# Total overlapping Schwarz' preconditioners for elliptic problems

Faker Ben Belgacem; Nabil Gmati; Faten Jelassi

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 1, page 91-113
- ISSN: 0764-583X

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topBen Belgacem, Faker, Gmati, Nabil, and Jelassi, Faten. "Total overlapping Schwarz' preconditioners for elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 45.1 (2011): 91-113. <http://eudml.org/doc/197464>.

@article{BenBelgacem2011,

abstract = {
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.
},

author = {Ben Belgacem, Faker, Gmati, Nabil, Jelassi, Faten},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Total Overlapping Schwarz method;
minimum residual Krylov methods; numerical zooms; cracked or perforated domains; Laplace boundary value problems; total overlapping Schwarz preconditioner; minimum residual Krylov algorithms; convergence; Laplace equation; generalized minimal residual (GMRES) method},

language = {eng},

month = {1},

number = {1},

pages = {91-113},

publisher = {EDP Sciences},

title = {Total overlapping Schwarz' preconditioners for elliptic problems},

url = {http://eudml.org/doc/197464},

volume = {45},

year = {2011},

}

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

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 1

SP - 91

EP - 113

AB -
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.

LA - eng

KW - Total Overlapping Schwarz method;
minimum residual Krylov methods; numerical zooms; cracked or perforated domains; Laplace boundary value problems; total overlapping Schwarz preconditioner; minimum residual Krylov algorithms; convergence; Laplace equation; generalized minimal residual (GMRES) method

UR - http://eudml.org/doc/197464

ER -

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