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  • 1985-1989  (4)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 24-46 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die Vektor Projektions Methode zur Lösung linearer Gleichungssysteme ist darauf begründet, daß jede Gleichung eine Hyperebene definiert und daß die Berechnung der Projektionspunkte linear ist. Wie bei der Gauss'schen Eliminierung wird die Anzahl der Multiplikationen durch ein kubisches Polynom mit höchstem Koeffizientenn 3/3 beschrieben. Zwei Vorteile der neuen Methode sind, daß nur etwan 2/4 Speicherplätze benötigt werden, und daß Null-Koeffizienten im Gleichungsystem erhalten bleiben. Damit kann die Anzahl der Rechenoperationen bei dünnbesetzten Matrizen erheblich reduziert werden. Die gute Genauigkeit des neuen Verfahrens wird am Beispiel der numerischen Inversion von Hilbert-Matrizen verschiedener Größe gezeigt.
    Notes: Abstract The Focal Point method of solving systems of linear equations is based on the linearity of matrix transformations and the fact that each equation in the system defines a hyperplane of solutions. As with Gaussian elimination the number of multiplications is a cubic polynomial inn with leading coefficientn 3/3. Some of the benefits of this new method are that it needs approximatelyn 2/4 storage registers and that the zeroes of the system are preserved. Thus for sparse systems the operation count can be significantly reduced. Numerical examples using initial segments of the Hilbert matrix demonstrate that this new method can be very accurate.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 329-347 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 709-712 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, ‘Laplacian’ smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 1985-01-01
    Print ISSN: 0044-2275
    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
    Published by Springer
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