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  • Articles: DFG German National Licenses  (2)
  • Mathematics Subject Classification (1991):65N30  (1)
  • Schwarz Alternating Method  (1)
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  • Articles: DFG German National Licenses  (2)
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Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    On the spectra of sums of orthogonal projections with applications to parallel computing (1991)
    Springer
    BIT 31 (1991), S. 76-88 
    Details
    ISSN: 1572-9125
    Keywords: 65N30 ; 65J10 ; 35J20 ; 15A18 ; Orthogonal Projections ; Parallel Computing ; Domain Decomposition ; Grid Refinement ; Schwarz Alternating Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method is determined by the spectrum of the product of complementary projections. We study spectral properties of sums of orthogonal projections and in the case of two projections, characterize the spectrum of the sum completely in terms of the spectrum of the product.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01952785
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence of a substructuring method with Lagrange multipliers (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 473-487 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We analyze the convergence of a substructuring iterative method with Lagrange multipliers, proposed recently by Farhat and Roux. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, we prove the asymptotic bound on the condition number $C (1+\log (H/h))^\gamma$ , $\gamma=2$ or $3$ ,where $h$ is the characteristic element size and $H$ subdomain size.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050201
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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