### 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

This 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.

mathematics subject classification 2000: 65F05, 68W10, 65M60

reference: Vol. 36, 2017, No. 2, pp. 423–448