Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
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AbstractIn 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 O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) 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 O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) 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. © 2014 Elsevier Ltd. All rights reserved.
SponsorsThe work of KK was supported by the Polish National Science Center Grant No. NN 519 447739. The work of MP was supported by the Polish National Science Center Grant Nos. NN 519 447739 and DEC-2011/01/B/ST6/00674. The work of MW was supported by Polish National Science Grant Nos. DEC-2011/01/B/ST6/00674 and 2012/07/B/ST6/01229. The work of DP was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511, the Laboratory of Mathematics (UFI 11/52), and the Ibero American Project CYTED 2011 (P711RT0278).