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  • 1
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    The Hierarchical Basis Multigrid Method. (1987)
    Details
    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 2
    Electronic Resource
    Electronic Resource
    The hierarchical basis multigrid method (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 427-458 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; 65F35 ; 65N20 ; 65N30 ; CR:G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary 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 multigridV-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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01462238
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Capillary flow as the cause of ring stains from dried liquid drops (1997)
    [s.l.] : Macmillan Magazines Ltd.
    Nature 389 (1997), S. 827-829 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] When a spilled drop of coffee dries on a solid surface, it leaves a dense, ring-like deposit along the perimeter (Fig. 1a). The coffee—initially dispersed over the entire drop—becomes concentrated into a tiny fraction of it. Such ring deposits are common wherever drops ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/39827
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    Paper (German National Licenses)
    Fulltext
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