@misc{MaierhoeferSkorobohatyj1989, author = {Maierh{\"o}fer, Gerhard and Skorobohatyj, Georg}, title = {Implementierung des parallelen TRAPEX auf Transputern.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4649}, number = {TR-89-08}, year = {1989}, abstract = {Der folgende Bericht ist eine Erg{\"a}nzung des ZIB Technical Report TR 88-05. Entsprechend wird hier nicht auf die grunds{\"a}tzlichen Fragen der Parallelisierbarkeit des sequentiellen TRAPEX eingegangen. Diese sind im TR 88-5 er{\"o}rtert, die dort beschriebenen Algorithmen (vertikale und horizontale Parallelisierung) werden auch f{\"u}r die Transputerarchitektur verwendet. Meßergebnisse sind im letzten Teil angef{\"u}gt.}, language = {de} } @misc{GrammelMaierhoeferSkorobohatyj1989, author = {Grammel, Martin and Maierh{\"o}fer, Gerhard and Skorobohatyj, Georg}, title = {Trapex in POOL-Implementierung eines numerischen Algorithmus in einer parallelen objektorientierten Sprache.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4696}, number = {TR-90-05}, year = {1989}, abstract = {Die Parallelisierung eines vorhandenen sequentiellen Programmes erfolgt im allgemeinen in der Weise, daß es auf Grund einer Analyse der Datenabh{\"a}ngigkeiten in mehrere parallel ausf{\"u}hrbare Teile zerlegt wird, die ihrerseits sequentiell ablaufen und untereinander Daten austauschen. Eine parallele Programmiersprache sollte diese Vorgehensweise unterst{\"u}tzen, indem sie Sprachmittel zur Verf{\"u}gung stellt, mittels derer sich die Modularisierung und Kommunikation bequem formulieren l{\"a}ßt. Nun l{\"a}ßt sich prinzipiell jede vorhandene sequentielle Programmiersprache um solche Konstrukte erweitern; g{\"u}nstiger in Hinblick auf die Strukturierung eines parallelen Programmes erscheint es aber m{\"o}glicherweise, eine solche Programmiersprache zu verwenden, die die genannten Konzepte als elementare zur Verf{\"u}gung stellt. Dies ist offensichtlich bei objektorientierten Programmiersprachen der Fall. Im vorliegenden Bericht wird an Hand eines Beispiels - TRAPEX -, das in POOL-T implementiert wurde, untersucht, inwieweit eine objektorientierte Sprache zur effektiven Programmierung eines numerischen Algorithmus geeignet ist. {\bf Key Words:} parallele objektorientierte Programmiersprache, Message Passing, Abstract Data Typing, Klassenhierarchi, Modul-Import-Mechanismus, Client/Server-Prinzip, Load Balancing, adaptive numerische Algorithmen, Ordnungs- und Schrittweitensteuerung, Romberg-Quadratur.}, language = {de} } @misc{Bornemann1989, author = {Bornemann, Folkmar A.}, title = {Adaptive multilevel discretization in time and space for parabolic partial differential equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4638}, number = {TR-89-07}, year = {1989}, abstract = {The present paper developes an adaptive multilevel approach for parabolic PDE's - as a first step, for one linear scalar equation. Full adaptivity of the algorithm is conceptually realized by simultaneous multilevel discretization in both time and space. Thus the approach combines multilevel time discretization, better known as extrapolation methods, and multilevel finite element space discretization such as the hierarchical basis method. The algorithmic approach is theoretically backed by careful application of fundamental results from semigroup theory. These results help to establish the existence of asymptotic expansions (in terms of time-steps) in Hilbert space. Finite element approximation then leads to perturbed expansions, whose perturbations, however, can be pushed below a necessary level by means of an adaptive grid control. The arising space grids are not required to satisfy any quasi- uniformity assumption. Even though the theoretical presentation is independent of space dimension details of the algorithm and numerical examples are given for the 1-D case only. For the 1-D elliptic solver, which is used, an error estimator is established, which works uniformly well for a family of elliptic problems. The numerical results clearly show the significant perspectives opened by the new algorithmic approach.}, language = {en} } @misc{HuamoShuli1989, author = {Huamo, Wu and Shuli, Yang}, title = {MmB-A New Class of Accurate High Resolution Schemes for Conservation Laws in Two Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-248}, number = {SC-89-06}, year = {1989}, abstract = {In this paper we present the MmB schemes, which preserve the local maximum and minimum bounds of the initial data in the smallest union of mesh elements of previous time step containing the domain of dependence of the solution on the mesh element with center at point \$ P \$\ under consideration. In 1-D, the MmB schemes are almost identical with TVD schemes. As well-known, there is no second-order TVD scheme in 2-D, nevertheless, we present here two classes of 2-D second-order accurate MmB-schemes. It is proved that 1-D discrete MmB (or TVD) and 1-D semi-discrete TVD schemes may have second-order accuracy at (nonsonic) critical points, but cannot be of uniformly second-order accurate in the whole neighborhood of the critical points. New accurate high resolution flux limiters are suggested. Numerical results for 1-D and 2-D test problems are given. {\bf Keywords:} Difference scheme, TVD, MmB, flux limiter.}, language = {en} } @misc{BuddeWulkow1989, author = {Budde, Uwe and Wulkow, Michael}, title = {Computation of Molecular Weight Distributions for Free Radical Polymerization Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-253}, number = {SC-89-07}, year = {1989}, abstract = {Modeling of free radical polymerization leads to very large and usually stiff systems of ordinary differential equations which cannot be solved directly in an efficient way. This paper presents the application of a new approach called discrete Galerkin method to a realistic example - the polymerization of methyl methacrylate(MMA). The method is characterized by a Galerkin approximation on the basis of orthogonal polynomials of a discrete variable which represents the polymer degree. It allows the efficient computation of solutions of complete kinetic schemes with time- or moment-dependent reaction coefficients by reducing the complexity to a few differential equations. The approximation error can be controlled by an error estimation. In the case of MMA polymerization a reduction of computational effort by a factor of about 25 compared to a standard method can be obtained for the quasi-steady-state approximation of the model. In addition solutions of the instationary kinetic scheme can be easily computed.}, language = {en} } @misc{Huamo1989, author = {Huamo, Wu}, title = {On the Possible Accuracy of TVD Schemes.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-212}, number = {SC-89-03}, year = {1989}, abstract = {The paper presents a detailed analysis of the possible accuracy available for TVD schemes in one dimension with emphasis to the semi-discrete 1-D TVD schemes. The analysis shows that the widely accepted statement [1] of degeneration of accuracy at critical points for TVD schemes should be corrected. We have theorem: TVD schemes using flux limiters \$ \varphi \$ of the form [1], [2] may be second-order accurate at critical points if \$ \varphi \$ (3) + \$ \varphi \$(-1) = 2, but cannot be uniformly second-order accurate in the whole neighborhood of critical point. If \$ \varphi \$(1) = 1, then the TVD schemes are second-order accurate in the region of smooth solutions sufficiently far from the critical points. Two ways are suggested to improve the accuracy. Numerical example is given. {\bf Keywords:} Semi-discrete schemes, TVD, flux limiter, degeneration of accuracy.}, language = {en} } @misc{Moeller1989, author = {M{\"o}ller, H. Michael}, title = {Multivariate Rational Interpolation: Reconstruction of Rational Functions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-227}, number = {SC-89-04}, year = {1989}, abstract = {In this paper we consider the problem of reconstructing a multivariate rational function, when only its values at sufficiently many points are known. We use for the reconstruction of bivariate rational functions a bivariate rational interpolation operator investigated by Siemaszko [7] and a new one, compare both by examples in a Computer Algebra system, and present their multivariate generalizations. {\bf Keywords:} Multivariate rational interpolation, reconstruction, symbolic computation.}, language = {en} } @misc{KornhuberRoitzsch1989, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-230}, number = {SC-89-05}, year = {1989}, abstract = {We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resolution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. It is demonstrated by several numerical examples that compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. {\bf Keywords:} Adaptive finite elements, directed refinement, adaptive grid orientation, convection diffusion equation, internal and boundary layers.}, language = {en} } @misc{MelenkNeun1989, author = {Melenk, Herbert and Neun, Winfried}, title = {Implementation of Portable Standard LISP for the SPARC Processor.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4625}, number = {TR-89-06}, year = {1989}, abstract = {The SPARC processor is a RISC (Reduced Instruction Set Computer) microcomputer, built into the SUN4 workstations. Since RISC processors are very well-suited for LISP processing, the implementation of a dialect of LISP (Portable Standard LISP, PSL) boded well for a great speed-up in comparison with other types of microcomputers. A first approach was done at The RAND Corporation in Santa Monica, which was derived from classical processor types like MC68000 or VAX. At the Konrad- Zuse-Zentrum f{\"u}r Informationstechnik Berlin (ZIB) that initial implementation was redesigned in order to adapt PSL to the specific features of the SPARC processor. The present implementation, in some parts, is very close to Cray PSL version also done in ZIB. Some timing informations are given in the appendix.}, language = {en} } @misc{Roitzsch1989, author = {Roitzsch, Rainer}, title = {KASKADE Programmer's Manual.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4617}, number = {TR-89-05}, year = {1989}, abstract = {The Programmers Manual contains the documentation of the C-KASKADE implementation. KASKADE is an adaptive finite element code (see SC ). The interfaces of all modules are described.}, language = {en} } @misc{Roitzsch1989, author = {Roitzsch, Rainer}, title = {KASKADE User's Manual.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4605}, number = {TR-89-04}, year = {1989}, abstract = {The Users Manual contains an introduction to the usage of the C-KASKADE implementation. KASKADE is an adaptive finite element code (see SC ). The manual includes a description of all commands, a simple recipe to define a new problem by changing the KASKADE source and a complete example.}, language = {en} } @misc{OPUS4-985, title = {Jahresbericht 1988}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9858}, number = {1988}, year = {1989}, language = {de} } @misc{Zha1989, author = {Zha, Hongyuan}, title = {Restricted Singular Value Decomposition of Matrix Triplets.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-205}, number = {SC-89-02}, year = {1989}, abstract = {In this paper we introduce the concept of restricted singular values (RSV's) of matrix triplets. A theorem concerning the RSV's of a general matrix triplet \$ (A,B,C) \$, where \$ A \in C^{m\times n} \$, \$B\in C^{m\times p} \$ and \$ C\in C^{q\times n} \$, which is called restricted singular value decomposition (RSVD) of matrix triplets, is derived. This result generalizes the wellknown SVD, GSVD and the recently proposed product induced SVD (PSVD). Connection of RSV's with the problem of determination of matrix rank under restricted perturbation is also discussed. {\bf Keywords:} Matrix rank, singular values, generalized singular values, product induced singular values, restricted singular values, matrix decompositions.}, language = {en} } @misc{Deuflhard1989, author = {Deuflhard, Peter}, title = {Numerik von Anfangswertmethoden f{\"u}r gew{\"o}hnliche Differentialgleichungen.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4580}, number = {TR-89-02}, year = {1989}, abstract = {Das voliegende Skriptum entstand aus einer Vorlesung, die ich im WS 87/88 an der Freien Universit{\"a}t Berlin im Fachbereich Mathematik gehalten habe. Mein urspr{\"u}ngliches Vorlesungsmanuskript wurde von Herrn F. Bornemann in weiten Teilen {\"u}berarbeitet, reorganisiert und substantiell erg{\"a}nzt. Der Inhalt stammt gr{\"o}ßtenteils aus Originalarbeiten j{\"u}ngeren Datums. Dar{\"u}berhinaus finden sich zahlreiche Teile, die aus meiner jahrelangen Besch{\"a}ftigung mit dem Thema entstanden aber unpubliziert geblieben sind. Das Skriptum erhebt nicht den Anspruch, ein Lehrbuch zu sein. Es war zun{\"a}chst als Ausarbeitung f{\"u}r meinen studentischen H{\"o}rerkreis sowie als internes Arbeitspapier f{\"u}r das ZIB bestimmt. Die Kunde von der bloßen Existenz eines solchen Skriptums hat jedoch zu einer derart regen Nachfrage gef{\"u}hrt, daß es hiermit als Technischer Report des ZIB einer breiteren ffentlichkeit zug{\"a}nglich gemacht werden soll. In der vorliegenden Form richtet es sich in erster Linie an Mathematiker; es soll sich jedoch auch f{\"u}r Naturwissenschaftler und Ingenieure eignen, die sich einen Einblick in den theoretischen und algorithmischen Hintergrund der von ihnen verwendeten wissenschaftlichen Software verschaffen wollen.}, language = {de} } @misc{Walter1989, author = {Walter, Artur}, title = {Ein Finite-Element-Verfahren zur numerischen L{\"o}sung von Erhaltungsgleichungen.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4597}, number = {TR-89-03}, year = {1989}, abstract = {A new approach for the discretisation of hyperbolic conservation laws via a finite element method is developed and analysed. Appropriate forms of the Eulers equation of gas dynamic are considered to employ the algorithm in a reasonable way for this system of nonlinear equations. Both mathematical and physical stability results are obtained. A main part of the paper is devoted to the convergence proof with energy methods under strong regularity of the solution of a scalar nonlinear conservation law. Some hints on the implementation and numerical results for the calculation of transonic gasflow through a Laval nozzle are given. The necessary amount of numerical work is compared to an established finite difference method and the efficiency of the algorithm is shown. A survey on recent literature about finite element methods for hyperbolic problem is included.}, language = {de} } @misc{Zha1989, author = {Zha, Hongyuan}, title = {A Numerical Algorithm for Computing the Restricted Singular Value Decomposition of Matrix Triplets.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-194}, number = {SC-89-01}, year = {1989}, abstract = {This paper presents a numerical algorithm for computing the restricted singular value decomposition of matrix triplets (RSVD). It is shown that one can use unitary transformations to separate the regular part from a general matrix triplet. After preprocessing on the regular part, one obtains a matrix triplet consisting of three upper triangular matrices of the same dimensions. The RSVD of this special matrix triplet is computed using the implicit Kogbetliantz technique. The algorithm is well suited for parallel computation. {\bf Keywords:} Restricted singular values, matrix triplets, unitary transformations, implicit Kogbetliantz technique.}, language = {en} } @misc{ChowDengFiedler1989, author = {Chow, Shui-Nee and Deng, Bo and Fiedler, Bernold}, title = {Homoclinic Bifurcation at Resonant Eigen-values.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-181}, number = {SC-88-10}, year = {1989}, language = {en} } @misc{OPUS4-457, title = {CRAY-HANDBUCH. Einf{\"u}hrung in die Benutzung der CRAY X-MP unter UNICOS. (veraltet)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4574}, number = {TR-89-01}, year = {1989}, language = {de} } @misc{KornhuberRoitzsch1989, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {Adaptive Finite-Elemet- Methoden f{\"u}r konvektionsdominierte Randwertprobleme bei partiellen Differentialgleichungen.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-170}, number = {SC-88-09}, year = {1989}, abstract = {Ausgangspunkt bei der Behandlung konvektiv dominierter, elliptischer Probleme sind die bekannten hierarchischen Finite-Element-Methoden f{\"u}r den rein elliptischen Fall. Als stabile Erweiterung des Standard-Galerkin-Verfahrens wird das Stromlinien-Diffusions-Verfahren durch physikalische {\"U}berlegungen motiviert und kurz diskutiert. Anschließend zeigen wir, daß diese Methode erst in Verbindung mit einer hier erstmals vorgestellten lokalen Ausrichtung der Kanten wirksam eingesetzt werden kann. Zusammen mit einer ebenfalls neu entwickelten richtungsorientierten Verfeinerungsstrategie erh{\"a}lt man eine erheblich stabilere, genauere und schnellere Aufl{\"o}sung von Grenzschichten als mit herk{\"o}mmlichen Methoden.}, language = {de} } @misc{MaierhoeferSkorobohatyj1988, author = {Maierh{\"o}fer, Gerhard and Skorobohatyj, Georg}, title = {Parallel-TRAPEX (Ein paralleler adaptiver Algorithmus zur numerischen Integration; seine Implementierung f{\"u}r SUPRENUM-artige Architekturen mit SUSI).}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4560}, number = {TR-88-05}, year = {1988}, abstract = {This paper describes some ways of transforming a sequential adaptive algorithm for numerical evaluation of an integral (Romberg- Quadrature with polynomial Extrapolation method) to a parallel one, such as have been implementad by the authors. We developed an algorithm which preserves the sequential adaptivity and is capable of running on various architectures, dynamically controlling the number of avtive processors depending on the problem. To study the time behaviour, we used the simulator SUSI(SUprenum SImulatur) which is able to simulate SUPRENUM-like architectures. Results are given in part 3. {\bf Keywords:} Romberg quadrature; numerical integration; parallel adaptive algorithm; SUSI; simulation; SUPRENUM; MIMD-Fortran; computer architecture; granularity; load balacing; master-slave-principle.}, language = {de} } @misc{HoppeKornhuber1988, author = {Hoppe, Ronald H. W. and Kornhuber, Ralf}, title = {Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-160}, number = {SC-88-08}, year = {1988}, abstract = {Induction heating of large steel slabs can be described by a coupled system of nonlinear evolution equations of Stefan type representing the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi-grid algorithms are given which combined with a nested iteration type continuation strategy to proceed in time result in computationally highly efficient schemes for the numerical simulation of the induction heating process. {\bf Keywords:} induction heating, system of two coupled Stefan equations, multi-grid algorithms. {\bf Subject Classification:} AMS(MOS): 35K60, 35R35, 65H10, 65N05, 65N20, 78A25, 78A55.}, language = {en} } @misc{MelenkMoellerNeun1988, author = {Melenk, Herbert and M{\"o}ller, H. Michael and Neun, Winfried}, title = {Symbolic Solution of Large Stationary Chemical Kinetics Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-157}, number = {SC-88-07}, year = {1988}, abstract = {The paper presents a new application of computer algebra to the treatment of steady states of reaction systems. The method is based on the Buchberger algorithm. This algorithm was modified such that it can exploit the special structure of the equations derived from reaction systems, so even large systems can be handled. In contrast to numerical approximation techniques, the algebraic solution gives a complete and definite overview of the solution space and it is even applicable when parameter values are unknown or undetermined. The algorithm, its adaptation to the problem class and its application to selected examples are presented.}, language = {en} } @misc{DeuflhardWulkow1988, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-140}, number = {SC-88-06}, year = {1988}, abstract = {The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown to avoid the disadvantages and preserve the adventages of either of them. The basic idea of the method is the construction of a discrete inner product associated with a reasonably chosen probability density function. For the so-called Schulz-Flory distribution one thus obtains the discrete Laguerre polynomials, whereas the Poisson distribution leads to the Charlier polynomials. Numerical experiments for selected polyreaction mechanisms illustrate the efficiency of the proposed method.}, language = {en} } @misc{DeuflhardLeinenYserentant1988, author = {Deuflhard, Peter and Leinen, P. and Yserentant, Harry}, title = {Concepts of an Adaptive Hierarchical Finite Element Code.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-131}, number = {SC-88-05}, year = {1988}, abstract = {The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between iterative solver, local error estimator, and local mesh refinement device - which are the main components of an adaptive PDE code. Without use of standard multigrid techniques, the same kind of computational complexity is achieved - independent of any uniformity restrictions on the applied meshes. In addition, the method is extremely simple and all computations are purely local - making the method particularly attractive in view of parallel computing. The algorithmic approach is illustrated by a well-known critical test problem. {\bf Keywords:} finite elements, hierarchical basis, adaptive mesh refinement, preconditioned conjugate gradient methods.}, language = {en} } @misc{BuhtzLangendorfPaetsch1988, author = {Buhtz, Danuta Anna and Langendorf, Jens and Paetsch, Olaf}, title = {GRAZIL - 3D. Ein graphisches Anwendungsprogramm zur Darstellung von Kurven- und Funktionsverl{\"a}ufen im r{\"a}umlichen Koordinatensystem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4556}, number = {TR-88-04}, year = {1988}, abstract = {GRAZIL - 3D ist ein interaktives Programmpaket zur graphischen Darstellung von dreidimensionalen Kurvenverl{\"a}ufen. Das Aussehen der r{\"a}umlichen Ausgabe des Bildes wird durch Angabe des Blickwinkels und der Perspektive festgelegt.}, language = {de} } @misc{OPUS4-986, title = {Jahresbericht 1987}, issn = {0933-7903}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9860}, number = {1987}, year = {1988}, language = {de} } @misc{MelenkNeun1988, author = {Melenk, Herbert and Neun, Winfried}, title = {Parallel Polynomial Operations in the Buchberger Algorithm.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-125}, number = {SC-88-04}, year = {1988}, abstract = {The Buchberger algorithm is a basic tool for the solution of systems of polynomial equations in an environment of computer algebra applications. A model for overlapped processing of different steps of the algorithm is presented, which uses the data structure of the polynomials (distributive representation) for synchronization. The model can be applied for multi processors with fast access to shared data. It is tested with Cray X-MP multi processors based on a parallel version of Portable Standard Lisp (PSL 3.4).}, language = {en} } @misc{MelenkNeun1988, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4539}, number = {TR-88-02}, year = {1988}, abstract = {This document describes operating procedures for running REDUCE specific to the CRAY 1 and CRAY X-MP computers running the Operating System UNICOS. The document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L. R. Seward, The Rand Corporation, Santa Monica, (CP85).}, language = {en} } @misc{MelenkNeun1988, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4541}, number = {TR-88-03}, year = {1988}, abstract = {This guide describes the CRAY/UNICOS REDUCE distribution tape and the procedures for installing, testing and maintaining REDUCE on a CRAY 1 or CRAY X-MP running UNICOS. This document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L.R. Seward, The Rand Corporation, Santa Monica, publication CP84.}, language = {en} } @misc{BuhtzBuhtz1988, author = {Buhtz, Rainer and Buhtz, Danuta Anna}, title = {TDLG 3.1 - Ein interaktives Programm zur Darstellung dreidimensionaler Modelle auf Rastergraphikger{\"a}ten.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4522}, number = {TR-88-01}, year = {1988}, abstract = {TDLG 3.1 dient zur Darstellung von dreidimensionalen Objekten, die sich aus offenen Linienz{\"u}gen, Dreieck- und Viereckelementen zusammensetzen. Dabei k{\"o}nnen verschiedene Visualisierungstechniken benutzt werden: Drahtmodell, Schattierung mit und ohne Lichtquelle, Hidden Surface Removal. Durch Verwendung von Konvertierungsprogrammen k{\"o}nnen auch IGES- und VDAFS- Dateien dargestellt werden.}, language = {de} } @misc{MelenkMoellerNeun1988, author = {Melenk, Herbert and M{\"o}ller, H. Michael and Neun, Winfried}, title = {On Gr{\"o}bner Bases Computation on a Supercomputer Using REDUCE.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-107}, number = {SC-88-02}, year = {1988}, abstract = {Gr{\"o}bner bases are the main tool for solving systems of algebraic equations and some other problems in connection with polynomial ideals using Computer Algebra Systems. The procedure for the computation of Gr{\"o}bner bases in REDUCE 3.3 has been modified in order to solve more complicated algebraic systems of equations by some general improvements and by some tools based on the specific resources of the CRAY X-MP. We present this modification and illustrate it by examples.}, language = {en} } @misc{AlexanderFiedler1988, author = {Alexander, J. C. and Fiedler, Bernold}, title = {Global Decoupling of Coupled Symmetric Oscillators.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-113}, number = {SC-88-03}, year = {1988}, abstract = {We model a symmetric system of coupled oscillators as a graph with symmetry group \$\gamma\$. Each vertex of the graph represents an "oscillator" or a "cell" of reactants. The magnitude (concentration) of the reactants in the \$ i \$ th cell is represented by a vector \$ x^i \$. The edges represent the coupling of the cells. The cells are assumed to evolve by identical reaction-diffusion equation which depends on the sum of the reactants in the nearest neighbors. Thus the dynamics of the system is described by a nonlinear differential system \begin{flushleft} \[ \mbox {(*) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \dot{x}^i = f (x^i,\sum_{j \in N_i} x^j), \mbox { \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] \end{flushleft} where the sum ranges over the set \$ N_i \$ of neighbors of cell \$ i \$ . If \$ f \$ also has a symmetry (e.g., oddness), there are geometric conditions on the graph such that the nonlinear system \$ (*) \$ decouples globally into a product flow on certain sums of isotropy subspaces. Thus we may detect higher-dimensional tori of solutions of \$ (*) \$ which are not amenable to other types of analysis. We present a number of examples, such as bipartite graphs, complete graphs, the square, the octahedron, and a 6-dimensional cube.}, language = {en} } @misc{NeunMelenk1988, author = {Neun, Winfried and Melenk, Herbert}, title = {Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93}, number = {SC-88-01}, year = {1988}, abstract = {Portable Standard LISP (PSL, Version 3.4) and REDUCE 3 were implemented for CRAY1 and Cray X- MP computers at the Konrad-Zuse-Zentrum Berlin in 1986. As an special aspect of the implementation of PSL, an interface to the vector hardware of CRAY processors was defined. With that interface and mostly driven by the needs of REDUCE applications (e.g. extensive calculations of Gr{\"o}bner bases), the arbitrary precision integer arithmetic of PSL was rebuild using full power of the vector hardware. A modular arithmetic using vector hardware was also constructed.}, language = {en} } @misc{LangendorfPaetsch1987, author = {Langendorf, Jens and Paetsch, Olaf}, title = {GRAZIL (Graphical ZIB Language).}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4518}, number = {TR-87-07}, year = {1987}, abstract = {GRAZIL ist ein interaktives Programmpaket zur graphischen Darstellung von zwei-dimensionalen Kurvenverl{\"a}ufen. Dem Benutzer stehen zahlreiche Kommandos zum Gestalten des Layouts der Zeichnung zur Verf{\"u}gung. Die Eingabedaten m{\"u}ssen dem ZUGRIFF- Konzept gen{\"u}gen, wodurch die genaue Struktur der Daten erst zur Laufzeit bekannt sein muß und somit eine hohe Flexibilit{\"a}t und eine große Bandbreite der Einsatzm{\"o}glichkeiten erreicht wird. GRAZIL wurde mit der graphischen Grundsoftware BIZEPS2 und GKS entwickelt. Dadurch kann ein breites Rechner- und Ausgabeger{\"a}tespektrum genutzt werden.}, language = {de} } @misc{Yserentant1987, author = {Yserentant, Harry}, title = {Preconditioning Indefinite Discretization Matrices.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81}, number = {SC-87-06}, year = {1987}, abstract = {The finite element discretization of many elliptic boundary value problems leads to linear systems with positive definite and symmetric coefficient matrices. Many efficient preconditioners are known for these systems. We show that these preconditioning matrices can be used also for the linear systems arising from boundary value problems which are potentially indefinite due to lower order terms in the partial differential equation. Our main tool is a careful algebraic analysis of the condition numbers and the spectra of perturbed matrices which are preconditioned by the same matrices as in the unperturbed case. {\bf Keywords: }Preconditioned conjugate gradient methods, finite elements. {\bf Subject Classification: } AMS(MOS):65F10, 65N20, 65N30.}, language = {en} } @misc{MelenkNeun1987, author = {Melenk, Herbert and Neun, Winfried}, title = {Portable Standard LISP Implementation for CRAY X+MP Computers. Release of PSL 3.4 for COS.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4465}, number = {TR-87-02}, year = {1987}, abstract = {Portable Standard LISP (PSL) is a portable implementation of the programming language LISP constructed at the University of Utah. The version 3.4 of PSL was implemented for CRAY X-MP computers by Konrad Zuse-Zentrum Berlin; this implementation is based to an important part on the earlier implementation of PSL 3.2 at Salt Lake City, Los Alamos and Mendota Heights.}, language = {en} } @misc{MelenkNeun1987, author = {Melenk, Herbert and Neun, Winfried}, title = {Portable Common LISP Subset Implementation for CRAY X+MP Computers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4479}, number = {TR-87-03}, year = {1987}, abstract = {This document describes the installation procedure and maintenance for the Portable Common LISP Subset (PCLS) developed at the University of Utah.}, language = {en} } @misc{MelenkNeun1987, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE Installation Guide for CRAY 1 / X-MP Systems Running COS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4486}, number = {TR-87-04}, year = {1987}, abstract = {This guide describes the CRAY/COS REDUCE distribution tape and the procedures for installing, testing and maintaining REDUCE on a CRAY 1 or CRAY X-MP running COS. This document was derived from the corresponding document for Vax/Unix prepared by A. C. Hearn and L. R. Seward, The Rand Corporation, Santa Monica, publication CP84.}, language = {en} } @misc{MelenkNeun1987, author = {Melenk, Herbert and Neun, Winfried}, title = {REDUCE Users Guide for the CRAY 1 / X-MP Series Running COS. Version 3.3.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4498}, number = {TR-87-05}, year = {1987}, abstract = {This document describes operating procedures for running REDUCE specific to the CRAY 1 and CRAY X-MP computers running the CRAY Operating System (COS). The document was derived from the corresponding document for Vax/UNIX prepared by A.C. Hearn and L.R. Seward, The Rand Corporation, Santa Monica, (CP85).}, language = {en} } @misc{Deuflhard1987, author = {Deuflhard, Peter}, title = {A Note on Extrapolation Methods for Second Order ODE Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79}, number = {SC-87-05}, year = {1987}, abstract = {A slight modification of the extended Stoermer discretization for non self-adjoint second order ODE systems is derived on the basis of a simple stability analysis. This discretization easily extends to implicit ODE systems, which are known to arise e.g. in mechanical engineering. In addition, a special variant of semi-implicit Euler discretization is proposed, which essentially treats the state variables explicitly, but their derivatives implicitly. Numerical tests over critical parameter values of the van der Pol oscillator illustrate the domain of efficiency of the suggested discretizations.}, language = {en} } @misc{Buhtz1987, author = {Buhtz, Rainer}, title = {CGM-Concepts and their Realizations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68}, number = {SC-87-04}, year = {1987}, abstract = {Requirements and Design Concepts. Common Graphics Manager (CGM) is the name given to the implementation of GKS, Level 2b, developed at the Free University of Berlin (1,6). This paper is a survey over the "early GKS implementation phase" 1982. Work commenced in February 1980. At the outset some basic design decisions were necessary on account of the special scientific computer environment in Berlin, because the "Berlin GKS" was intended to be a common graphical software package for all the machines.}, language = {en} } @misc{BuhtzLangendorfPaetschetal.1987, author = {Buhtz, Rainer and Langendorf, Jens and Paetsch, Olaf and Buhtz, Danuta Anna}, title = {ZUGRIFF - Eine vereinheitlichte Datenspezifikation f{\"u}r graphische Darstellungen und ihre graphische Aufbereitung.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4506}, number = {TR-87-06}, year = {1987}, abstract = {ZUGRIFF ist eine Dateischnittstelle f{\"u}r Graphikausgabe speziell numerischer Anwenderprogramme. Dieser Report beschreibt den Leistungsumfang der Spezifikation sowie die interaktive graphische Verarbeitung von ZUGRIFF- Dateien.}, language = {de} } @misc{Deuflhard1987, author = {Deuflhard, Peter}, title = {Uniqueness Theorems for Stiff ODE Initial Value Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53}, number = {SC-87-03}, year = {1987}, abstract = {The paper presents a new uniqueness theory for ODE initial value problems, derived in view of numerical stiff integration. The theory supplies stepsize bounds for stiff integrators that can easily be estimated in extrapolation methods. The additional devices lead to a significant speed-up of computations - in particular in combustion PDE problems.}, language = {en} } @misc{OPUS4-987, title = {T{\"a}tigkeitsbericht 1986}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9871}, number = {1986}, year = {1987}, language = {de} } @misc{BankDupontYserentant1987, author = {Bank, Randolph and Dupont, Todd F. and Yserentant, Harry}, title = {The Hierarchical Basis Multigrid Method.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-44}, number = {SC-87-02}, year = {1987}, abstract = {We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß- Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigrid V-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.}, language = {en} } @misc{BuschPoehleStech1987, author = {Busch, Hubert and P{\"o}hle, Uwe and Stech, Wolfgang}, title = {CRAY-Handbuch. - Einf{\"u}hrung in die Benutzung der CRAY.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4459}, number = {TR-87-01}, year = {1987}, abstract = {Das vorliegende Handbuch wendet sich an alle Benutzer des f{\"u}r den Norddeutschen Vektorrechnerverbund im ZIB installierten Rechners CRAY X-MP/24. Ein großer Teil der Darstellung ist der Optimierung von Programmen gewidmet, die in FORTRAN geschrieben sind. Gerade weil die CRAY einer der schnellsten Rechner der Welt ist, wird jeder Benutzer fr{\"u}her oder sp{\"a}ter selbst auf dieses Thema stoßen, denn die Maschine ist vornehmlich f{\"u}r Probleme bestimmt, die f{\"u}r die meisten anderen Rechner zu komplex sind. Maschinen der CRAY-Leistungsklasse beziehen einen erheblichen Teil ihrer Geschwindigkeit aus der parallelen Arbeit vieler Komponenten. Programme, die die jeweilige Architektur der Maschine ber{\"u}cksichtigen, k{\"o}nnen um Gr{\"o}ßenordnungen schneller (also wirtschaftlicher) sein als Programme, deren Autor beim Schreiben einen sogenannten "klassischen" Rechner vor seinem geistigen Auge hatte. Daher wird auch der technische Aufbau der CRAY X-MP im Handbuch erl{\"a}utert. Weitere Teile des Handbuches besch{\"a}ftigen sich mit den Vorrechnern und dem Rechnernetz.}, language = {de} } @misc{AndersonGalwayKessleretal.1987, author = {Anderson, J. and Galway, W. and Kessler, R. and Melenk, Herbert and Neun, Winfried}, title = {The Implementation and Optimization of Portable Standard LISP for the CRAY.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-31}, number = {SC-87-01}, year = {1987}, abstract = {Portable Standard LISP (PSL), a dialect of LISP developed at the University of Utah, has been implemented and optimized for the CRAY 1 and CRAY X-MP supercomputers. This version uses a new implementation technique that permits a step-by-step development of the PSL kernel. The initial CRAY version was acceptable, although the execution speed of the PSL was not as fast as had been anticipated. CRAY-specific optimizations were undertaken that in some cases provided a ten-fold speed improvement, resulting in a fast LISP implementation.}, language = {en} } @misc{MelenkNeun1986, author = {Melenk, Herbert and Neun, Winfried}, title = {Portable Standard LISP for CRAY X-MP Computers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-28}, number = {SC-86-02}, year = {1986}, abstract = {Portable Standard LISP (PSL) is a portable implementation of the programming language LISP constructed at the University of Utah. The version 3.4 of PSL was implemented for CRAY X-MP computers by Konrad-Zuse-Zentrum Berlin; this implementation is based to an important part on the earlier implementation of PSL 3.2 at the University of Utah, Los Alamos National Laboratories and CRAY Research Inc. at Mendota Heights. During the work on implementing PSL the language LISP was investigated for areas which can be supported by vector hardware. One area was found in the COMMON LISP sequence functions and some typical application areas of LISP programming can be improved by vector processing too. A model for the implementation of vector instructions in LISP was developed. For arithmetic an experimental vectorizing extent of the PSL compiler was constructed. With this means full vector hardware capacity can become available for LISP applications.}, language = {en} } @misc{Schuster1986, author = {Schuster, H. J.}, title = {T{\"a}tigkeitsbericht-1985.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4443}, number = {TR-86-01}, year = {1986}, language = {de} } @misc{DeuflhardNowak1986, author = {Deuflhard, Peter and Nowak, Ulrich}, title = {Efficient Numerical Simulation and Identification of Large Chemical Reaction Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14}, number = {SC-86-01}, year = {1986}, abstract = {New, highly efficient techniques for the numerical simulation and parameter identification of large chemical reaction systems are surveyed. The survey particularly addresses to chemists, which are understood to be potential users of the distributed software packages. These packages are written in the form of interactive dialogue systems - thus enabling chemists to concentrate on the chemistry of their problem. Large scale examples from chemical research environments are included.}, language = {en} } @misc{OPUS4-988, title = {T{\"a}tigkeitsbericht 1985}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9885}, number = {1985}, year = {1986}, language = {de} }