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  • 1985-1989  (10)
  • 1988  (10)
  • ddc:000  (10)
  • English  (10)
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  • 1985-1989  (10)
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Keywords
  • ddc:000  (10)
Language
  • 1
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    Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 2
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    Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs. (1988)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 3
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    On Gröbner Bases Computation on a Supercomputer Using REDUCE. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 4
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    Concepts of an Adaptive Hierarchical Finite Element Code. (1988)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 5
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    REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 6
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    Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable. (1988)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
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    Symbolic Solution of Large Stationary Chemical Kinetics Problems. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 8
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    REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
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    Global Decoupling of Coupled Symmetric Oscillators. (1988)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 10
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    Parallel Polynomial Operations in the Buchberger Algorithm. (1988)
    Details
    Publication Date: 2018-12-06
    Description: 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).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
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