Parallel fast isogeometric solvers for explicit dynamics

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^6N_Ct_comp) and communication complexity is O (^N_c^2/3t_comm) where p denotes the polynomial order of B-spline basis with C ^p-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 tcomm. 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.