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  • 1990-1994  (56)
  • 1992  (56)
  • English  (56)
  • 1
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    Discrete Mathematics in Manufacturing. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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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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    Publication Date: 2014-02-26
    Description: 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.
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  • 3
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    Packing Steiners Trees: A Cutting Plane Algorithm and Computational Results. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 4
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    Packing Steiner Trees: Polyhedral Investigations. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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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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    Publication Date: 2020-10-05
    Description: 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.
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  • 6
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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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    Publication Date: 2014-02-26
    Description: 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.
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  • 7
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    A Polyhedral Approach to Network Connectivity Problems (Extended Abstract). (1992)
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    Publication Date: 2020-12-14
    Description: We present a polyhedral approach for the general problem of designing a minimum-cost network with specified connectivity requir
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  • 8
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    Group Theoretical Mode Interactions with Different Symmetries. (1992)
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    Publication Date: 2014-02-26
    Description: 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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  • 9
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    Packing Steiner Trees: Separation Algorithms. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 10
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    Stochastic Versus Deterministic Numerical ODE Integration (1992)
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    Publication Date: 2020-03-06
    Language: English
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  • 11
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    Asymptotic Mesh Independence for Newton-Galerkin Methods via a Refined Mysovskii Theorem (1992)
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    Publication Date: 2020-12-15
    Language: English
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  • 12
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    Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions (1992)
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    Publication Date: 2020-03-20
    Language: English
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  • 13
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    Theoretical and practical aspects of combinatorial problem solving (1992)
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    Publication Date: 2020-08-05
    Language: English
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  • 14
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    Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints (1992)
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    Publication Date: 2020-08-05
    Language: English
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  • 15
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    Clique-Web Facets for Multicut Polytopes (1992)
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    Publication Date: 2020-08-05
    Language: English
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  • 16
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    Facets for polyhedra arising in the design of communication networks with low-connectivity constraints (1992)
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    Publication Date: 2020-08-05
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  • 17
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    A cutting plane algorithm for the windy postman problem (1992)
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    Publication Date: 2020-08-05
    Language: English
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  • 18
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    Computation of Bifurcation Graphs. (1992)
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    Publication Date: 2014-02-26
    Description: 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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  • 19
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    Routing in Grid Graphs by Cutting Planes. (1992)
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    Publication Date: 2014-02-26
    Description: {\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.}
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  • 20
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    An Adaptive Continuation Method for Implicitly Defined Surfaces. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 21
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    Discretization and Iterative Solution of Convection Diffusion Equations. (1992)
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    Publication Date: 2021-03-16
    Description: 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.
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  • 22
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    Dynamic Sparsing in Stiff Extrapolation Methods. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 23
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    Packing Steiner Trees: Further Facets. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 24
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    A Basic Norm Equivalence for the Theory of Multilevel Methods. (1992)
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    Publication Date: 2014-02-26
    Description: 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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  • 25
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    Combinatorics in Statistical Physics (1992)
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    Publication Date: 2014-02-26
    Keywords: ddc:000
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  • 26
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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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    Publication Date: 2014-02-26
    Description: 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.
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  • 27
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    Medians of Binary Relations: Computational Complexity. (1992)
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    Publication Date: 2014-02-26
    Description: 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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  • 28
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    MEXX - Numerical Software for the Integration of Constrained Mechanical Systems. (1992)
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    Publication Date: 2020-11-16
    Description: 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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  • 29
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    Adaptive Multilevel-Methods in 3-Space Dimensions. (1992)
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    Publication Date: 2019-05-10
    Description: 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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  • 30
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    The Numerical Solution of Constrained Hamiltonian Systems. (1992)
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    Publication Date: 2021-01-21
    Description: 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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  • 31
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    MmB schemes on regular triangular meshes for 2-D conservation laws. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 32
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    On decomposing systems of polynomial equations with finitely many solutions. (1992)
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    Publication Date: 2014-02-26
    Description: 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.
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  • 33
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    Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 34
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    Shellability of Chessboard Complexes. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 35
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    Numerical Riemann solutions in multi-pieces for 2-D gas dynamics systems I. Contact discontinuities. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 36
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    An Algorithm for Optimizing a Linear Function over the Integer Efficient Set. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 37
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    Ab initio Quantum Chemical Calculations with GAMESS-UK and GAUSSIAN90 Program Packeges - A Comparison -. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 38
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    Computational Chemistry Software at ZIB. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 39
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    A Family of Newton Codes for Systems of Highly Nonlinear Equations. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 40
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    Modular Design of Extrapolation Codes. (1992)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 41
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    Adaptive Multilevel Beam Propagation Method (1992)
    Details
    Publication Date: 2022-07-07
    Language: English
    Type: article , doc-type:article
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  • 42
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    An Adaptive Approach to a Beam Propagation Method (1992)
    Details
    Publication Date: 2022-07-07
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 43
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    Improved Method of Mode Determination in Planar Optical Waveguides Using Line Transmission Approach (1992)
    Details
    Publication Date: 2022-07-07
    Language: English
    Type: article , doc-type:article
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  • 44
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    Hadron Spectroscopy on a 32^3 * 48 Lattice (1992)
    Details
    Publication Date: 2022-07-19
    Language: English
    Type: article , doc-type:article
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  • 45
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    AGIL - the Adaptable Graphical Interface Layer, Programmierer-Handbuch (1992)
    Details
    Publication Date: 2022-07-19
    Language: English
    Type: other , doc-type:Other
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  • 46
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    SU(3) Renormalization Group Study on Parallel Computer AP 1000 (1992)
    Details
    Publication Date: 2022-07-19
    Language: English
    Type: article , doc-type:article
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  • 47
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    Conference Report: Parallel Computing 91 (1992)
    Details
    Publication Date: 2022-07-19
    Language: English
    Type: article , doc-type:article
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  • 48
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    QCD on the Highly Parallel Computer AP 1000 (1992)
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    Publication Date: 2022-07-19
    Language: English
    Type: article , doc-type:article
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  • 49
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    Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of Raman Spectroscopy. (1992)
    Details
    Publication Date: 2023-08-14
    Language: English
    Type: article , doc-type:article
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  • 50
    Book
    Book
    Markov processes : an introduction for physical scientists (1992)
    Boston :Academic Press,
    Details
    Title: Markov processes : an introduction for physical scientists
    Author: Gillespie, Daniel T.
    Edition: 1
    Publisher: Boston :Academic Press,
    Year of publication: 1992
    Pages: XXI, 565 S.
    ISBN: 0-12-283955-2
    Type of Medium: Book
    Language: English
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  • 51
    Book
    Book
    IEEE transactions on image processing : a publication of the IEEE Signal Processing Society (1992)
    New York, NY :Inst., ; 1.1992 -
    Details
    Title: IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
    Author: Institute of Electrical and Electronics Engineers / Computer Group
    Contributer: Signal Processing Society
    Publisher: New York, NY :Inst.,
    Year of publication: 1992
    Dates of Publication: 1.1992 -
    ISSN: 1057-7149
    Type of Medium: Book
    Language: English
    Parallel Title: Internetausg. ---〉:Institute of Electrical and Electronics Engineers: IEEE transactions on image processing
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  • 52
    Book
    Book
    Riemannian geometry / (1992)
    Boston [u.a.] :Birkhäuser,
    Details
    Title: Riemannian geometry /
    Author: Carmo, Manfredo P. do
    Uniform Title: Geometria riemanniana 〈engl.〉
    Edition: 2. print.
    Publisher: Boston [u.a.] :Birkhäuser,
    Year of publication: 1992
    Pages: 300 S.
    Series Statement: Mathematics: Theory and applications
    ISBN: 0-8176-3490-8 , 3-7643-3490-8
    Type of Medium: Book
    Language: English
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  • 53
    Book
    Book
    Mathematical modelling of industrial processes : held in Bari, Italy, Sept. 24 - 29, 1990; 1990,3, 1521 (1992)
    Berlin [u.a.] :Springer,
    Details
    Title: Mathematical modelling of industrial processes : held in Bari, Italy, Sept. 24 - 29, 1990; 1990,3, 1521
    Contributer: Busenberg, Stavros N. , Forte, Bruno , Kuiken, Hendrik K. , Capasso, Vincenzo
    Publisher: Berlin [u.a.] :Springer,
    Year of publication: 1992
    Pages: 162 S. : graph. Darst.
    Series Statement: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (CIME) 1990,3
    ISBN: 3-540-55595-1 , 0-387-55595-1
    Type of Medium: Book
    Language: English
    URL: https://zbmath.org/?q=an:00053914
    URL: Inhaltsverzeichnis
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  • 54
    Book
    Book
    Lectures on semiparametric econometrics / (1992)
    Louvain-la-Neuve :CORE Foundation,
    Details
    Title: Lectures on semiparametric econometrics /
    Author: Stoker, Thomas M.
    Publisher: Louvain-la-Neuve :CORE Foundation,
    Year of publication: 1992
    Pages: III, 138 S. : graph. Darst.
    Series Statement: CORE lectures series
    Type of Medium: Book
    Language: English
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  • 55
    Book
    Book
    Reliability in computational mechanics /; 101.1992,1/3 (1992)
    Amsterdam [u.a.] :North-Holland,
    Details
    Title: Reliability in computational mechanics /; 101.1992,1/3
    Contributer: Demkowicz, L. , Oden, J. T.
    Publisher: Amsterdam [u.a.] :North-Holland,
    Year of publication: 1992
    Pages: 485 S.
    Series Statement: Computer methods in applied mechanics and engineering 101.1992,1/3
    Type of Medium: Book
    Language: English
    URL: http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0783.00021
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  • 56
    Book
    Book
    CAST: methods in modelling : computer aided systems theory for the design of intelligent machines (1992)
    Berlin [u.a.] :Springer,
    Details
    Title: CAST: methods in modelling : computer aided systems theory for the design of intelligent machines
    Contributer: Pichler, Franz
    Publisher: Berlin [u.a.] :Springer,
    Year of publication: 1992
    Pages: XIII, 376 S. : Ill., graph. Darst.
    ISBN: 3-540-55405-X , 0-387-55405-X
    Type of Medium: Book
    Language: English
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