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Browsing by Subject "Alternating Direction Solver"

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    Item type:Article, Access status: Open Access ,
    Applications of alternating direction solver for simulations of time-dependent problems
    (Wydawnictwa AGH, 2017) Łoś, Marcin Mateusz; Paszyński, Maciej
    This paper deals with the application of an Alternating Direction Solver (ADS) to a non-stationary linear elasticity problem solved with the isogeometric finite element method (IGA-FEM). Employing a tensor product $B$-spline basis in isogeometric analysis under some restrictions leads to a system of linear equations with a matrix possessing a tensor product structure. The ADI algorithm is a direct method that exploits this Kronecker product structure to solve the system in $O (N)$, where $N$ is the number of degrees of freedom (basis functions). This is asymptotically faster than state-of-the-art, general-purpose, multi-frontal direct solvers when applied to explicit dynamics. In this paper, we also present a complexity analysis of the ADS incorporating dependence on the $B$-spline basis of order $p$.