Klawonn, Axel; Rheinbach, Oliver; Widlund, Olof B.:
An analysis of a FETI-DP algorithm on irregular subdomains in the plane
In: SIAM Journal on Numerical Analysis, Jg. Vol. 46 (2008), Heft No. 5, S. 2484 - 2504
2008Artikel/Aufsatz in Zeitschrift
MathematikFakultät für Mathematik
Damit verbunden: 1 Publikation(en)
Titel in Englisch:
An analysis of a FETI-DP algorithm on irregular subdomains in the plane
Autor*in:
Klawonn, AxelUDE
GND
114308489
LSF ID
5339
ORCID
0000-0003-0548-4350ORCID iD
ORCID
0000-0003-4765-7387ORCID iD
Sonstiges
der Hochschule zugeordnete*r Autor*in
;
Rheinbach, OliverUDE
LSF ID
5604
ORCID
0000-0002-9310-8533ORCID iD
Sonstiges
der Hochschule zugeordnete*r Autor*in
;
Widlund, Olof B.
Erscheinungsjahr:
2008
Sprache des Textes:
Englisch

Abstract in Englisch:

n the theory for domain decomposition algorithms of the iterative substructuring family, each subdomain is typically assumed to be the union of a few coarse triangles or tetrahedra. This is an unrealistic assumption, in particular if the subdomains result from the use of a mesh partitioner, in which case they might not even have uniformly Lipschitz continuous boundaries. The purpose of this study is to derive bounds for the condition number of these preconditioned conjugate gradient methods which depend only on a parameter in an isoperimetric inequality, two geometric parameters characterizing John and uniform domains, and the maximum number of edges of any subdomain. A related purpose is to explore to what extent well-known technical tools previously developed for quite regular subdomains can be extended to much more irregular subdomains. Some of these results are valid for any John domain, while an extension theorem, which is needed in this study, requires that the subdomains have complements which are uniform. The results, so far, are complete only for problems in two dimensions. Details are worked out for a FETI–DP algorithm and numerical results support the findings. Some of the numerical experiments illustrate that care must be taken when selecting the scaling of the preconditioners in the case of irregular subdomains.