Parallel Fast Isogeometric Solvers for Explicit Dynamics

Authors

  • Maciej Woźniak AGH University of Science and Technology, Krakow
  • Marcin Łoś AGH University of Science and Technology, Krakow
  • Maciej Paszyński AGH University of Science and Technology, Krakow
  • Lisandro Dalcin King Abdullah University of Science and Technology, Thuwal
  • Victor Manuel Calo Applied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA, Australia & King Abdullah University of Science and Technology

Keywords:

Isogeometric finite element method, alternating direction solver, fast parallel solver, non-stationary problems, nonlinear flows in highly-heterogeneous porous media

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(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.

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Author Biographies

Maciej Woźniak, AGH University of Science and Technology, Krakow

Department of Computer Science, PhD student

Marcin Łoś, AGH University of Science and Technology, Krakow

Department of Computer Science, master degree student

Maciej Paszyński, AGH University of Science and Technology, Krakow

Department of Computer Science, associated professor, co-director

Lisandro Dalcin, King Abdullah University of Science and Technology, Thuwal

Center for Numerical Porous Media, Post-doc

Victor Manuel Calo, Applied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA, Australia & King Abdullah University of Science and Technology

Center for Numerical Porous Media, associated professor, co-director

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Published

2017-06-12

How to Cite

Woźniak, M., Łoś, M., Paszyński, M., Dalcin, L., & Calo, V. M. (2017). Parallel Fast Isogeometric Solvers for Explicit Dynamics. Computing and Informatics, 36(2), 423–448. Retrieved from https://www.cai.sk/ojs/index.php/cai/article/view/2017_2_423