Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations Technical Report 461 September, 1989 Classic Reprint

Xiao-Chuan Cai

ISBN 10: 065619300X / ISBN 13: 9780656193004

Verlag: Forgotten Books, 2018

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New Book. Shipped from UK. Established seller since 2000.

Bestandsnummer des Verkäufers LX-9780656193004

Bibliografische Details

• Titel: Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations Technical Report 461 September, 1989 Classic Reprint
• Verlag: Forgotten Books
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 065619300X
• ISBN-13: 9780656193004
• Einband: HRD
• Zustand: New
• Gewicht: 335 Gramm

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Inhaltsangabe

Excerpt from Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989

The iterative methods most commonly used are the conjugate gradient method for the symmetric, positive definite case and the generalized conju gate residual methods (gmres) for the general, nonsymmetric case. If the symmetric part of the operator is positive definite, with respect to a suitable inner product, convergence can be guaranteed. In this thesis, the rate of convergence of all algorithms will be estimated. We show that the additive Schwarz algorithm is optimal for both elliptic and parabolic problems in R2 and R3 in the sense that the rate of convergence is independent of both the coarse mesh size, defined by the substructures, and the fine mesh size. The iterative substructuring algorithm is not optimal in the above sense, however, in the R2 case the corresponding rate of convergence depends only mildly on the mesh parameters. A modified additive Schwarz algorithm is also introduced for parabolic problems in R2. The rate of convergence is independent of the fine mesh size.

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