Parallel Fast Isogeometric Solvers for Explicit Dynamics
Keywords:Isogeometric finite element method, alternating direction solver, fast parallel solver, non-stationary problems, nonlinear flows in highly-heterogeneous porous media
AbstractThis paper presents a parallel implementation of the fast isogeometric solvers for explicit dynamics for solving non-stationary time-dependent problems. The algorithm is described in pseudo-code. We present theoretical estimates of the computational and communication complexities for a single time step of the parallel algorithm. The computational complexity is O(p^6 N/c t_comp) and communication complexity is O(N/(c^(2/3)t_comm) where p denotes the polynomial order of B-spline basis with Cp-1 global continuity, N denotes the number of elements and c is number of processors forming a cube, t_comp refers to the execution time of a single operation, and t_comm refers to the time of sending a single datum. We compare theoretical estimates with numerical experiments performed on the LONESTAR Linux cluster from Texas Advanced Computing Center, using 1 000 processors. We apply the method to solve nonlinear flows in highly heterogeneous porous media.
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How to Cite
Woźniak, M., Łoś, M., Paszyński, M., Dalcin, L., & Calo, V. M. (2017). Parallel Fast Isogeometric Solvers for Explicit Dynamics. COMPUTING AND INFORMATICS, 36(2), 423–448. Retrieved from https://www.cai.sk/ojs/index.php/cai/article/view/2017_2_423