Overlapping Domain Decomposition Methods with FreeFem++

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 98)


In this note, the performances of a framework for two-level overlapping domain decomposition methods are assessed. Numerical experiments are run on Curie, a Tier-0 system for PRACE, for two second order elliptic PDE with highly heterogeneous coefficients: a scalar equation of diffusivity and the system of linear elasticity. Those experiments yield systems with up to ten billion unknowns in 2D and one billion unknowns in 3D, solved on few thousands cores.


Domain Decomposition Method Finite Element Space Master Process Krylov Method Local Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported in part by ANR through COSINUS program (project PETALh no. ANR-10-COSI-0013 and projet HAMM no. ANR-10-COSI-0009). It was granted access to the HPC resources of TGCC@CEA made available within the Distributed European Computing Initiative by the PRACE-2IP, receiving funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement RI-283493.


  1. 1.
    Amestoy, P., Duff, I., L’Excellent, J.Y., Koster, J.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1), 15–41 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Amestoy, P., Guermouche, A., L’Excellent, J.Y., Pralet, S.: Hybrid scheduling for the parallel solution of linear systems. Parallel Comput. 32(2), 136–156 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bangerth, W., Hartmann, R., Kanschat, G.: deal.II—a general-purpose object-oriented finite element library. ACM Trans. Math. Softw. 33(4), 24–27 (2007)Google Scholar
  4. 4.
    Cai, X.C., Sarkis, M.: Restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21(2), 792–797 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chevalier, C., Pellegrini, F.: PT-Scotch: a tool for efficient parallel graph ordering. Parallel Comput. 34(6), 318–331 (2008)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Geuzaine, C., Remacle, J.F.: Gmsh: a 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Hénon, P., Ramet, P., Roman, J.: PaStiX: a high performance parallel direct solver for sparse symmetric positive definite systems. Parallel Comput. 28(2), 301–321 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Hernandez, V., Roman, J., Vidal, V.: SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Jolivet, P., Dolean, V., Hecht, F., Nataf, F., Prud’homme, C., Spillane, N.: High performance domain decomposition methods on massively parallel architectures with FreeFem++. J. Numer. Math. 20(4), 287–302 (2012)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Lehoucq, R., Sorensen, D., Yang, C.: ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, vol. 6. Society for Industrial and Applied Mathematics, Philadelphia (1998)CrossRefGoogle Scholar
  12. 12.
    Prud’homme, C., Chabannes, V., Doyeux, V., Ismail, M., Samake, A., Pena, G.: Feel++: a computational framework for Galerkin methods and advanced numerical methods. In: ESAIM: Proceedings, vol. 38, pp. 429–455 (2012)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Schenk, O., Gärtner, K.: Solving unsymmetric sparse systems of linear equations with PARDISO. Future Gener. Comput. Syst. 20(3), 475–487 (2004)CrossRefGoogle Scholar
  14. 14.
    Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C., Scheichl, R.: A robust two-level domain decomposition preconditioner for systems of PDEs. C. R. Math. 349(23), 1255–1259 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Tang, J., Nabben, R., Vuik, C., Erlangga, Y.: Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods. J. Sci. Comput. 39(3), 340–370 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Toselli, A., Widlund, O.: Domain Decomposition Methods—Algorithms and Theory. Series in Computational Mathematics, vol. 34. Springer, Berlin (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, CNRS UMR 7598Université Pierre et Marie CurieParisFrance
  2. 2.Laboratoire Jean Kuntzmann, CNRS UMR 5224Université Joseph FourierGrenoble Cedex 9France
  3. 3.Institut de Recherche Mathématique Avancée, CNRS UMR 7501Université de StrasbourgStrasbourg CedexFrance

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