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    Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

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    Type
    Article
    Authors
    Woźniak, Maciej
    Paszyński, Maciej R.
    Pardo, D. cc
    Dalcin, Lisandro cc
    Calo, Victor M. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2015-02
    Permanent link to this record
    http://hdl.handle.net/10754/564032
    
    Metadata
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    Abstract
    This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order O(log(N)p2) for the one dimensional (1D) case, O(Np2) for the two dimensional (2D) case, and O(N4/3p2) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N. For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20% for 256 processors for a 3D example with 1283 unknowns and linear B-splines with C0 global continuity, and 15% for a 3D example with 643 unknowns and quartic B-splines with C3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.
    Citation
    Woźniak, M., Paszyński, M., Pardo, D., Dalcin, L., & Calo, V. M. (2015). Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines. Computer Methods in Applied Mechanics and Engineering, 284, 971–987. doi:10.1016/j.cma.2014.11.020
    Publisher
    Elsevier BV
    Journal
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2014.11.020
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cma.2014.11.020
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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