Parallel fast isogeometric solvers for explicit dynamics

Maciej Woźniak, Marcin Loś, Maciej Paszyński, Lisandro Dalcin, Victor Manuel Calo

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 (p6NCtcomp) and communication complexity is O (Nc2/3tcomm) 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, tcomp 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 languageEnglish (US)
Pages (from-to)423-448
Number of pages26
JournalComputing and Informatics
Issue number2
StatePublished - 2017


  • 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


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