Data di Pubblicazione:
2012
Citazione:
Overlapping schwarz methods for isogeometric analysis / L. Beirao da Veiga, D. Cho, L.F. Pavarino, S. Scacchi. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 50:3(2012 May 31), pp. 1394-1416.
Abstract:
We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an $h$-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and „overlap sizes” for fixed polynomial degree $p$ and regularity $k$ of the basis functions. Numerical results in two- and three-dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters $h, p, k$, number of subdomains $N$, overlap size, and also jumps in the coefficients of the elliptic operator.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
domain decomposition methods; overlapping Schwarz; scalable preconditioners; isogeometric analysis; finite elements; NURBS
Elenco autori:
L. Beirao da Veiga, D. Cho, L.F. Pavarino, S. Scacchi
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