TY - JOUR A1 - Barahona, Francisco A1 - Grötschel, Martin A1 - Jünger, Michael A1 - Reinelt, Gerhard T1 - An application of combinatorial optimization to statistical physics and circuit layout design JF - Operations Research Y1 - 1988 VL - 36 IS - 3 SP - 493 EP - 513 ER - TY - BOOK A1 - Grötschel, Martin A1 - Lovász, Lászlo A1 - Schrijver, Alexander T1 - Geometric Algorithms and Combinatorial Optimization T3 - Algorithms and Combinatorics Y1 - 1988 SN - 3-540-13624-X, 0-387-13624-X (U.S.) VL - 2 PB - Springer ER - TY - JOUR A1 - Böck, J. A1 - Deuflhard, Peter A1 - Hoeft, A. A1 - Korb, H. A1 - Steinmann, J. A1 - Wolpers, H. A1 - Hellige, G. T1 - Evaluation of monoexponential extrapolation of transpulmonary thermal-dye kinetics by use of a new model-free deconvolution algorithm JF - Med Instrum Y1 - 1988 VL - 22 IS - 1 SP - 20 EP - 28 ER - TY - JOUR A1 - Böck, J. A1 - Deuflhard, Peter A1 - Hoeft, A. A1 - Korb, H. A1 - Wolpers, H. A1 - Steinmann, J. A1 - Hellige, G. T1 - Thermal recovery after passage of the pulmonary circulation assessed by deconvolution JF - J. Appl. Physiol. Y1 - 1988 VL - 64 IS - 3 SP - 1210 EP - 1216 ER - TY - GEN A1 - Maierhöfer, Gerhard A1 - Skorobohatyj, Georg T1 - Parallel-TRAPEX (Ein paralleler adaptiver Algorithmus zur numerischen Integration; seine Implementierung für SUPRENUM-artige Architekturen mit SUSI). N2 - 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. T3 - ZIB-Report - TR-88-05 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4560 ER - TY - GEN A1 - Hoppe, Ronald H. W. A1 - Kornhuber, Ralf T1 - Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs. N2 - 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. T3 - ZIB-Report - SC-88-08 KW - induction heating KW - system of two coupled Stefan equations KW - multi-grid algorithms Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-160 ER - TY - GEN A1 - Melenk, Herbert A1 - Möller, H. Michael A1 - Neun, Winfried T1 - Symbolic Solution of Large Stationary Chemical Kinetics Problems. N2 - 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. T3 - ZIB-Report - SC-88-07 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-157 ER - TY - GEN A1 - Deuflhard, Peter A1 - Wulkow, Michael T1 - Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable. N2 - 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. T3 - ZIB-Report - SC-88-06 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-140 ER - TY - GEN A1 - Deuflhard, Peter A1 - Leinen, P. A1 - Yserentant, Harry T1 - Concepts of an Adaptive Hierarchical Finite Element Code. N2 - 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. T3 - ZIB-Report - SC-88-05 KW - finite elements KW - hierarchical basis KW - adaptive mesh refinement KW - preconditioned conjugate gradient methods Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-131 ER - TY - GEN A1 - Buhtz, Danuta Anna A1 - Langendorf, Jens A1 - Paetsch, Olaf T1 - GRAZIL - 3D. Ein graphisches Anwendungsprogramm zur Darstellung von Kurven- und Funktionsverläufen im räumlichen Koordinatensystem. N2 - GRAZIL - 3D ist ein interaktives Programmpaket zur graphischen Darstellung von dreidimensionalen Kurvenverläufen. Das Aussehen der räumlichen Ausgabe des Bildes wird durch Angabe des Blickwinkels und der Perspektive festgelegt. T3 - ZIB-Report - TR-88-04 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4556 ER - TY - GEN T1 - Jahresbericht 1987 T3 - Jahresbericht - 1987 KW - Annual Report Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9860 SN - 0933-7903 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - Parallel Polynomial Operations in the Buchberger Algorithm. N2 - 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). T3 - ZIB-Report - SC-88-04 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-125 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3. N2 - 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). T3 - ZIB-Report - TR-88-02 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4539 ER - TY - GEN A1 - Melenk, Herbert A1 - Neun, Winfried T1 - REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3. N2 - 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. T3 - ZIB-Report - TR-88-03 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4541 ER - TY - GEN A1 - Buhtz, Rainer A1 - Buhtz, Danuta Anna T1 - TDLG 3.1 - Ein interaktives Programm zur Darstellung dreidimensionaler Modelle auf Rastergraphikgeräten. N2 - TDLG 3.1 dient zur Darstellung von dreidimensionalen Objekten, die sich aus offenen Linienzügen, Dreieck- und Viereckelementen zusammensetzen. Dabei können verschiedene Visualisierungstechniken benutzt werden: Drahtmodell, Schattierung mit und ohne Lichtquelle, Hidden Surface Removal. Durch Verwendung von Konvertierungsprogrammen können auch IGES- und VDAFS- Dateien dargestellt werden. T3 - ZIB-Report - TR-88-01 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4522 ER - TY - GEN A1 - Melenk, Herbert A1 - Möller, H. Michael A1 - Neun, Winfried T1 - On Gröbner Bases Computation on a Supercomputer Using REDUCE. N2 - Gröbner 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 Gröbner 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. T3 - ZIB-Report - SC-88-02 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-107 ER - TY - GEN A1 - Alexander, J. C. A1 - Fiedler, Bernold T1 - Global Decoupling of Coupled Symmetric Oscillators. N2 - 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. T3 - ZIB-Report - SC-88-03 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-113 ER - TY - GEN A1 - Neun, Winfried A1 - Melenk, Herbert T1 - Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor. N2 - 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 Gröbner 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. T3 - ZIB-Report - SC-88-01 Y1 - 1988 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93 ER -