Abstract
In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.
| Original language | English (US) |
|---|---|
| Title of host publication | Domain Decomposition Methods in Science and Engineering XVIII |
| Pages | 87-98 |
| Number of pages | 12 |
| Volume | 70 LNCSE |
| DOIs | |
| State | Published - 2009 |
| Event | 18th International Conference of Domain Decomposition Methods - Jerusalem, Israel Duration: Jan 12 2008 → Jan 17 2008 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Volume | 70 LNCSE |
| ISSN (Print) | 14397358 |
Other
| Other | 18th International Conference of Domain Decomposition Methods |
|---|---|
| Country | Israel |
| City | Jerusalem |
| Period | 1/12/08 → 1/17/08 |
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ASJC Scopus subject areas
- Engineering(all)
- Computational Mathematics
- Control and Optimization
- Discrete Mathematics and Combinatorics
- Modeling and Simulation
Cite this
Accomodating irregular subdomains in domain decomposition theory. / Widlund, Olof B.
Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 LNCSE 2009. p. 87-98 (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Accomodating irregular subdomains in domain decomposition theory
AU - Widlund, Olof B.
PY - 2009
Y1 - 2009
N2 - In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.
AB - In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=78651586748&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78651586748&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02677-5_8
DO - 10.1007/978-3-642-02677-5_8
M3 - Conference contribution
AN - SCOPUS:78651586748
SN - 9783642026768
VL - 70 LNCSE
T3 - Lecture Notes in Computational Science and Engineering
SP - 87
EP - 98
BT - Domain Decomposition Methods in Science and Engineering XVIII
ER -