Overlapping domain decomposition preconditioners for elliptic and parabolic problems in primal and mixed form

0471115 - ÚGN 2018 CZ eng K - Konferenční příspěvek (tuzemská konf.)
Blaheta, Radim
Overlapping domain decomposition preconditioners for elliptic and parabolic problems in primal and mixed form.
SNA´17 - Seminar on Numerical Analysis. Ostrava: Ústav geoniky AV ČR, 2017 - (Blaheta, R.; Starý, J.), s. 109-119. ISBN 978-80-86407-64-7.
[SNA ’17. Seminar on Numerical Analysis. Ostrava (CZ), 30.01.2017-03.02.2017]
Grant CEP: GA MŠMT LQ1602; GA MŠMT LD15105
Institucionální podpora: RVO:68145535
Klíčová slova: preconditioners * Schwarz method * matrix Ma
Obor OECD: Applied mathematics
http://www.ugn.cas.cz/actually/event/2017/sna/sna-sbornik.pdf

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].
Trvalý link: http://hdl.handle.net/11104/0268565