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(p6 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.

Keywords

MSC

65F05, 68W10, 65M60

Cite this article

@article{cai-2471,
  author  = {Maciej Woźniak and Marcin Łoś and Maciej Paszyński and Lisandro Dalcin and Victor Manuel Calo},
  title   = {Parallel Fast Isogeometric Solvers for Explicit Dynamics},
  journal = {Computing and Informatics},
  volume  = {36},
  number  = {2},
  pages   = {423--448},
  year    = {2017},
  issn    = {1335-9150},
  doi     = {10.4149/cai_2017_2_423}
}
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