@misc{DeuflhardHegeSedlmayred1994, author = {Deuflhard, Peter and Hege, Hans-Christian and Sedlmayr(ed.), E.}, title = {Scientific Computing in der Theoretischen Physik. Collected Abstracts.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5068}, number = {TR-94-01}, year = {1994}, abstract = {Die von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem gleichnamigen GAMM-Fachausschuss organisierte Tagung \glqq Scientific Computing in der Theoretischen Physik\grqq~fand vom 16. - 18. M{\"a}rz 1994 am Fachbereich Mathematik und Informatik der Freien Universit{\"a}t Berlin statt. Ziel des Workshops war, die Kontakte zwischen den Fachleuten der Gebiete {\em Computational Physics} und {\em Scientific Computing} zu intensivieren. Schwerpunkte des Workshops waren numerische Simulation von Transportmodellen der Astrophysik und Halbleiterphysik, Multilevel-Methoden f{\"u}r partielle Differentialgleichungen sowie Monte-Carlo-Methoden und molekulardynamische Verfahren f{\"u}r Probleme der Statistischen Physik und Quantenfeldtheorie. Der Workshop fand ein {\"a}usserst positives Echo und f{\"u}hrte {\"u}ber 70 Teilnehmer der verschiedenen Teilgebiete der Theoretischen Physik und ca. 50 Teilnehmer aus dem Bereich der Numerischen Mathematik zusammen. \originalTeX}, language = {en} } @misc{SeebassSullivanWustetal.1994, author = {Seebass, Martin and Sullivan, Dennis and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {The Berlin Extension of the Stanford Hyperthermia Treatment.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1304}, number = {SC-93-35}, year = {1994}, abstract = {In the field of deep regional hyperthermia, one of the most widely used devices is the BSD--2000 Hyperthermia System which employs the Sigma 60 applicator. The Sigma 60 consists of four independent sources, giving it the potential to control the energy pattern within the patient. The independent amplitudes and phases, as well as frequency selection and applicator position, present a large number of parameters for the operator to determine. Computer simulation has long been recognized as an attractive approach to optimizing these parameters. A treatment planning program was used in clinical practice at Stanford University Medical Center for two years. It demonstrated the feasibility of computer simulation for deep regional hyperthermia in a clinical situation. However, several parts of this system were written in a language specific to one workstation, which severely restricted the wider distribution of the program to other users of the Sigma 60. A new treatment planning system for the BSD 2000 has been developed and put into clinical practice at the Rudolf Virchow Clinic of the Free University of Berlin. The new method, which we will refer to as the Berlin system, has a simpler model construction program and a considerably better graphics capability. However, the most important feature is that all programs are written in FORTRAN, C, or the X Window graphics system. Therefore, the entire treatment planning system is completely portable to other workstations.}, language = {en} } @misc{Weismantel1994, author = {Weismantel, Robert}, title = {On the 0/1 Knapsack Polytope.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1312}, number = {SC-94-01}, year = {1994}, abstract = {{\def\N{{\mbox{{\rm I\kern-0.22emN}}}} Given a set \$N\$ of items and a capacity \$b \in \N\$, and let \$N_j\$ be the set of items with weight \$j\$, \$1 \leq j \leq b\$. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality \$\$\sum_{j=1}^b \sum_{i \in N_j} jx_i \leq b.\$\$ In this paper we first present a complete linear description of the 0/1 knapsack polytope for two special cases: (a) \$N_j = \emptyset\$ for all \$1 < j \leq \lfloor {b \over 2} \rfloor\$ and (b) \$N_j = \emptyset\$ for all \$1 < j \leq \lfloor {b \over 3} \rfloor\$ and \$N_j = \emptyset\$ for all \$j \geq \lfloor {b \over 2} \rfloor + 1\$. It turns out that the inequalities that are needed for the complete description of these special polytopes are derived by means of some ``reduction principle''. This principle is then generalized to yield valid and in many cases facet defining inequalities for the general 0/1 knapsack polytope. The separation problem for this class of inequalities can be solved in pseudo polynomial time via dynamic programming techniques.}}, language = {en} } @misc{GroetschelMartinWeismantel1994, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {The Steiner Tree Packing Problem in VLSI-Design.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1328}, number = {SC-94-02}, year = {1994}, abstract = {In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.}, language = {en} } @misc{GroetschelPadberg1994, author = {Gr{\"o}tschel, Martin and Padberg, Manfred}, title = {Ulysses 2000: In Search of Optimal Solutions to Hard Combinatorial Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1296}, number = {SC-93-34}, year = {1994}, abstract = {Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a pace that is unprecedented in human history. We survey here in layman's terms some of the fundamental concepts and principles that have led this progress. (This article will appear -- possibly in modified form -- in a popular science magazine.)}, language = {en} } @phdthesis{Nowak1993, author = {Nowak, Ulrich}, title = {Adaptive Linienmethoden f{\"u}r nichtlineare parabolische Systeme in einer Raumdimension.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5059}, number = {TR-93-14}, year = {1993}, abstract = {A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi--implicit Euler discretization. Space discretization is done with finite differences on non--uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously. Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way.}, language = {en} } @misc{Bornemann1993, author = {Bornemann, Folkmar A.}, title = {Interpolation Spaces and Optimal Multilevel Preconditioners.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1285}, number = {SC-93-33}, year = {1993}, abstract = {This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality in \$H^{1+\epsilon}\$, \$\epsilon > 0\$. This machinery constructs so-called {\em approximation spaces}, which characterize a certain rate of approximation by finite elements and relates them with interpolation spaces, which characterize a certain smoothness.}, language = {en} } @misc{Zumbusch1993, author = {Zumbusch, Gerhard}, title = {Symmetric Hierarchical Polynomials for the h-p-Version of Finite Elements.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1275}, number = {SC-93-32}, year = {1993}, abstract = {Adaptive numerical methods using the \$h\$-\$p\$-version of finite elements require special kinds of shape functions. Desirable properties of them are symmetry, hierarchy and simple coupling. In a first step it is demonstrated that for standard polynomial vector spaces not all of these features can be obtained simultaneously. However, this is possible if these spaces are extended. Thus a new class of polynomial shape functions is derived, which is well-suited for the \$p\$- and \$h\$-\$p\$-version of finite elements on unstructured simplices. The construction is completed by minimizing the condition numbers of the arising finite element matrices. The new shape functions are compared with standard functions widely used in the literature.}, language = {en} } @phdthesis{Hohmann1993, author = {Hohmann, Andreas}, title = {Inexact Gauss Newton Methods for Parameter Dependent Nonlinear Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5049}, number = {TR-93-13}, year = {1993}, abstract = {A new approach to inexact Gauss Newton methods for the solution of underdetermined nonlinear problems is presented. It is based on a convergence theorem being invariant under affine transformations of the domain and results in an easily implementable accuracy matching strategy for the arising linear subproblems which guarantees the quadratic convergence. Thanks to the weak assumptions on the given nonlinear problem, the results provide a general framework for multilevel Newton and continuation methods. As an example, a new multilevel Newton h-p collocation method for boundary value problems of ordinary differential equations is developed. It combines the inexact Newton method with a linear collocation solver using adaptive refinement and variable orders. The performance of the resulting C++ class library {\sc Cocon} is demonstrated by some numerical examples including singular perturbed problems. In addition, the new method is applied to a realistic railway bogie model in which a branch of periodic solutions emanates from a branch of fixed points at a Hopf bifurcation.}, language = {en} } @misc{GruntzKoepf1993, author = {Gruntz, Dominik and Koepf, Wolfram}, title = {Formal Power Series.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1267}, number = {SC-93-31}, year = {1993}, abstract = {{\newcommand{\C}{{\rm {\mbox{C{\llap{{\vrule height1.52ex}\kern.4em}}}}}} \newcommand{\Z} {{\rm {\mbox{\protect\makebox[.2em][l]{\sf Z}\sf Z}}}} \newcommand{\Maple}{{\sc Maple}} Formal Laurent-Puiseux series of the form \[ f(x)=\sum\limits_{k=k_0}^{\infty}a_{k}x^{k/n} \label{eq:formalLPS} \] with coefficients \$a_{k}\in\C\;(k\in\Z)\$ are important in many branches of mathematics. \Maple\ supports the computation of {\em truncated\/} series with its {\tt series} command, and through the {\tt powerseries} package infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients. This is known as {\em lazy evaluation\/}. But these tools fail, if one is interested in an explicit formula for the coefficients \$a_k\$. In this article we will describe the \Maple\ implementation of an algorithm presented in several papers of the second author which computes an {\em exact\/} formal power series of a given function. This procedure will enable the user to reproduce most of the results of the extensive bibliography on series. We will give an overview of the algorithm and then present some parts of it in more detail. This package is available through the \Maple-share library with the name {\tt FPS}. We flavor this procedure with the following example. \%\begin{maple} \begin{verbatim}> FormalPowerSeries(sin(x), x=0);\end{verbatim} \begin{samepage} \begin{verbatim} infinity ----- k (2 k + 1) \ (-1) x ) ---------------- / (2 k + 1)! ----- k = 0 \end{verbatim} \end{samepage} }}, language = {en} } @misc{Zuse1993, author = {Zuse, Konrad}, title = {Cellular Structured Space (Rechnender Raum) and Physical Phenomena.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5039}, number = {TR-93-12}, year = {1993}, abstract = {The problem of nonlocal correlation and symmetry in space is of great importance in physical phenomena like the \underline{Einstein-Poloski-Rosen-Paradox} and others. It is shown that in Cellular Automata (Rechnender Raum) the structure of the space offers solutions for such problems.}, language = {en} } @misc{BornemannErdmannKornhuber1993, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Kornhuber, Ralf}, title = {A Posteriori Error Estimates for Elliptic Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1257}, number = {SC-93-29}, year = {1993}, abstract = {{\def\enorm {\mathop{\mbox{\boldmath{\$|\!|\$}}}\nolimits} Let \$u \in H\$ be the exact solution of a given self--adjoint elliptic boundary value problem, which is approximated by some \$\tilde{u} \in {\cal S}\$, \$\cal S\$ being a suitable finite element space. Efficient and reliable a posteriori estimates of the error \$\enorm u - \tilde{u}\enorm \$, measuring the (local) quality of \$\tilde{u}\$, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well--known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions. The theoretical results are illustrated by numerical computations.}}, language = {en} } @misc{GrammelHegeWunderling1993, author = {Grammel, Martin and Hege, Hans-Christian and Wunderling, Roland}, title = {On the Impact of Communication Latencies on Distributed Sparse LU Factorization.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1245}, number = {SC-93-28}, year = {1993}, abstract = {Sparse LU factorization offers some potential for parallelism, but at a level of very fine granularity. However, most current distributed memory MIMD architectures have too high communication latencies for exploiting all parallelism available. To cope with this, latencies must be avoided by coarsening the granularity and by message fusion. However, both techniques limit the concurrency, thereby reducing the scalability. In this paper, an implementation of a parallel LU decomposition algorithm for linear programming bases is presented for distributed memory parallel computers with noticable communication latencies. Several design decisions due to latencies, including data distribution and load balancing techniques, are discussed. An approximate performance model is set up for the algorithm, which allows to quantify the impact of latencies on its performance. Finally, experimental results for an Intel iPSC/860 parallel computer are reported and discussed.}, language = {en} } @misc{Koepf1993, author = {Koepf, Wolfram}, title = {A package on formal power series.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1231}, number = {SC-93-27}, year = {1993}, abstract = {Formal Laurent-Puiseux series of the form \[ f(x)=\sum \limits_{k=k_0}^{\infty}a_{k}x^{k/n} \] are important in many branches of mathematics. Whereas {\sc Mathematica} supports the calculation of truncated series with its {\tt Series} command, and the {\sc Mathematica} package {\tt SymbolicSum} that is shipped with {\sc Mathematica} version 2 is able to convert formal series of the type mentioned above in some instances to their corresponding generating functions, in six publications of the author we developed an algorithmic procedure to do these conversions that is implemented by the author, A.\ Rennoch and G.\ St{\"o}lting in the {\sc Mathematica} package {\tt PowerSeries}. The implementation enables the user to reproduce most of the results of the extensive bibliography on series of Hansen, E.\ R.: A table of series and products. Prentice-Hall, 1975. Moreover a subalgorithm of its own significance generates differential equations satisfied by the input function.}, language = {en} } @misc{GroetschelMartinWeismantel1993, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Optimum Path Packing on Wheels: The Noncrossing Case.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1225}, number = {SC-93-26}, year = {1993}, abstract = {We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that no two terminal pairs cross, then a path packing, i.~e.,a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.}, language = {en} } @misc{RichterGebertZiegler1993, author = {Richter-Gebert, J{\"u}rgen and Ziegler, G{\"u}nter M.}, title = {Zonotopal Tilings and the Bohne-Dress Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1212}, number = {SC-93-25}, year = {1993}, abstract = {We prove a natural bijection between the polytopal tilings of a zonotope \$Z\$ by zonotopes, and the one-element-liftings of the oriented matroid \${\cal M}(Z)\$ associated with \$Z\$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.}, language = {en} } @misc{DeuflhardSchmidt1993, author = {Deuflhard, Peter and Schmidt, Frank}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1205}, number = {SC-93-24}, year = {1993}, abstract = {The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schr{\"o}dinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.}, language = {en} } @misc{DeuflhardBoellingBott1993, author = {Deuflhard, Peter and B{\"o}lling, Reinhard and Bott, Raoul H.}, title = {Materialien zur Euler-Vorlesung in Sanssouci.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5029}, number = {TR-93-10}, year = {1993}, abstract = {Aus dem Inhalt: Vorwort; Leonhard Euler - aus der Zeit seines Wirkens in Berlin; Introductory Remarks.}, language = {de} } @misc{Deuflhard1993, author = {Deuflhard, Peter}, title = {Cascadic Conjugate Gradient Methods for Elliptic Partial Differential Equations I. Algorithm and Numerical Results.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1197}, number = {SC-93-23}, year = {1993}, abstract = {Cascadic conjugate gradient methods for the numerical solution of elliptic partial differential equations consists of Galerkin finite element methods as outer iteration and (possibly preconditioned) conjugate gradient methods as inner iteration. Both iterations are known to minimize the energy norm of the arising iterations errors. A simple but efficient strategy to control the discretization errors versus the PCG iteration errors in terms of energy error norms is derived and worked out in algorithmic detail. In a unified setting, the relative merits of different preconditioners versus the case of no preconditioning is compared. Surprisingly, it appears that the cascadic conjugate gradient method without any preconditioning is not only simplest but also fastest. The numerical results seem to indicate that the cascade principle in itself already realizes some kind of preconditioning. A theoretical explanation of these observations will be given in Part II of this paper.}, language = {en} } @misc{Lang1993, author = {Lang, Jens}, title = {KARDOS - KAskade Reaction Diffusion One-dimensional System.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5019}, number = {TR-93-09}, year = {1993}, abstract = {A software package for the adaptive solution of time--dependent reaction--diffusion systems and linear elliptic systems in one space dimension is presented. The used algorithm is based on fundamental arguments in J.~Lang, A.~Walter: {\it A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction--Diffusion Systems.} IMPACT of Computing in Science and Engineering, 4, p.~269--314 (1992). Here, only brief outlines of the algorithm are given. This software package is based on the KASKADE toolbox B.~Erdmann, J.~Lang, R.~Roitzsch: {\it KASKADE -- Manual.} To appear as Technical Report TR 93--5, Konrad--Zuse--Zentrum (ZIB) (1993).}, language = {en} } @misc{DeuflhardAckermann1993, author = {Deuflhard, Peter and Ackermann, J{\"o}rg}, title = {Adaptive Discrete Galerkin-Methods for Macromolecular Processes.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1180}, number = {SC-93-22}, year = {1993}, abstract = {In this paper, a rather recent algorithmic approac to the numerical simulation of macromolecula processes is surveyed. It avoids the numerical stiff integration o thousands up to millions of ODE's by constructing a scale of discret Hilbert spaces, especially weighted sequence spaces, and establishing corresponding Galerkin method. Examples including polyreactions o industrial relevance and ecological waste management by biochemica recycling illustrate the importance and efficiency of the algorithm.}, language = {en} } @misc{StoerDahl1993, author = {Stoer, Mechthild and Dahl, Geir}, title = {A Polyhedral Approach to Multicommodity Survivable Network Design.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1162}, number = {SC-93-20}, year = {1993}, abstract = {The design of cost-efficient networks satisfying certain survivability constraints is of major concern to the telecommunications industry. In this paper we study a problem of extending the capacity of a network by discrete steps as cheaply as possible, such that the given traffic demand can be accommodated even when a single edge or node in the network fails. We derive valid and non-redundant inequalities for the polyhedron of capacity design variables, by exploiting its relationship to connectivity network design and knapsack-like subproblems. Computational work using this model and the additional inequalities is in progress.}, language = {en} } @misc{KornhuberYserentant1993, author = {Kornhuber, Ralf and Yserentant, Harry}, title = {Multilevel Methods for Elliptic Problems on Domains not Resolved by the Coarse Grid.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1170}, number = {SC-93-21}, year = {1993}, abstract = {Elliptic boundary value problems are frequently posed on complicated domains which cannot be covered by a simple coarse initial grid as it is needed for multigrid like iterative methods. In the present article, this problem is resolved for selfadjoint second order problems and Dirichlet boundary conditions. The idea is to construct appropriate subspace decompositions of the corresponding finite element spaces by way of an embedding of the domain under consideration into a simpler domain like a square or a cube. Then the general theory of subspace correction methods can be applied.}, language = {en} } @misc{Kornhuber1993, author = {Kornhuber, Ralf}, title = {Monotone Multigrid Methods for Elliptic Variational Inequalities I.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1147}, number = {SC-93-18}, year = {1993}, abstract = {Extending well--known linear concepts of successive subspace correction, we arrive at extended relaxation methods for elliptic variational inequalities. Extended underrelaxations are called monotone multigrid methods, if they are quasioptimal in a certain sense. By construction, all monotone multigrid methods are globally convergent. We take a closer look at two natural variants, which are called symmetric and unsymmetric multigrid methods, respectively. While the asymptotic convergence rates of the symmetric method suffer from insufficient coarse--grid transport, it turns out in our numerical experiments that reasonable application of the unsymmetric multigrid method may lead to the same efficiency as in the linear, unconstrained case.}, language = {en} } @misc{Kornhuber1993, author = {Kornhuber, Ralf}, title = {Monotone Multigrid Methods for Elliptic Variational Inequalities II.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1151}, number = {SC-93-19}, year = {1993}, abstract = {We derive fast solvers for discrete elliptic variational inequalities of the second kind as resulting from the approximation by piecewise linear finite elements. Following the first part of this paper, monotone multigrid methods are considered as extended underrelaxations. Again, the coarse grid corrections are localized by suitable constraints, which in this case are fixed by fine grid smoothing. We consider the standard monotone multigrid method induced by the multilevel nodal basis and a truncated version. Global convergence results and asymptotic estimates for the convergence rates are given. The numerical results indicate a significant improvement in efficiency compared with previous multigrid approaches.}, language = {en} } @misc{Hohmann1993, author = {Hohmann, Andreas}, title = {An Implementation of Extrapolation Codes in C++.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5009}, number = {TR-93-08}, year = {1993}, abstract = {This report describes the new object oriented implementation of extrapolation codes {\sc Eulex, Eulsim, Difex} for ordinary differential equations. The resulting C++ class library provides a simple and flexible interface to these methods and incorporates advanced features like continuous output and order-stepsize freezing. The interface of the ODE classes allows in particular a user-defined solver for the linear systems occuring in the linearly implicit discretization scheme. The library also provides some classes for numerical objects such as vectors and (full) matrices. Due to the underlying data-view concept it is possible to access substructures without copying. In addition, we included several utility classes such as a timer and a minimal command language that may be useful in other contexts, too.}, language = {en} } @misc{DiaconicsSturmfels1993, author = {Diaconics, Persi and Sturmfels, Bernd}, title = {Algebraic Algorithms for Sampling from Conditional Distributions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1131}, number = {SC-93-17}, year = {1993}, abstract = {We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.}, language = {en} } @misc{MartinWeismantel1993, author = {Martin, Alexander and Weismantel, Robert}, title = {Packing Paths and Steiner Trees: Routing of Electronic Circuits.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1113}, number = {SC-93-15}, year = {1993}, abstract = {One of the challenging problems in the design of electronic circuits is the so-called routing problem. Roughly speaking, the task is to connect so-called terminal sets via wires on a predefined area. In addition, certain design rules are to be taken into account and an objective function such as the wiring length must be minimized. The routing problem in general is too complex to be solved in one step. Depending on the user's choice of decomposing the chip design problem into a hierarchy of stages, on the underlying technology, and on the given design rules, various subproblems arise. We discuss several variants of practically relevant routing problems and give a short overview on the underlying technologies and design rules. Many of the routing problems that come up this way can be formulated as the problem of packing so-called Steiner trees in certain graphs. We consider the Steiner tree packing problem from a polyhedral point of view and present three possibilities to define an appropriate polyhedron. Weighing their pros and cons we decide for one of these polytopes and sketch some of our investigations.}, language = {en} } @misc{GroetschelLovasz1993, author = {Gr{\"o}tschel, Martin and Lov{\´a}sz, L{\´a}szlo}, title = {Combinatorial Optimization.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1098}, number = {SC-93-13}, year = {1993}, abstract = {This paper will appear as Chapter 28 of the forthcoming "Handbook on Combinatorics" (editors: R. Graham, M. Gr{\"o}tschel, L. Lovasz) to be published in 1994, by North-Holland.}, language = {en} } @misc{GatermannWerner1993, author = {Gatermann, Karin and Werner, Bodo}, title = {Secondary Hopf Bifurcation Caused by Steady-State Steady-State Mode Interaction.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1122}, number = {SC-93-16}, year = {1993}, abstract = {In two-parameter systems with symmetry two steady state bifurcation points of different symmetry types coalesce generically within one point. Under certain group theoretic conditions involving the action of the symmetry group on the kernels, we show that secondary Hopf bifurcation is borne by the mode interaction. We explain this phenomenon by using linear representation theory. For motivation an example with \$D_3\$-symmetry is investigated where the main properties causing the Hopf bifurcation are summarized.}, language = {en} } @misc{HegeHoellererStalling1993, author = {Hege, Hans-Christian and H{\"o}llerer, Tobias and Stalling, Detlev}, title = {Volume Rendering - Mathematicals Models and Algorithmic Aspects.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4994}, number = {TR-93-07}, year = {1993}, abstract = {In this paper various algorithms for rendering gaseous phenomena are reviewed. In computer graphics such algorithms are used to model natural scenes containing clouds, fog, flames and so on. On the other hand it has become an important technique in scientific visualization to display three dimensional scalar datasets as cloudy objects. Our emphasis is on this latter subject of so-called {\em direct volume rendering}. All algorithms will be discussed within the framework of linear transport theory. The equation of transfer is derived. This equation is suitable to describe the radiation field in a participating medium where absorption, emission, and scattering of light can occur. Almost all volume rendering algorithms can be shown to solve special cases of the equation of transfer. Related problems like the mapping from data values to model parameters or possible parallelization strategies will be discussed as well.}, language = {en} } @misc{SchuetteHohmannDinand1993, author = {Sch{\"u}tte, Christof and Hohmann, Andreas and Dinand, Manfred}, title = {Numerical Simulation of Relaxation Oscillations of Waveguide-Lasers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1106}, number = {SC-93-14}, year = {1993}, abstract = {An analysis of relaxation oscillations in local Er-doped optically pumped lasers is reported. It is based on a time dependent rate equation model for a quasi-two-level-system with wavelength dependent emission- and absorption cross-sections. For the first time a numerically reliable simulation of the characteristic laser behaviour was possible: the onset and decay of the oscillations, the time-dependent repetition period and the steady state signal output power. The characteristic waveguide parameters, as the erbium-concentration profile, the polarization dependent pump- and signal mode intensity profiles, the scattering losses, the cavity length and the front and rear reflectivities were all taken into account. The basic formulas are general and can also be used for Er-doped fiber lasers. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. The used algorithmic replacement procedure is motivated and discussed in detail. Here, pump- and signal evolution versus time are presented for an planar Er-diffused \$\rm Ti\$:\$\rm LiNbO_{3}\$ waveguide laser. The numerically obtained results show a nearly quantitative agreement with experimental investigations. Simultanously they supply knowledge about non-measureable (space-dependent population dynamic of the Er-atoms) and till today not measured data (dynamical response of the laser by a sharp peak in the external pump).}, language = {en} } @misc{Ziegler1993, author = {Ziegler, G{\"u}nter M.}, title = {Lectures on Polytopes.}, number = {TR-93-06}, year = {1993}, abstract = {These lecture notes have several aims: \begin{itemize} \item to give an introduction to some basic facts about convex polytopes, with an emphasis on the basic methods that yield them (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms and oriented matroids), \item to discuss some important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associahedra, fiber polytopes, the Lawrence construction) \item and to illustrate why polytope theory is exciting, with highlights like Kalai's new diameter bounds, the construction of non-rational polytopes, the Bohne-Dress tiling theorem, shellability and the upper bound theorem, .... \end{itemize} For several of these topics the decisive break-through is very recent, which suggests that there is much more discovered.}, language = {en} } @misc{OPUS4-966, title = {Jahresbericht 1993}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9668}, number = {1993}, year = {1993}, language = {de} } @misc{OPUS4-968, title = {Jahresbericht 1992}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9686}, number = {1992}, year = {1993}, language = {de} } @misc{GroetschelLueggerSperber1993, author = {Gr{\"o}tschel, Martin and L{\"u}gger, Joachim and Sperber, Wolfram}, title = {Wissenschaftliches Publizieren und Elektronische Fachinformation im Umbruch: ein Situationsbericht aus der Sicht der Mathematik.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4966}, number = {TR-93-04}, year = {1993}, abstract = {In diesem Aufsatz geben wir einen Bericht {\"u}ber den Stand der elektronischen Fachinformation in der Mathematik in Deutschland. Wir sehen diesen Bereich nicht als ein organisatorisch isoliertes Unterfangen, sondern eingebettet in weltweite Bestrebungen und Entwicklungen in der Informationstechnik, im wissenschaftlichen Publikationswesen und nat{\"u}rlich auch in der Mathematik selber. Unser Artikel endet mit einigen weitreichenden (und einigen Lesern m{\"o}glicherweise spektakul{\"a}r erscheinenden) Vorschl{\"a}gen, die sowohl die Informationsanbieter (wie die Fachinformationszentren und Verlage), die {\"o}ffentlichen Geldgeber als auch die mathematischen Organisationen (wie z.~B.~ die DMV und die mathematischen Fachbereiche) betreffen. Um den gegenw{\"a}rtigen Zustand der elektronischen Fachinformation und unsere Gedanken zu diesem Thema ad{\"a}quat beschreiben zu k{\"o}nnen, pr{\"a}sentieren wir eine breit angelegte Situationsanalyse. Wir stellen den gegenw{\"a}rtigen Stand der technologischen Entwicklung im elektronischen Publizieren dar und skizzieren seine Auswirkungen. Wir beschreiben das Feld der Interessen und Kr{\"a}fte im Bereich des mathematischen Publizierens. Wir geben einen kurzen historischen Abriss der Geschichte der Klassifikation und des Referatewesens und zeigen, wie dieses in die elektronische Fachinformation auf dem Gebiet der Mathematik m{\"u}ndete und dann zum DMV-Projekt Fachinformation f{\"u}hrte, das der Anlass zur Abfassung dieses Artikels war. Wir skizzieren die gegenw{\"a}rtige Rezeption elektronischer Fachinformation in der Mathematik in Deutschland. Ausgehend von einer Darstellung und Bewertung verschiedener Modelle des Referatewesens zeigen wir unter Einbeziehung der vorhandenen technischen Gegebenheiten (elektronische Netze etc.) verschiedene M{\"o}glichkeiten zur Liberalisierung und Rationalisierung des weltweiten mathematischen Informationswesens auf. Wir sehen den Austausch von Information in engem Zusammenhang mit dem Austausch von Software im Wissenschaftsbereich und regen auch in diesem Bereich an, internationale Kooperation und Offenheit anzustreben. \originalTeX}, language = {de} } @misc{AckermannRoitzsch1993, author = {Ackermann, J{\"o}rg and Roitzsch, Rainer}, title = {On a Two-Dimensional Multilevel Adaptive Finite Element Method for the Time-Independent Schr{\"o}dinger-Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1086}, number = {SC-93-12}, year = {1993}, abstract = {The subject of this study is a multilevel Finite Element Method based on an error estimator and step by step grid refinement as an universal tool for solving time--independent Schr{\"o}dinger--eigenvalue problems. Numerical results for standard problems appearing in vibrational motion and molecular electronic structure calculations are given and discussed.}, language = {en} } @misc{ErdmannLangRoitzsch1993, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {Kaskade Manual - Version 2.0.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4970}, number = {TR-93-05}, year = {1993}, abstract = {The KASKADE toolbox defines an interface to a set of C subroutines which can be used to implement adaptive multilevel Finite Element Methods solving systems of elliptic equations in two and three space dimensions. The manual contains the description of the data structures and subroutines. The main modules of the toolbox are a runtime environment, triangulation and node handling, assembling, direct and iterative solvers for the linear systems, error estimators, refinement strategies, and graphic utilities. Additionally, we included appendices on the basic command language interface, on file formats, and on the definition of the partial differential equations which can be solved. The software is available on the ZIB ftp--server {\tt elib} in the directory {\tt pub/kaskade}. TR 93--5 supersedes TR 89--4 and TR 89--05.}, language = {en} } @misc{ReinerZiegler1993, author = {Reiner, Victor and Ziegler, G{\"u}nter M.}, title = {Coxeter-associahedra.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1075}, number = {SC-93-11}, year = {1993}, abstract = {\def\KPA{\hbox{\rm KPA}}\def\A{{\rm A}}\def\KPW{\hbox{\rm KPW}}\def\W{{\rm W}}\def\B{{\rm B}} \def\D{{\rm D}} Recently M.~M.~Kapranov [Kap] defined a poset \$\KPA_{n-1}\$, called the {\it permuto-associahedron}, which is a hybrid between the face poset of the permutahedron and the associahedron. Its faces correspond to the partially parenthesized, ordered, partitions of the set \$\{1,2,\ldots,n\}\$, with a natural partial order. Kapranov showed that \$\KPA_{n-1}\$ is the face poset of a CW-ball, and explored its connection with a category-theoretic result of MacLane, Drinfeld's work on the Knizhnik-Zamolodchikov equations, and a certain moduli space of curves. He also asked the question of whether this CW-ball can be realized as a convex polytope. We show that this permuto-associahedron corresponds to the type \$\A_{n-1}\$ in a family of convex polytopes \$\KPW\$ associated to each of the classical Coxeter groups, \$\W = \A_{n-1}, \B_n, \D_n\$. The embedding of these polytopes relies on the secondary polytope construction of the associahedron due to Gel'fand, Kapranov, and Zelevinsky. Our proofs yield integral coordinates, with all vertices on a sphere, and include a complete description of the facet-defining inequalities. Also we show that for each \$\W\$, the dual polytope \$\KPW^*\$ is a refinement (as a CW-complex) of the Coxeter complex associated to \$\W\$, and a coarsening of the barycentric subdivision of the Coxeter complex. In the case \$\W=\A_{n-1}\$, this gives an elementary proof of Kapranov's original sphericity result.}, language = {en} } @misc{LangendorfPaetsch1993, author = {Langendorf, Jens and Paetsch, Olaf}, title = {GRAZIL - Beschreibung der Version 6.0 des Plotpaketes.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4930}, number = {TR-93-01}, year = {1993}, abstract = {GRAZIL ist ein interaktives Programmpaket zur grafischen Darstellung von zwei-dimensionalen Kurvenverl{\"a}ufen. Dem Benutzer stehen zahlreiche Kommandos und ein grafisches User-Interface zum Gestalten des Layouts der Zeichnung zur Verf{\"u}gung. Die Eingabedaten m{\"u}ssen dem GRAZIL-Eingabe-Format gen{\"u}gen. Somit wird eine hohe Flexibilit{\"a}t und eine gro\"se Bandbreite der Einsatzm{\"o}glichkeiten erreicht. GRAZIL wurde mit der grafischen Grundsoftware GKS entwickelt. Dadurch kann ein breites Rechner- und Ausgabeger{\"a}tespektrum genutzt werden.}, language = {de} } @misc{Schuette1993, author = {Sch{\"u}tte, Christof}, title = {A quasiresonant smoothing algorithm for the fast analysis of selective vibrational excitation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1066}, number = {SC-93-10}, year = {1993}, abstract = {One key problem in modern chemistry is the simulation of the dynamical reaction of a molecule subjected to external radiation. This is described by the Schr{\"o}dinger equation, which, after eigenfunction expansion, can be written in form of a system of ordinary differential equations, whose solutions show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. This idea leads to the construction of a quasiresonant smoothing algorithm (QRS). In QRS, a natural and computationally available splitting parameter \$\delta\$ controls the smoothing properties. The performance of QRS is demonstrated in two applications treating the selective excitation of vibrational states by picosecond laser pulses. In comparison with standard methods a speedup factor of 60--100 is observed. A closer look to purely physically motivated quasiresonant approximations such as WFQRA shows some additional advantages of the above smoothing idea. Among these the possibility of an adaptive formulation of QRS via the parameter \$\delta\$ is of particular importance.}, language = {en} } @misc{ErdmannHoppeKornhuber1993, author = {Erdmann, Bodo and Hoppe, Ronald H. W. and Kornhuber, Ralf}, title = {Adaptive Multilevel-Methods for Obstacle Problems in Three Space Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1049}, number = {SC-93-08}, year = {1993}, abstract = {We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub--problems are solved iteratively by preconditioned cg--iterations. We propose a variant of the BPX preconditioner and prove an \$O(j)\$ estimate for the resulting condition number. To allow for local mesh refinement we derive semi--local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations.}, language = {en} } @misc{GroetschelMonmaStoer1993, author = {Gr{\"o}tschel, Martin and Monma, Clyde and Stoer, Mechthild}, title = {Design of Survivable Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1054}, number = {SC-93-09}, year = {1993}, language = {en} } @misc{WeismantelFerreiraMartin1993, author = {Weismantel, Robert and Ferreira, Carlos E. and Martin, Alexander}, title = {A Cutting Plane Based Algorithm for the Multiple Knapsack Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1031}, number = {SC-93-07}, year = {1993}, abstract = {In this paper we describe a cutting plane based algorithm for the multiple knapsack problem. We use our algorithm to solve some practical problem instances arising in the layout of electronic circuits and in the design of main frame computers, and we report on our computational experience. This includes a discussion and evaluation of separation algorithms, an LP-based primal heuristic and some implementation details. The paper is based on the polyhedral theory for the multiple knapsack polytope developed in our companion paper SC 93-04 and meant to turn this theory into an algorithmic tool for the solution of practical problems.}, language = {en} } @misc{BorndoerferGroetschelKlostermeieretal.1993, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Klostermeier, Fridolin and K{\"u}ttner, Christian}, title = {Telebus-Disposition: Ein Konzept zur Serviceverbesserung bei gleichzeitiger Kostensenkung.[nur hausintern]}, number = {TR-93-03}, year = {1993}, abstract = {"`Telebus"' ist der soziale Behindertenfahrdienst im Land Berlin. Das Telebus-Forschungsprojekt des Konrad-Zuse-Zentrums f{\"u}r Informationstechnik (ZIB) hat das Ziel, den Fahrdienst (insbesondere die Disposition der Telebusse) zu verbessern, d.h. kundenfreundlicher zu gestalten und gleichzeitig billiger zu machen. In diesem Bericht werden die bisherigen Ergebnisse dargestellt und weitere M{\"o}glichkeiten zur Verbesserung des Service und zur Reduzierung der Kosten skizziert. \originalTeX}, language = {de} } @misc{Deuflhard1993, author = {Deuflhard, Peter}, title = {A Study of Lanczos-Type Iterations for Symmetric Indefinite Linear Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1029}, number = {SC-93-06}, year = {1993}, abstract = {The Lanczos iteration for symmetric indefinite linear systems seems to be well--known for quite a while. However, in order to modify it with the aim of improved performance, the present paper studies certain aspects in terms of an adjoint scalar three--term recurrence. Thus, at least a different view is opened. Moreover, an alternative \$3n\$--implementation in terms of the Euclidean orthogonal basis has been found that easily permits generalizations. The study is understood as a start--off for further numerical investigations and experiments.}, language = {en} } @misc{RichterGebert1993, author = {Richter-Gebert, J{\"u}rgen}, title = {Mechanical Theorem Proving in Projective Geometry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1013}, number = {SC-93-05}, year = {1993}, abstract = {We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this power and present a series of examples treated by the prover, including {\it Pappos' and Desargues' Theorems,} the {\it Sixteen Point Theorem, Saam's Theorem, }the {\it Bundle Condition,} the uniqueness of a harmonic Point and {\it Pascal's Theorem.}}, language = {en} } @misc{FerreiraMartinWeismantel1993, author = {Ferreira, Carlos E. and Martin, Alexander and Weismantel, Robert}, title = {Facets for the Multiple Knapsack Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1007}, number = {SC-93-04}, year = {1993}, abstract = {In this paper we consider the multiple knapsack problem which is defined as follows: given a set \$N\$ of items with weights \$f_i\$, \$i \in N\$, a set \$M\$ of knapsacks with capacities \$F_k\$, \$k \in M\$, and a profit function \$c_{ik}, i \in N, k \in M\$; find an assignment of a subset of the set of items to the set of knapsacks that yields maximum profit (or minimum cost). With every instance of this problem we associate a polyhedron whose vertices are in one to one correspondence to the feasible solutions of the instance. This polytope is the subject of our investigations. In particular, we present several new classes of inequalities and work out necessary and sufficient conditions under which the corresponding inequality defines a facet. Some of these conditions involve only properties of certain knapsack constraints, and hence, apply to the generalized assignment polytope as well. The results presented here serve as the theoretical basis for solving practical problems. The algorithmic side of our study, i.e., separation algorithms, implementation details and computational experience with a branch and cut algorithm are discussed in the companion paper SC 93-07.}, language = {en} } @misc{Melenk1993, author = {Melenk, Herbert}, title = {Algebraic Solution of Nonlinear Equation Systems in REDUCE.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4944}, number = {TR-93-02}, year = {1993}, abstract = {The strategy for solving nonlinear equation systems automatically in the computer algebra system REDUCE is described. Kernel of the solver is a factoring Buchberger algorithm. Pre -- and postprocessors enable the use of the Gr{\"o}bner techniques in a black box manner. In addition to polynomials equations with surds, trigonometric functions and separable transcendental functions are covered.}, language = {en} } @misc{FerreiraGroetschelKiefletal.1993, author = {Ferreira, Carlos E. and Gr{\"o}tschel, Martin and Kiefl, Stefan and Krispenz, Ludwig and Martin, Alexander and Weismantel, Robert}, title = {Some Integer Programs Arising in the Design of Main Frame Computers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-957}, number = {SC-92-25}, year = {1993}, abstract = {In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult -- at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are also \$NP\$-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.}, language = {en} } @misc{GroetschelMonmaStoer1993, author = {Gr{\"o}tschel, Martin and Monma, Clyde and Stoer, Mechthild}, title = {Polyhedral and Computational Investigations for Designing Communication Networks with High Survivability Requirements.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-944}, number = {SC-92-24}, year = {1993}, abstract = {We consider the important practical and theoretical problem of designing a low-cost communications network which can survive failures of certain network components. Our initial interest in this area was motivated by the need to design certain ``two-connected" survivable topologies for fiber optic communication networks of interest to the regional telephone companies. In this paper, we describe some polyhedral results for network design problems with higher connectivity requirements. We also report on some preliminary computational results for a cutting plane algorithm for various real-world and random problems with high connectivity requirements which shows promise for providing good solutions to these difficult problems. \def\NP{\$\cal NP\$}}, language = {en} } @misc{GatermannWerner1992, author = {Gatermann, Karin and Werner, Bodo}, title = {Group Theoretical Mode Interactions with Different Symmetries.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-994}, number = {SC-93-03}, year = {1992}, abstract = {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.}, language = {en} } @misc{OPUS4-492, title = {Handbuch zur Visualisierung am ZIB}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4920}, number = {TR-92-07}, year = {1992}, abstract = {Scientists intending to employ scientific visualization techniques are confronted with the unpleasant task of choosing visualization software that meets their specific needs. A good choice requires consideration of several aspects. Most important are functionality, i.e. the set of supported visual representations, and restrictions due to the user's production environment (i.e. available hardware and software platforms, software compatibility constraints, need of specific input and output formats, network distribution requirements). Crucial are quality demands, ranging from simple graphics for interactive control of simulations, to images of highest quality (glossy prints, slides or video movies) for presentation purposes. Further aspects of consideration are: ease of use, level on which the user is willing to program, portability, conformity to prevalent standards, availability in the world-wide user community, future dissemination, as well as emerging trends in computer graphics and scientific visualization. The aim of this manual is to give a survey on the graphics and visualization software that is currently being provided at ZIB (mainly for internal use). The whole range of computer graphics software relevant in mathematical, natural and technical sciences is covered: image synthesis (basic and higher graphics libraries, plot programs, visualization environments, combined text and drawing programs, renderers), image processing and storage (raster and vector formats, page description languages, raster toolkits for image processing and format conversion), capturing of images as well as printing on paper and recording on photographic film or video tape. This information together with a glossary and recommendations for further reading should help prospective users in getting started and assist them in making good choices of graphics and visualization software.}, language = {de} }