@phdthesis{Weismantel1992, author = {Weismantel, Robert}, title = {Plazieren von Zellen: Theorie und L{\"o}sung eines quadratischen 0/1- Optimierungsproblems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4883}, number = {TR-92-03}, year = {1992}, abstract = {Die vorliegende Arbeit besch{\"a}ftigt 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 komplexit{\"a}tstheoretisch. Der zweite Aspekt der Arbeit bezieht sich auf die L{\"o}sung praktischer Problembeispiele im sogenannten Sea of cells"-Entwurfsstil. Zur L{\"o}sung 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, besch{\"a}ftigen. Dabei steht einerseits im Vordergrund, wie diese Probleme heuristisch gel{\"o}st werden k{\"o}nnen und wie die Integration des Ansatzes in das Plazierungsprogramm erfolgt. Andererseits soll das Clusteringproblem polyedrisch untersucht werden.}, language = {de} } @phdthesis{Martin1992, author = {Martin, Alexander}, title = {Packen von Steinerb{\"a}umen: Polyedrische Studien und Anwendung.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4894}, number = {TR-92-04}, year = {1992}, abstract = {Gegeben sei ein Graph \$G=(V,E)\$ mit positiven Kantenkapazit{\"a}ten \$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 h{\"o}chstens \$c_e\$ Kantenmengen aus \$S_1,\ldots,S_N\$ vorkommt. Eine zul{\"a}ssige L{\"o}sung dieses Problems nennen wir eine Steinerbaumpackung. Ist zus{\"a}tzlich eine Gewichtung der Kanten gegeben und nach einer bez{\"u}glich 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 Optimalit{\"a}tskriterien auf einer Grundfl{\"a}che 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 L{\"o}sung des Schnittebenenverfahrens liefert eine untere Schranke f{\"u}r die Optimall{\"o}sung und dient als Grundlage f{\"u}r 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.}, language = {de} } @misc{LeimkuhlerReich1992, author = {Leimkuhler, Benedict and Reich, Sebastian}, title = {The Numerical Solution of Constrained Hamiltonian Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-868}, number = {SC-92-16}, year = {1992}, abstract = {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.}, language = {en} } @misc{Moeller1992, author = {M{\"o}ller, H. Michael}, title = {On decomposing systems of polynomial equations with finitely many solutions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-851}, number = {SC-92-15}, year = {1992}, abstract = {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 Gr{\"o}bner 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, Gr{\"o}bner bases, systems of nonlinear equations.}, language = {en} } @misc{BornemannErdmannKornhuber1992, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Kornhuber, Ralf}, title = {Adaptive Multilevel-Methods in 3-Space Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-843}, number = {SC-92-14}, year = {1992}, abstract = {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.}, language = {en} } @misc{Gatermann1992, author = {Gatermann, Karin}, title = {Computation of Bifurcation Graphs.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-837}, number = {SC-92-13}, year = {1992}, abstract = {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.}, language = {en} } @misc{OPUS4-982, title = {Jahresbericht 1991}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9825}, number = {1991}, year = {1992}, language = {de} } @misc{LubichNowakPoehleetal.1992, author = {Lubich, Christian and Nowak, Ulrich and P{\"o}hle, Uwe and Engstler, Ch.}, title = {MEXX - Numerical Software for the Integration of Constrained Mechanical Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-823}, number = {SC-92-12}, year = {1992}, abstract = {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.}, language = {en} } @misc{Bixby1992, author = {Bixby, Robert E.}, title = {Das Implementieren des Simplex- Verfahrens: Die Startbasis.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-816}, number = {SC-92-11}, year = {1992}, abstract = {Dieses Paper enth{\"a}lt die ersten beiden Teile einer geplanten Serie von Aufs{\"a}tzen {\"u}ber die \$CPLEX^2\$-Implementierung des Simplex- Verfahrens. Der erste Teil ist eine Einf{\"u}hrung: er liefert eine kurze Beschreibung des Verfahrens f{\"u}r Probleme mit beschr{\"a}nkten Variablen, zusammen mit einer relativ ausf{\"u}hrlichen Diskussion der numerischen Eigenschaften der Netlib-Probleme. Diese Probleme bilden auch das Fundament der rechnerischen Untersuchungen in den folgenden Teilen. Der zweite Teil enth{\"a}lt die Hauptergebnisse dieses Papers, eine Beschreibung der Methode, die von CPLEX verwendet wird, um eine Startbasis zu konstruieren.}, language = {de} } @misc{GroetschelMartinWeismantel1992, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiner Trees: Polyhedral Investigations.}, doi = {10.1007/BF02592085}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-786}, number = {SC-92-08}, year = {1992}, abstract = {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.}, language = {en} } @misc{GroetschelMartinWeismantel1992, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiners Trees: A Cutting Plane Algorithm and Computational Results.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-792}, number = {SC-92-09}, year = {1992}, abstract = {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.}, language = {en} } @misc{JuengerMartinReineltetal.1992, author = {J{\"u}nger, Michael and Martin, Alexander and Reinelt, Gerhard and Weismantel, Robert}, title = {Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-803}, number = {SC-92-10}, year = {1992}, abstract = {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.}, language = {en} } @misc{SchuetteWulkow1992, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of RamanSpectroscopy.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-778}, number = {SC-92-07}, year = {1992}, abstract = {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.}, language = {en} } @misc{KornhuberWittum1992, author = {Kornhuber, Ralf and Wittum, Gabriel}, title = {Discretization and Iterative Solution of Convection Diffusion Equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-762}, number = {SC-92-06}, year = {1992}, abstract = {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.}, language = {en} } @misc{LangWalter1992, author = {Lang, Jens and Walter, Artur}, title = {A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-755}, number = {SC-92-05}, year = {1992}, abstract = {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.}, language = {en} } @misc{Groetschel1992, author = {Gr{\"o}tschel, Martin}, title = {Discrete Mathematics in Manufacturing.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-738}, number = {SC-92-03}, year = {1992}, abstract = {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.}, language = {en} } @misc{Wakabayashi1992, author = {Wakabayashi, Yoshiko}, title = {Medians of Binary Relations: Computational Complexity.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-746}, number = {SC-92-04}, year = {1992}, abstract = {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.}, language = {en} } @misc{Schoeffel1992, author = {Sch{\"o}ffel, Klaus}, title = {Computational Chemistry Software at ZIB.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4879}, number = {TR-92-02}, year = {1992}, abstract = {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.}, language = {en} } @misc{AckermannHELFRICH1992, author = {Ackermann, J{\"o}rg and HELFRICH, K.}, title = {Radius of Convergence of the 1/Z-Expansion for Diatomic Molecules: The Ground State of the Isoelectronic H2Sequence.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-721}, number = {SC-92-02}, year = {1992}, abstract = {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.}, language = {en} } @misc{BornemannYserentant1992, author = {Bornemann, Folkmar A. and Yserentant, Harry}, title = {A Basic Norm Equivalence for the Theory of Multilevel Methods.}, doi = {10.1007/BF01388699}, number = {SC-92-01}, year = {1992}, abstract = {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.}, language = {en} } @misc{NowakWeimann1992, author = {Nowak, Ulrich and Weimann, Lutz}, title = {A Family of Newton Codes for Systems of Highly Nonlinear Equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4855}, number = {TR-91-10}, year = {1992}, abstract = {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.}, language = {en} } @misc{Schoeffel1992, author = {Sch{\"o}ffel, Klaus}, title = {Ab initio Quantum Chemical Calculations with GAMESS-UK and GAUSSIAN90 Program Packeges - A Comparison -.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4867}, number = {TR-92-01}, year = {1992}, abstract = {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.}, language = {en} } @misc{Hohmann1992, author = {Hohmann, Andreas}, title = {An Adaptive Continuation Method for Implicitly Defined Surfaces.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-705}, number = {SC-91-20}, year = {1992}, abstract = {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.}, language = {en} } @misc{GodsilGroetschelWelsh1992, author = {Godsil, C. D. and Gr{\"o}tschel, Martin and Welsh, D. J. A.}, title = {Combinatorics in Statistical Physics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-694}, number = {SC-91-19}, year = {1992}, language = {en} } @misc{Wulkow1991, author = {Wulkow, Michael}, title = {Adaptive Treatment of Polyreactions in Weighted Sequence Spaces.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-673}, number = {SC-91-17}, year = {1991}, abstract = {Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and statistics. They can be considered as ordinary differential equations in sequence spaces. In this work, a fully adaptive algorithm for the computational treatment of such systems is developed. The method is based on a time discretization of an abstract Cauchy problem in Hilbert space and a discrete Galerkin approach for the discretization of the arising stationary subproblems. The Galerkin method uses 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 are solved adaptively either by use of analytical properties of the orthogonal functions or by an appropriate numerical summation. The resulting algorithm CODEX is applied to examples of technological interest, in particular from polymer chemistry.}, language = {en} } @misc{AckermannWulkow1991, author = {Ackermann, J{\"o}rg and Wulkow, Michael}, title = {The Treatment of Macromolecular Processes with Chain-Length-Dependent Reaction Coefficients - An Examplefrom Soot Formation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-682}, number = {SC-91-18}, year = {1991}, abstract = {The description of chain length distributions in macromolecular reaction kinetics leads to so-called countable systems of differential equations. In particular, when the appearing reaction rate coefficients depend on the chain length of the reacting macromolecules itself, an efficient numerical treatment of these systems is very difficult. Then even the evaluation of the right-hand side of the system can become prohibitively expensive with respect to computing time. In this paper we show how the discrete Galerkin method can be applied to such problems. The existing algorithm CODEX is improved by use of a multiplicative error correction scheme for time discretization and a new type of numerical preprocessing by means of a Gauss summation. Both ideas are exemplary for a wide class of approximation types and are described very briefly here. The new numerical techniques are tested on an example from soot formation, where the coagulation of molecules is modeled in terms of reaction coefficients depending on the surface of the particles and their collision frequency.}, language = {en} } @misc{SchoepfDeuflhard1991, author = {Sch{\"o}pf, R. and Deuflhard, Peter}, title = {OCCAL: A mixed symbolic- numeric Optimal Control CALculator.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-638}, number = {SC-91-13}, year = {1991}, abstract = {The numerical solution of optimal control problems by indirect methods (such as multiple shooting or collocation) requires a considerable amount of analytic calculation to establish a numerically tractable system. These analytic calculations, though being rather tedious in realistic examples, are nowadays mostly still done by hand-and thus prone to calculation errors. The paper aims at automating this analytic processing to a reasonable extent by means of a modern symbolic manipulation language (here: REDUCE). In its present stage of development the package OCCAL (mnemotechnically for \underline{O}ptimal \underline{C}ontrol \underline{CAL}culator) permits an interactive use, covering tasks like automatic determination of control and, in case of a singular control, of its order. In simpler problems, the present version of OCCAL automatically produces the full subroutine input for a MULtiple shooting code (MULCON) with adaptive numerical CONtinuation. In more complicate problems where singular sub-arcs may occur or where the sequence of sub-arcs of the optimal trajectory is unclear OCCAL is a significant help in reducing analytic pre-processing. Numerical examples illustrate the performance of OCCAL/MULCON.}, language = {en} } @misc{HoppeKornhuber1991, author = {Hoppe, Ronald H. W. and Kornhuber, Ralf}, title = {Adaptive Multilevel - Methods for Obstacle Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-667}, number = {SC-91-16}, year = {1991}, abstract = {We consider the discretization of obstacle problems for the Laplacian by piecewise linear finite elements. Assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies, the linear problems are solved iteratively by preconditioned c-g iterations. The proposed preconditioners are treated theoretically as abstract additive Schwarz methods and are implemented as truncated hierarchical basis preconditioners. To allow for local mesh refinement we derive semi-local and local a posteriori error estimates, providing lower and upper estimates for the discretization error. The theoretical results are illustrated by numerical computations.}, language = {en} } @misc{GatermannHohmann1991, author = {Gatermann, Karin and Hohmann, Andreas}, title = {Hexagonal Lattice Dome - Illustration of a Nontrivial Bifurcation Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-587}, number = {SC-91-08}, year = {1991}, abstract = {The deformation of a hexagonal lattice dome under an external load is an example of a parameter dependent system which is equivariant under the symmetry group of a regular hexagon. In this paper the mixed symbolic-numerical algorithm SYMCON is applied to analyze its steady state solutions automatically showing their different symmetry and stability properties.}, language = {en} } @misc{Ziegler1991, author = {Ziegler, G{\"u}nter M.}, title = {On the Difference Between Real and Complex Arrangements.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-648}, number = {SC-91-14}, year = {1991}, abstract = {If \$B\$ is an arrangement of linear complex Hyperplanes in \$C^d\$, then the following can be constructed from knowledge of its intersection lattice: (a) the cohomology groups of the complement [Br], (b) the cohomology algebra of the complement [OS], (c) the fundamental group of the complement, if \$d\le2\$, (d) the singularity link up to homeomorphism, if \$d\le3\$, (e) the singularity link up to homotopy type [ZZ]. If \$B'\$ is, more generally, a 2-arrangement in \$ R^{2d}\$ (an arrangement of real subspaces of codimension 2 with even-dimensional intersections), then the intersection lattice still determines (a) the cohomology groups of the complement [GM] and (e) the homotopy type of the singularity link [ZZ]. We show, however, that for 2-arrangements the data (b), (c) and (d) are not determined by the intersection lattice. They require the knowledge of extra information on sign patterns, which can be computed as determinants of linear relations, or (equivalently) as linking coefficients in the sense of knot theory.}, language = {en} } @misc{ZieglerZivaljevic1991, author = {Ziegler, G{\"u}nter M. and Zivaljevic, R. T.}, title = {Homotopy Types of Subspace Arrangements via Diagrams of Spaces.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-658}, number = {SC-91-15}, year = {1991}, abstract = {We prove combinatorial formulas for the homotopy type of the union of the subspaces in an (affine, compactified affine, spherical or projective) subspace arrangement. From these formulas we derive results of Goresky \& MacPherson on the homology of the arrangement and the cohomology of its complement. The union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset. A closely related space is obtained by taking the homotopy direct limit of this diagram. Our method consists in constructing a combinatorial model diagram over the same poset, whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces.}, language = {en} } @misc{Schmidt1991, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-628}, number = {SC-91-12}, year = {1991}, abstract = {An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1D cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. Fresnel's wave equation being formally equivalent to Schroedinger's equation uniquely defines an initial-boundary-value problem, which is solved numerically by a stepwise calculation of the propagating field. Discretization in longitudinal direction first with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite element method. Thus full adaptivity of the algorithm is realized. The numerical examples are concentrated on taper structures playing an essential role in integrated optics devices for telecommunication systems.}, language = {en} } @misc{SturmfelsZiegler1991, author = {Sturmfels, Bernd and Ziegler, G{\"u}nter M.}, title = {Extension Spaces of Oriented Matriods.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-618}, number = {SC-91-11}, year = {1991}, abstract = {We study the space of all extensions of a real hyperplane arrangement by a new pseudo- hyperplane, and, more generally, of an oriented matroid by a new element. The question whether this space has the homotopy type of a sphere is a special case of the "Generalized Baues Problem" of Billera, Kapranov \& Sturmfels, via the Bohne-Dress Theorem on zonotopal tilings. We prove that the extension space is spherical for the class of strongly euclidean oriented matroids. This class includes the alternating matroids and all oriented matroids of rank at most 3 or of corank at most 2. In general it is not even known whether the extension space is connected. We show that the subspace of realizable extensions is always connected but not necessarily spherical.}, language = {en} } @misc{Ziegler1991, author = {Ziegler, G{\"u}nter M.}, title = {Higher Bruhat Orders and Cyclic Hyperplane Arrangements.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-607}, number = {SC-91-10}, year = {1991}, abstract = {We study the higher Bruhat orders \$B(n,k)\$ of Manin \& Schechtman [MaS] and - characterize them in terms of inversion sets, - identify them with the posets \$U(C^{n+1,r},n+1)\$ of uniform extensions of the alternating oriented matroids \$C^{n,r}\$ for \$r:=n-k\$ (that is, with the extensions of a cyclic hyperplane arrangement by a new oriented pseudoplane), - show that \$B(n,k)\$ is a lattice for \$k =1\$ and for \$r\le 3\$, but not in general, - show that \$B(n,k)\$ is ordered by inclusion of inversion sets for \$k=1\$ and for \$r\le 4\$. However, \$B(8,3)\$ is not ordered by inclusion. This implies that the partial order \$B_\subseteq (n,k)\$ defined by inclusion of inversion sets differs from \$B(n,k)\$ in general. We show that the proper part of \$B_\subseteq (n,k)\$ is homotopy equivalent to \$S^{r-2}\$. Consequently, - \$B(n,k)\simeq S^{r-2}\$ for \$k=1\$ and for \$r\le 4\$. In contrast to this, we find that the uniform extension poset of an affine hyperplane arrangement is in general not graded and not a lattice even for \$r=3\$, and that the proper part is not always homotopy equivalent to \$S^{r(M)-2}\$.}, language = {en} } @misc{DeuflhardNowakPoehleetal.1991, author = {Deuflhard, Peter and Nowak, Ulrich and P{\"o}hle, Uwe and Schmidt, B. Ch. and Weyer, J.}, title = {Die Ausbreitung von HIV/AIDS in Ballungsgebieten.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4844}, number = {TR-91-09}, year = {1991}, abstract = {The rapidly increasing number of AIDS cases requires a realistic estimation of the future development of the HIV/AIDS disease. For that purpose we develop a large system of coupled nonlinear differential equations describing simultaneously the dynamics of the development of the disease, the population size, the gender and age structure. A set of 1650 coupled equations are linked by balanced parameters. The balancing procedure is described by a set of (formally) 2,178,000 additional algebraic conditions. As the considered system is stiff, it requires new special extrapolation methods combined with techniquees of dynamical sparsing for the solution of sparsely filled systems. According to our simulations we expect 19,0,000 deaths caused by AIDS in the Federal Republic of Germany (former territories) in the year 2000. Such an epidemical spread would tie up about 4-7 percent of the actual health care workers.}, language = {de} } @misc{Bornemann1991, author = {Bornemann, Folkmar A.}, title = {A Sharpened Condition Number Estimate for the BPX Preconditioner of Elliptic Finite Element Problems on Highly Nonuniform Triangulations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-596}, number = {SC-91-09}, year = {1991}, abstract = {In this paper it is shown that for highly nonuniformly refined triangulations the condition number of the BPX preconditioner for elliptic finite element problems grows at most linearly in the depth of refinement. This is achieved by viewing the computational available version of the BPX preconditioner as an abstract additive Schwarz method with exact solvers. {\bf AMS CLASSIFICATION:} 65F10, 65F35, 65N20, 65N30.}, language = {en} } @misc{DeuflhardPotra1991, author = {Deuflhard, Peter and Potra, Florian}, title = {A Refined Gauss-Newton- Mysovskii Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-541}, number = {SC-91-04}, year = {1991}, abstract = {The present paper contains a generalization of a refinement of the Newton- Mysovskii theorem, recently obtained by the authors, to the case of Gauss-Newton procedures for solving nonlinear least-squares problems with full Jacobians. Invariant sufficient conditions are given that ensure the convergence of the Gauss-Newton iterates towards a solution of the problem, as well as the uniqueness of that solution in an explicitely defined neighborhood. It is shown by a counter- example that the results do not carry over to the rank deficient case.}, language = {en} } @misc{HoppeKornhuber1991, author = {Hoppe, Ronald H. W. and Kornhuber, Ralf}, title = {Multilevel Preconditioned CG-Iterations for Variational Inequalities.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-561}, number = {SC-91-06}, year = {1991}, abstract = {We consider such variational inequalities which either describe obstacle problems or result from an implicit time discretization of moving boundary problems of two phase Stefan type. Based on a discretization in space by means of continuous, piecewise linear finite elements with respect to a nested hierarchy of triangulations, in both cases we use iterative processes consisting of inner and outer iterations. The outer iterations are either active set strategies or generalized Newton methods while the inner iterations are preconditioned cg- iterations with multilevel preconditioners.}, language = {en} } @misc{GajewskiEdDeuflhardMarkowiched1991, author = {Gajewski(Ed.), Herbert and Deuflhard, Peter and Markowich(ed.), A.}, title = {Tagung NUMSIM '91 5.-08. Mai 1991. Collected Abstracts and Papers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4838}, number = {TR-91-08}, year = {1991}, abstract = {NUMSIM 91 fand vom 6.-08. Mai 1991 im Wissenschaftlichen Kommunikations- \& Konferenz- Zentrum der Humboldt-Universit{\"a}t in Gosen bei Berlin statt. Im Mittelpunkt dieses Seminars standen Probleme der numerischen Simulation von Ladungstransport- und Technologieprozessen der Mikro- und Optoelektronik. Es f{\"u}hrte Spezialisten der physikalischen Modellierung, der numerischen Mathematik und mathematischen Analysis sowie Nutzer von Simulationsprogrammen aus dem deutschsprachigen Raum zusammen. Ziel war die Vermittlung und der Austausch von Erfahrungen, die Diskussion gemeinsamer Aufgabenstellungen und Projekte und - in Anbetracht der deutschen Vereinigung nicht zuletzt - das gegenseitige Kennen- und Verstehenlernen.}, language = {en} } @misc{Bornemann1991, author = {Bornemann, Folkmar A.}, title = {An Adaptive Multilevel Approach to Parabolic Equations in Two Space Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4821}, number = {TR-91-07}, year = {1991}, abstract = {A new adaptive multilevel approach for linear partial differential equations is presented, which is able to handle complicated space geometries, discontinuous coefficients, inconsistent initial data. Discretization in time first (Rothe's method) with order and stepsize control is perturbed by an adaptive finite element discretization of the elliptic subproblems, whose errors are controlled independently. Thus the high standards of solving adaptively ordinary differential equations and elliptic boundary value problems are combined. A theory of time discretization in Hilbert space is developed which yields to an optimal variable order method based on a multiplicative error correction. The problem of an efficient solution of the singularly perturbed elliptic subproblems and the problem of error estimation for them can be uniquely solved within the framework of preconditioning. A Multilevel nodal basis preconditioner is derived, which allows the use of highly nonuniform triangulations. Implementation issues are discussed in detail. Numerous numerical examples in one and two space dimensions clearly show the significant perspectives opened by the new algorithmic approach. Finally an application of the method is given in the area of hyperthermia, a recent clinical method for cancer therapy.}, language = {en} } @misc{FiedlerScheurle1991, author = {Fiedler, Bernold and Scheurle, J.}, title = {Discretization of Homoclinic Orbits, Rapid Forcing and "Invisible" Chaos.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-552}, number = {SC-91-05}, year = {1991}, abstract = {One-step discretizations of order \$p\$ and step size \$\varepsilon\$ of ordinary differential equations can be viewed as time-\$\varepsilon\$ maps of \begin{displaymath} \dot{x} (t) = f(\lambda ,x(t)) + \varepsilon^p g(\varepsilon,\lambda,t/\varepsilon,x(t)), x \in R^N,\lambda \in R, \end{displaymath} where \$g\$ has period \$\varepsilon\$ in \$t\$. This is a rapidly forced nonautonomous system. We study the behavior of a homoclinit orbit \$\Gamma\$ for \$\varepsilon = 0, \lambda =0\$, under discretization. Under generic assumptions we show that \$\Gamma\$ becomes transverse for positive \$\in\$. The transversality effects are estimated from above to be exponentially small in \$\in\$. For example, the length \$l(\varepsilon\$) of the parameter interval of \$\lambda\$ for which \$\Gamma\$ persists can be estimated by \begin{displaymath} l(\varepsilon)\le Cexp(-2\pi\eta/\varepsilon), \end{displaymath} where \$C,\eta\$ are positive constants. The coefficient \$\eta\$ is related to the minimal distance from the real axis of the poles of \$\Gamma(t)\$ in the complex time domain. Likewise, the region where complicated, "chaotic" dynamics prevail is estimated to be exponentially small, provided \$x \in R^2\$ and the saddle quantity of the associated equilibrium is nonzero. Our results are visualized by high precision numerical experiments. The experiments show that, due to exponential smallness, homoclinic transversality becomes pratically invisible under normal circumstances, already for only moderately small step size. {\bf Keywords:} Homoclinic orbit, ordinary differential equations, discretization, transversality, averaging, exponential smallness, chaos. {\bf Subject Classifications:} (AMS): 34C15, 34C35, 58F14, 65L60}, language = {en} } @misc{LangWalter1991, author = {Lang, Jens and Walter, Artur}, title = {An Adaptive Discontinuous Finite Element Method for the Transport Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-579}, number = {SC-91-07}, year = {1991}, abstract = {In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.}, language = {en} } @misc{Schoeffel1991, author = {Sch{\"o}ffel, Klaus}, title = {Computational Chemistry Software for CRAY X-MP/2.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4816}, number = {TR-91-06}, year = {1991}, abstract = {The following report intends to provide a survey over the computational chemistry molecular structure software installed on CRAY X-MP/24 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.}, language = {en} } @misc{Griewank1991, author = {Griewank, Andreas}, title = {Sequential Evaluation of Adjoints and Higher Derivative Vectors by Overloading and Reverse Accumulation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-539}, number = {SC-91-03}, year = {1991}, abstract = {Most nonlinear computations require the evaluation of first and higher derivatives of vector functions defined by computer programs. It is shown here how vectors of such partial derivatives can be obtained automatically and efficiently if the computer language allows overloading (as is or will be the case for C++, PASCAL-XSC, FORTRAN90, and other modern languages). Here, overloading facilitates the extension of arithmetic operations and univariate functions from real or complex arguments to truncated Taylor-series (or other user- defined types), and it generates instructions for the subsequent evaluation of adjoints. Similar effects can be achieved by precompilation of FORTRAN77 programs. The proposed differentiation algorithm yields gradients and higher derivatives at a small multiple of the run-time and RAM requirement of the original function evaluation program. {\bf Keywords:} Automatic Differentiation, Chain Rule, Overloading, Taylor Coefficients, Gradients, Hessians, Reverse Accumulation, Adjoint Equations. {\bf Abbreviated title:} Automatic Differentiation by Overloading.}, language = {en} } @misc{OPUS4-983, title = {Jahresbericht 1990}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9831}, number = {1990}, year = {1991}, language = {de} } @misc{Gottschewski1991, author = {Gottschewski, J{\"u}rgen}, title = {Supercomputing During the German Reunification.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4803}, number = {TR-91-05}, year = {1991}, abstract = {The success of the German Reunification requires a unique migration from the traditional Eastern Block system to a modern free society. The successful migration must include a shift from a low state of the art in technology to the high level of science and technology present in the Western Community. The role of supercomputing in this transition will include leading the process of organizational change in research and development. The paper contains a short overview on the current state of this evolution, on the currently used political and administrative tools to keep this evolution on track, and on the influence on the Konrad-Zuse-Zentrum, which is, as a Berlin institution, in the geographical and cultural center of this transformation.}, language = {en} } @misc{KornhuberRoitzsch1991, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {Self Adaptive Computation of the Breakdown Voltage of Planar pn-Junctions with Multistep Field Plates.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-525}, number = {SC-91-02}, year = {1991}, abstract = {The breakdown voltage highly depends on the electric field in the depletion area whose computation is the most time consuming part of the simulation. We present a self adaptive Finite Element Method which reduces dramatically the required computation time compared to usual Finite Difference Methods. A numerical example illustrates the efficiency and reliability of the algorithm.}, language = {en} } @misc{Lang1991, author = {Lang, Jens}, title = {An Adaptive Finite Element Method for Convection-Diffusion Problems by Interpolation Techniques.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4795}, number = {TR-91-04}, year = {1991}, abstract = {For adaptive solution of convection- difussion problems with the streamline-diffusion finite element method, an error estimator based on interpolation techniques is developed. It can be shown that for correctness of this error estimator a restriction of the maximum angle is to be sufficient. Compared to usual methods, the adaptive process leads to more accurate solutions at much less computational cost. Numerical tests are enclosed. {\bf Keywords: } Adaptive finite elements, convection- diffusion equation, internal and boundary layers, streamline-diffusion. {\bf Subject Classifications:} AMS(MOS): 65N15, 65N30}, language = {en} } @misc{Noelle1991, author = {Noelle, Sebastian W. C.}, title = {On the Limits of Operator Splitting: Numerical Experiments for the Complex Burgers Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4789}, number = {TR-91-03}, year = {1991}, abstract = {A high resolution Godunov-type method is developed and applied to a two-dimensional version of the Burgers equation. On one-dimensional testproblems the scheme is second order accurate for smooth flow and resolves discontinuities sharply. On two-dimensional problems, however, large numerical oscillations are introduced when discontinuities traveling obliquely to the grid directions are present. These oscillations are caused by a Strang- type operator splitting, and cannot be eliminated using flux limiters or small timesteps. {\bf Keywords:} High resolution methods, Godunovs method, operator splitting, complex Burgers equation. {\bf AMS:} 35: A40, L45, L60, L65, L, 67. 65: M05, M10.}, language = {en} } @misc{LueggerDalitz1991, author = {L{\"u}gger, Joachim and Dalitz, Wolfgang}, title = {Verteilung mathematischer Software mittels elektronischer Netze: Die elektronische Softwarebibliothek eLib.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4774}, number = {TR-91-02}, year = {1991}, abstract = {Mit zunehmender Dezentralisierung im Bereich des Wissenschaftlichen Rechnens steigt auch der Bedarf an Softwarequellen qualitativ hochwertiger mathematischer Algorithmen. F{\"u}r den Software- und Informationsaustausch wird die Einrichtung {\"o}ffentlicher, elektronischer Softwarebibliotheken vorgeschlagen. Am Beispiel der eLib des ZIB werden die notwendigen technischen Konzepte, die u.a. auch in den heutigen Gegebenheiten der technischen Kommunikation begr{\"u}ndet sind, diskutiert. Die eLib ist fenster- und men{\"u}orientiert aufgebaut und folglich im Dialog sehr einfach zu benutzen. Sie kann aber auch mit ihrer Kommandosprache allein auf dem Wege {\"u}ber elektronische Post abgefragt werden. {\"U}ber die eLib sind, nach dem Verbund mit den Netzbibliotheken NetLib und Reduce-NetLib jetzt etwa 6000 mathematische Programme und allgemeine Dokumente verf{\"u}gbar. Das Dienstleistungsangebot der eLib setzt Beitr{\"a}ge aus einer aktiven Benutzergemeinschaft voraus. Es besteht die Hoffnung, daß durch den {\"o}ffentlichen Softwareaustausch sich Entwickler und Anwender wechselseitig in ihrer Arbeit befruchten.}, language = {de} } @misc{BornemannErdmannRoitzsch1991, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE - Numerical Experiments.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4762}, number = {TR-91-01}, year = {1991}, abstract = {The C-implementation of KASKADE, an adaptive solver for linear elliptic differential equations in 2D, is object of a set of numerical experiments to analyze the use of resources (time and memory) with respect to numerical accuracy. We study the dependency of the reliability, robustness, and efficiency of the program from the parameters controlling the algorithm.}, language = {en} }