Abstract
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(p(6)N/c(2/3) t(comp)) 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 tcomn, 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.