## 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^{6N}_{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 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.

Original language | English (US) |
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Pages (from-to) | 423-448 |

Number of pages | 26 |

Journal | Computing and Informatics |

Volume | 36 |

Issue number | 2 |

DOIs | |

State | Published - 2017 |

## Keywords

- Alternating direction solver
- Fast parallel solver
- Isogeometric finite element method
- Non-stationary problems
- Nonlinear flows in highly-heterogeneous porous media

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications
- Computational Theory and Mathematics