Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles: DFG German National Licenses  (5)
  • 1990-1994  (5)
Source
  • Articles: DFG German National Licenses  (5)
Material
Years
Year
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    On block diagonal and Schur complement preconditioning (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 79-93 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study symmetric positive definite linear systems, with a 2-by-2 block matrix preconditioned by inverting directly one of the diagonal blocks and suitably preconditioning the other. Using an approximate version of Young's “Property A”, we show that the condition number of the Schur complement is smaller than the condition number obtained by the block-diagonal preconditioning. We also get bounds on both condition numbers from a strengthened Cauchy inequality. For systems arising from the finite element method, the bounds do not depend on the number of elements and can be obtained from element-by-element computations. The results are applied to thep-version finite element method, where the first block of variables consists of degrees of freedom of a low order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385611
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Two-level domain decomposition preconditioning for the p-version finite element method in three dimensionsThis research was partially sponsored by the National Science Foundation under grant DMS-8704169. This paper was presented at the Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, U.S.A., April 9-14, 1989 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1095-1108 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p-version finite element method for three-dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290513
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Balancing domain decomposition (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 233-241 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Neumann-Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite-element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090307
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Preface (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 8 (1992), S. 561-561 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630080902
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...