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BPX-preconditioning for isogeometric analysis

Buffa, Annalisa and Harbrecht, Helmut and Kunoth, Angela and Sangalli, Giancarlo. (2013) BPX-preconditioning for isogeometric analysis. Computer methods in applied mechanics and engineering, Vol. 265 , S. 63–70.

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Official URL: http://edoc.unibas.ch/dok/A6164939

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Abstract

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or Nurbs mapping which we assume  to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of h. Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Elsevier
ISSN:0045-7825
Note:Publication type according to Uni Basel Research Database: Journal article
Last Modified:13 Sep 2013 07:59
Deposited On:13 Sep 2013 07:52

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