A balancing domain decomposition by constraints (BDDC) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling, is extended to isogeometric analysis of scalar elliptic problems. This new scaling turns out to be more powerful than the standard ?- and stiffness scalings considered in a previous isogeometric BDDC study. Our h-analysis shows that the condition number of the resulting deluxe BDDC preconditioner is scalable with a quasi-optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces. Extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings, in particular for large isogeometric polynomial degree and high regularity. © 2014 Society for Industrial and Applied Mathematics.

BEIRAO DA VEIGA, L., Pavarino, L., Scacchi, S., Widlund, O., Zampini, S. (2014). Isogeometric BDDC Preconditioning with Deluxe Scaling. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 36(3), 1118-1139 [10.1137/130917399].

Isogeometric BDDC Preconditioning with Deluxe Scaling

BEIRAO DA VEIGA, LOURENCO
Primo
;
2014

Abstract

A balancing domain decomposition by constraints (BDDC) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling, is extended to isogeometric analysis of scalar elliptic problems. This new scaling turns out to be more powerful than the standard ?- and stiffness scalings considered in a previous isogeometric BDDC study. Our h-analysis shows that the condition number of the resulting deluxe BDDC preconditioner is scalable with a quasi-optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces. Extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings, in particular for large isogeometric polynomial degree and high regularity. © 2014 Society for Industrial and Applied Mathematics.
Articolo in rivista - Articolo scientifico
BDDC preconditioners; Domain decomposition; Elliptic problems; Isogeometric analysis
English
2014
36
3
1118
1139
none
BEIRAO DA VEIGA, L., Pavarino, L., Scacchi, S., Widlund, O., Zampini, S. (2014). Isogeometric BDDC Preconditioning with Deluxe Scaling. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 36(3), 1118-1139 [10.1137/130917399].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98400
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