 86
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    Power-Law Type Solutions of Fourth-Order Gravity (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension $ d = 3 $ , the Einsteinian Kasner metric is still the most general power-law type solution, for $ d 〉 3 $ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the $ d $-dimensional space into a ( $ d - 3 $)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when $ d = 9 $).
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    Sprache: Englisch
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  • 87
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    Implementierung von parallelen Versionen der Gleichungslöser EULEX und EULSIM auf Transputern. (1990)
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    Publikationsdatum: 2014-02-26
    Beschreibung: Im vorliegenden Bericht wird die Parallelisierung zweier numerischer Algorithmen zur Lösung gewöhnlicher Differentialgleichungssysteme 1.Ordnung (explizite und semi-implizite Euler- Diskretisierung und $h$-Extrapolation) beschrieben. Implementiert wurden die Algorithmen mit OCCAM2 unter TDS (Transputer Development System) mit bis zu 4 Transputern T800. Meßwerte für die erreichten Beschleunigungen werden anhand mehrer Beispiele von Differentialgleichungs-systemen angegeben. {\bf Schlüsselwörter:} Adaptive, parallele Systeme; OCCAM2; Transputer; numerische Gleichungslöser; Euler-Diskretisierung; $h$-Extrapolation.
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  • 88
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    Zuses Werk weiterdenken. (Vortrag) (1990)
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    Publikationsdatum: 2014-02-26
    Schlagwort(e): ddc:000
    Sprache: Deutsch
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  • 89
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    BOXES - a Program to Generate Triangulations from a Rectangular Domain Description. (1990)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: BOXES computes a triangulation from a 2D domain description which consists of an arbitrary set of rectangles. Each rectangle may have attributes to control the triangulating process, define subdomain classes, or specify boundary conditions. The output of the program can be used as a coarse grid for KASKADE or one of its variants. Additional features are extensive checking of the user input, graphical display, and simple editing.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 90
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    GIANT - A Software Package for the Numerical Solution of Very Large Systems of Highly Nonlinear Equations. (1990)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: This report presents the final realization and implementation of a global inexact Newton method proposed by Deuflhard. In order to create a complete piece of software, a recently developed iterative solver (program GBIT) due to Deuflhard, Freund, Walter is adapted and serves as the standard iterative linear solver. Alternative linear iterative solvers may be adapted as well, e.g. the widely distributed code GMRES. The new software package GIANT (Global Inexact Affine Invariant Newton Techniques) allows an efficient and robust numerical solution of very large scale highly nonlinear systems. Due to the user friendly interface and its modular design, the software package is open for an easy adaptation to specific problems. Numerical experiments for some selected problems illustrate performance and usage of the package.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 91
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    Jahresbericht 1989 (1990)
    Details
    Publikationsdatum: 2019-10-24
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: annualzib , doc-type:report
    Format: application/pdf
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  • 92
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    Simulation und Herstellung von Faserschleifkopplern (1990)
    Details
    Publikationsdatum: 2022-07-07
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 93
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    Vectorization and Parallelization of Irregular Problems via Graph coloring. (1990)
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    Publikationsdatum: 2022-07-19
    Beschreibung: Efficient implementations of irregular problems on vector and parallel architectures are generally hard to realize. An important class of problems are Gauß-Seidel iteration schemes applied to irregular data sets. The unstructured data dependences arising there prevent restructuring compilers from generating efficient code for vector or parallel machines. It is shown, how to structure the data dependences by decomposing the underlying data set using graph coloring techniques and by specifying a particular execution order already on the algorithm level. Methods to master the irregularities originating from different types of tasks are proposed. An application is given and some open issues and future developments are discussed.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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