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  • Engineering  (1)
  • Mathematics Subject Classification (1991):65N30, 65F10  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 149-167 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):65N30, 65F10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. We consider two level overlapping Schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Standard finite element interpolation from the coarse to the fine grid may be used. Our theory requires no assumption on the substructures that constitute the whole domain, so the substructures can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved, and neither the coarse mesh nor the fine mesh need be quasi-uniform. In addition, the domains defined by the fine and coarse grid need not be identical. The one important constraint is that the closure of the coarse grid must cover any portion of the fine grid boundary for which Neumann boundary conditions are given. In this general setting, our algorithms have the same optimal convergence rate as the usual two level overlapping domain decomposition methods on structured meshes. The condition number of the preconditioned system depends only on the (possibly small) overlap of the substructures and the size of the coarse grid, but is independent of the sizes of the subdomains.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050189
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  • 2
    Digitale Medien
    Digitale Medien
    Low-rank revealing QR factorizations (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 33-44 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680010105
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