Details
| Originalsprache | Englisch |
|---|---|
| Titel des Sammelwerks | Fast Boundary Element Methods in Engineering and Industrial Applications |
| Herausgeber/-innen | Ulrich Langer, Olaf Steinbach, Martin Schanz, Wolfgang Wendland |
| Seiten | 93-109 |
| Seitenumfang | 17 |
| Publikationsstatus | Veröffentlicht - 2 Feb. 2012 |
Publikationsreihe
| Name | Lecture Notes in Applied and Computational Mechanics |
|---|---|
| Band | 63 LNAC |
| ISSN (Print) | 1613-7736 |
Abstract
For the Galerkin matrices of the hypersingular and weakly singular first kind integral equations on plane surfaces we present preconditioners obtained by additive Schwarz methods. When those integral equations are solved numerically by the Galerkin boundary element method the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the number of CG-iterations. We consider the hp version of the boundary element method and show how to decompose the boundary element spaces such that the resulting preconditioned Galerkin matrices have in the worst case condition numbers which are only polylogarithmically growing with respect to the discretization parameters, i.e. the mesh size h and the polynomial degree p.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Maschinenbau
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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Fast Boundary Element Methods in Engineering and Industrial Applications. Hrsg. / Ulrich Langer; Olaf Steinbach; Martin Schanz; Wolfgang Wendland. 2012. S. 93-109 (Lecture Notes in Applied and Computational Mechanics; Band 63 LNAC).
Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Beitrag in Buch/Sammelwerk › Forschung › Peer-Review
}
TY - CHAP
T1 - Additive Schwarz Methods for the hp Version of the Boundary Element Method in ℝ3
AU - Leydecker, Florian
AU - Stephan, Ernst P.
PY - 2012/2/2
Y1 - 2012/2/2
N2 - For the Galerkin matrices of the hypersingular and weakly singular first kind integral equations on plane surfaces we present preconditioners obtained by additive Schwarz methods. When those integral equations are solved numerically by the Galerkin boundary element method the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the number of CG-iterations. We consider the hp version of the boundary element method and show how to decompose the boundary element spaces such that the resulting preconditioned Galerkin matrices have in the worst case condition numbers which are only polylogarithmically growing with respect to the discretization parameters, i.e. the mesh size h and the polynomial degree p.
AB - For the Galerkin matrices of the hypersingular and weakly singular first kind integral equations on plane surfaces we present preconditioners obtained by additive Schwarz methods. When those integral equations are solved numerically by the Galerkin boundary element method the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the number of CG-iterations. We consider the hp version of the boundary element method and show how to decompose the boundary element spaces such that the resulting preconditioned Galerkin matrices have in the worst case condition numbers which are only polylogarithmically growing with respect to the discretization parameters, i.e. the mesh size h and the polynomial degree p.
UR - http://www.scopus.com/inward/record.url?scp=84860176488&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-25670-7_3
DO - 10.1007/978-3-642-25670-7_3
M3 - Contribution to book/anthology
AN - SCOPUS:84860176488
SN - 9783642256691
T3 - Lecture Notes in Applied and Computational Mechanics
SP - 93
EP - 109
BT - Fast Boundary Element Methods in Engineering and Industrial Applications
A2 - Langer, Ulrich
A2 - Steinbach, Olaf
A2 - Schanz, Martin
A2 - Wendland, Wolfgang
ER -