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Optimal multilevel preconditioners for isogeometric collocation methods

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  • Cho, Durkbin

Abstract

We present optimal additive and multiplicative multilevel methods, such as BPX preconditioner and multigrid V-cycle, for the solution of linear systems arising from isogeometric collocation discretizations of second order elliptic problems. These resulting preconditioners, accelerated by GMRES, lead to optimal complexity for the number of levels, and illustrate their good performance with respect to the isogeometric discretization parameters such as the spline polynomial degree and regularity of the isogeometric basis functions, as well as with respect to domain deformations.

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  • Cho, Durkbin, 2020. "Optimal multilevel preconditioners for isogeometric collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 76-89.
    • Handle: RePEc:eee:matcom:v:168:y:2020:i:c:p:76-89
    DOI: 10.1016/j.matcom.2019.08.003
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    Cited by:

    1. Jingwen Ren & Hongwei Lin, 2023. "A Survey on Isogeometric Collocation Methods with Applications," Mathematics, MDPI, vol. 11(2), pages 1-21, January.

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