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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 56 (1996), S. 259-301 
    ISSN: 1436-5057
    Keywords: 15A12 ; 35Q30 ; 65N30 ; 41A17 ; 41A63 ; Saddle point problems ; LBB condition ; multiresolution analysis ; wavelets ; time dependent problems ; Schur complements ; preconditioning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden Galerkin-Verfahren für das Stokes-Problem untersucht, die auf speziell angepaßten Multiresolution-Ansätzen beruhen. Insbesondere wird gezeigt, daß gewisse Konstruktionsprinzipien für Wavelets auf gleichförmigen Gittern für jede Raumdimension und beliebige gewünschte Exaktheitsordnung auf Parre von Ansatzräumen führen, die die Ladyšenskaja-Babuška-Brezzi-Bedingung erfüllen. Darüber hinaus ergeben sich auch im instationären Fall aus den entsprechenden stabilen Multiskalenzerlegungen effiziente Vorkonditionierer für die Schurkomplemente entsprechenden systemmatrizen. Die Ergebnisse werden anhand einiger konkreter Realisierungen und numerischer Tests illustriert.
    Notes: Abstract The purpose of this paper is to investigate Galerkin schemes for the Stokes equations based on a suitably adapted multiresolution analysis. In particular, it will be shown that techniques developed in connection with shift-invariant refinable spaces give rise to trial spaces of any desired degree of accuracy satisfying the Ladyšenskaja-Babuška-Brezzi condition for any spatial dimension. Moreover, in the time dependent case efficient preconditioners for the Schur complements of the discrete systems of equations can be based on corresponding stable multiscale decompositions. The results are illustrated by some concrete examples of adapted wavelets and corresponding numerical experiments.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Interface science 1 (1994), S. 291-308 
    ISSN: 1573-2746
    Keywords: grain boundaries ; misfit disloctions ; YBa2Cu3O7 films ; step-edge junction ; HREM
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The atomic structure of 90° [100] (or [010]) tilt grain boundaries in YBa2Cu3O7 thin-film step-edge junctions and, for comparison, in the interface between a-axis and c-axis oriented YBa2Cu3O7 grains is investigated by means of high-resolution transmission electron microscopy. For (100)(001)-type boundaries two different structures are found. In the first a (001) CuO2 plane of one grain faces a (100) Y−Ba−O plane of the other grain, in the second a (001) BaO plane faces a (100) Cu−O plane. In the former structure an incomplete unit cell of YBa2Cu3O7 terminates at the boundary and a smaller strain in the adjacent CuO2 planes is detected in comparison with the latter. It is found that a combination of a partial dislocation with a “124” stacking fault is a way to accommodate the lattice mismatch between c and 3a of YBa2Cu3O7 in the boundary. For a symmetric (103)(103)-type boundary a displacement of the Cu-atoms of the CuO2 planes is found near the boundary plane. From this a redistribution of the oxygen atoms around the Y-atoms located right in the boundary plane is inferred. The possible effect of the boundary structure on the superconducting properties of YBa2Cu3O7 films is discussed.
    Type of Medium: Electronic Resource
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