# Analysis of two-level domain decomposition preconditioners based on aggregation

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 5, page 765-780
- ISSN: 0764-583X

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topSala, Marzio. "Analysis of two-level domain decomposition preconditioners based on aggregation." ESAIM: Mathematical Modelling and Numerical Analysis 38.5 (2010): 765-780. <http://eudml.org/doc/194239>.

@article{Sala2010,

abstract = {
In this paper we present two-level overlapping domain decomposition
preconditioners for the finite-element discretisation of elliptic
problems in two and three dimensions. The computational domain is
partitioned into overlapping subdomains, and a coarse space correction
is added. We present an algebraic way to define the coarse space,
based on the concept of aggregation. This employs a (smoothed)
aggregation technique and does not require the introduction of a
coarse grid. We consider a set of assumptions on the coarse basis
functions, to ensure bound for the resulting preconditioned system.
These assumptions only involve geometrical quantities associated to
the aggregates, namely their diameter and the overlap. A condition
number which depends on the product of the relative overlap among the
subdomains and the relative overlap among the aggregates is proved.
Numerical experiments on a model problem are reported to illustrate
the performance of the proposed preconditioners.
},

author = {Sala, Marzio},

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

keywords = {Elliptic equations; domain decomposition; Schwarz methods;
aggregation coarse corrections.; domain decomposition method; preconditioning; aggregation; finite-element; elliptic problems},

language = {eng},

month = {3},

number = {5},

pages = {765-780},

publisher = {EDP Sciences},

title = {Analysis of two-level domain decomposition preconditioners based on aggregation},

url = {http://eudml.org/doc/194239},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Sala, Marzio

TI - Analysis of two-level domain decomposition preconditioners based on aggregation

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 5

SP - 765

EP - 780

AB -
In this paper we present two-level overlapping domain decomposition
preconditioners for the finite-element discretisation of elliptic
problems in two and three dimensions. The computational domain is
partitioned into overlapping subdomains, and a coarse space correction
is added. We present an algebraic way to define the coarse space,
based on the concept of aggregation. This employs a (smoothed)
aggregation technique and does not require the introduction of a
coarse grid. We consider a set of assumptions on the coarse basis
functions, to ensure bound for the resulting preconditioned system.
These assumptions only involve geometrical quantities associated to
the aggregates, namely their diameter and the overlap. A condition
number which depends on the product of the relative overlap among the
subdomains and the relative overlap among the aggregates is proved.
Numerical experiments on a model problem are reported to illustrate
the performance of the proposed preconditioners.

LA - eng

KW - Elliptic equations; domain decomposition; Schwarz methods;
aggregation coarse corrections.; domain decomposition method; preconditioning; aggregation; finite-element; elliptic problems

UR - http://eudml.org/doc/194239

ER -

## References

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