A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem et al., C. R. Acad. Sci., Sér. 1 Math. 336 (2003) 277-282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the behavior of the solution at infinity, when handling exterior problems. The main aim of the paper is to use this modified Schwarz procedure as a preconditioner to Krylov subspaces methods so to accelerate the calculations. A detailed study concludes to a super-linear convergence of GMRES and enables us to state accurate estimates on the convergence speed. Afterward, some implementation hints are discussed. Analytical and numerical examples are also provided and commented that demonstrate the reliability of the TOS-preconditioner.
Mots clés : total overlapping Schwarz method, minimum residual Krylov methods, numerical zooms
@article{M2AN_2011__45_1_91_0, author = {Ben Belgacem, Faker and Gmati, Nabil and Jelassi, Faten}, title = {Total overlapping {Schwarz'} preconditioners for elliptic problems}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {91--113}, publisher = {EDP-Sciences}, volume = {45}, number = {1}, year = {2011}, doi = {10.1051/m2an/2010032}, mrnumber = {2781132}, zbl = {1270.65073}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2010032/} }
TY - JOUR AU - Ben Belgacem, Faker AU - Gmati, Nabil AU - Jelassi, Faten TI - Total overlapping Schwarz' preconditioners for elliptic problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 91 EP - 113 VL - 45 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010032/ DO - 10.1051/m2an/2010032 LA - en ID - M2AN_2011__45_1_91_0 ER -
%0 Journal Article %A Ben Belgacem, Faker %A Gmati, Nabil %A Jelassi, Faten %T Total overlapping Schwarz' preconditioners for elliptic problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 91-113 %V 45 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010032/ %R 10.1051/m2an/2010032 %G en %F M2AN_2011__45_1_91_0
Ben Belgacem, Faker; Gmati, Nabil; Jelassi, Faten. Total overlapping Schwarz' preconditioners for elliptic problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 1, pp. 91-113. doi : 10.1051/m2an/2010032. http://www.numdam.org/articles/10.1051/m2an/2010032/
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