dc.contributor.author Wozniak, M. dc.contributor.author Kuznik, K. dc.contributor.author Paszynski, M. dc.contributor.author Calo, V.M. dc.contributor.author Pardo, D. dc.date.accessioned 2016-06-13T13:11:50Z dc.date.available 2016-06-13T13:11:50Z dc.date.issued 2014-12-31 dc.identifier.issn 0898-1221 dc.identifier.uri http://hdl.handle.net/20.500.11824/82 dc.description.abstract In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as $\mathcal{O}( p^2log(N/p))$ for one dimensional problems, $\mathcal{O}(Np^2)$ for two dimensional problems, and $\mathcal{O}(N^{4/3}p^2)$ for three dimensional problems, where $N$ is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to $\mathcal{O}(N p^2)$ for the one dimensional case, $\mathcal{O}(N^{1.5}p^3)$ for the two dimensional case, and $\mathcal{O}(N^2p^3)$ for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of $N$ and $p$. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Cost estimating dc.subject Polynomial approximation dc.subject Two dimensional dc.subject Computational costs dc.subject Direct solvers dc.subject Number of degrees of freedom dc.subject Nvidia CUDA dc.subject One dimensional problems dc.subject Shared-memory parallels dc.subject Three-dimensional problems dc.subject Two-dimensional problem dc.subject One dimensional dc.title Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1016/j.camwa.2014.03.017 dc.relation.publisherversion http://www.sciencedirect.com/science/article/pii/S0898122114001503 dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Computers and Mathematics with Applications en_US
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