Applications of Alternating Direction Solver for simulations of time-dependent problems - Łoś, Marcin Mateusz; Paszyński, Maciej (Computer Science, 2017)
This paper deals with application of Alternating Direction solver (ADS) to nonstationary linear elasticity problem solved with isogeometric FEM. Employing tensor product B-spline basis in isogeometric analysis under some restrictions leads to system of linear equations with matrix possessing tensor product structure. Alternating Direction Implicit algorithm is a direct method that exploits this structure to solve the system in O (N ), where N is a number of degrees of freedom (basis functions). This is asymptotically faster than state-of-theart general purpose multi-frontal direct solvers. In this paper we also present the complexity analysis of ADS incorporating dependence on order of B-spline basis.