Original title: Overlapping domain decomposition preconditioners for elliptic and parabolic problems in primal and mixed form
Authors: Blaheta, Radim
Document type: Papers
Conference/Event: SNA ’17. Seminar on Numerical Analysis, Ostrava (CZ), 20170130
Year: 2017
Language: eng
Abstract: In this lecture, we concern the numerical solution of PDE problems and describe overlapping domain decomposition, which provides a tool for the construction of parallelizable Schwarz type iterative solvers and preconditioners. The idea of using overlapping domain decomposition goes back to Schwarz alternating method from 1870, see [1]. The analysis of this alternating iterative method was evolved by great mathematicians, see e.g. S.L. Sobolev (1936), R. Courant and D. Hilbert (1937), S.G. Michlin (1951), M. Práger (1958), I. Babuška (1958), F.E. Browder (1958). The use of overlapping domain decomposition for parallel computations started in the late eighties in the work of M. Dryja and O. Widlund [4], P.L. Lions [5, 6], S. Nepomnyaschikh [7] and others and continue up to the present days. The origin of the alternating Schwarz method is nicely described in [8].
Keywords: matrix Ma; preconditioners; Schwarz method
Project no.: LQ1602 (CEP), LD15105 (CEP)
Funding provider: GA MŠk, GA MŠk
Host item entry: SNA´17 - Seminar on Numerical Analysis, ISBN 978-80-86407-64-7

Institution: Institute of Geonics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://www.ugn.cas.cz/actually/event/2017/sna/sna-sbornik.pdf
Original record: http://hdl.handle.net/11104/0268565

Permalink: http://www.nusl.cz/ntk/nusl-263317


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