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2013 | 1 | 27--32
Tytuł artykułu

Performance Evaluation of MPI/OpenMP Algorithm for 3D Time Dependent Problems

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the 3D time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, approached in terms of velocity and pressure. In a parallel algorithm, based on a novel direction splitting approach, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. In order to achieve good parallel performance, the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code was developed using MPI and OpenMP and tested on modern computer systems. The performed tests illustrate the parallel efficiency, and the scalability, of the direction-splitting based algorithm.(original abstract)
Słowa kluczowe
Rocznik
Tom
1
Strony
27--32
Opis fizyczny
Twórcy
autor
  • Bulgarian Academy of Sciences
  • Polish Academy of Sciences
autor
  • Polish Academy of Sciences
  • Intel Corporation
Bibliografia
  • Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Croz, J.D., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users' Guide. SIAM, Philadelphia, third edn. (1999)
  • Chandra, R., Menon, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J.: Parallel programming in OpenMP. Morgan Kaufmann (2000)
  • Chapman, B., Jost, G., Van Der Pas, R.: Using OpenMP: portable shared memory parallel programming, vol. 10. MIT press (2008)
  • Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comp. 22, 745-762 (1968)
  • Guermond, J.L., Minev, P.: A new class of fractional step techniques for the incompressible Navier-Stokes equations using direction splitting. Comptes Rendus Mathematique 348(9-10), 581-585 (2010)
  • Guermond, J.L., Minev, P.: A new class of massively parallel direction splitting for the incompressible navier-stokes equations. Computer Methods in Applied Mechanics and Engineering 200(23), 2083-2093 (2011)
  • Guermond, J.L., Minev, P., Shen, J.: An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg. 195, 6011-6054 (2006)
  • Guermond, J.L., Salgado, A.: A fractional step method based on a pressure poisson equation for incompressible flows with variable density. Comptes Rendus Mathematique 346(15-16), 913-918 (2008)
  • Guermond, J.L., Salgado, A.: A splitting method for incompressible flows with variable density based on a pressure Poisson equation. Journal of Computational Physics 228(8), 2834-2846 (2009)
  • Lirkov, I., Paprzycki, M., Ganzha, M.: Performance analysis of parallel alternating directions algorithm for time dependent problems. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) 9th international conference on Parallel Processing and Applied Mathematics, PPAM 2011, Part I. Lecture notes in computer science, vol. 7203, pp. 173-182. Springer (2012)
  • Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra, J.: MPI: The Complete Reference. Scientific and engineering computation series, The MIT Press, Cambridge, Massachusetts (1997), second printing
  • Temam, R.: Sur l'approximation de la solution des equations de Navier-Stokes par la ḿethode des pas fractionnaires. Arch. Rat. Mech. Anal. 33, 377-385 (1969)
  • Walker, D., Dongarra, J.: MPI: a standard Message Passing Interface. Supercomputer 63, 56-68 (1996)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171278591

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