39
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Parallel finite element computations of three-dimensional flow problems using padfem2

&
Pages 257-274 | Received 03 Apr 2006, Accepted 27 Oct 2006, Published online: 06 Apr 2009

References

  • Auteri , F. , Guermond , J.-L. and Parolini , N. 2001 . Role of the LBB condition in weak spectral projection methods . Journal of Computational Physics , 174 ( 1 ) : 405 – 420 .
  • Bey , J. 1995 . Tetrahedral grid refinement . Computing , 55 : 355 – 378 .
  • Blazy , S. , Kao , O. and Marquardt , O. 2003 . “ padfem2—an efficient, comfortable framework for massively parallel FEM-applications ” . In Proceedings of the European PVM/MPI User's Group Meeting, LNCS Edited by: Dongarra , J. , Laforenza , D. and Orlando , S. Vol. 2840 , 681 – 685 .
  • Bothe , D. , Hoffmann , M. , Schlueter , M. , Räbiger , N. , Blazy , S. , Stemich , C. and Warnecke , H.-J. 2003 . “ Experimental and numerical investigations of t-shaped micro-mixers ” . In Proceedings of 11th European Conference on Mixing, VDI-GVC 269 – 276 .
  • Braak , M. and Richter , T. 2006 . Solutions of 3d Navier–Stokes benchmark problems with adaptive finite elements . Computers and Fluids , 35 ( 44 ) : 372 – 392 .
  • Bramble , J.H. 1993 . “ Multigrid methods ” . In Pitman Research Notes in Mathematics , London : Longman Scientific & Technical . Series 294
  • Chorin , A.J. 1968 . Numerical solutions of the Navier–Stokes equations . Mathematics of Computation , 22 : 745 – 762 .
  • Diekmann , R. and Preis , R. 1997 . “ Party, a software library for graph partitioning ” . In Advances in Computational Mechanics with Parallel and Distributed Processing 63 – 71 .
  • Douglas , J. and Russel , T.F. 1982 . Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures . SIAM Journal on Numerical Analysis , 19 ( 5 ) : 871 – 885 .
  • Falgout , R.D. , Jones , J.E. and Yang , U.M. 2006 . “ The design and implementation of hypre, a library of parallel high performance preconditioners ” . In Numerical Solution of Partial Differential Equations on Parallel Computers , Edited by: Bruaset , A.M. and Tveito , A. 267 – 294 . New York : Springer-Verlag .
  • Karypis, G. and Kumar, V., 1996, Parallel multilevel k-way partitioning scheme for irregular graphs, Technical Report 36, MN 55454.
  • George , P.-L. and Borouchaki , H. 1998 . Delaunay Triangulation and Meshing—Application to Finite Elements Editions HERMES, Paris
  • Girault , V. and Raviart , P. 1996 . Finite Element Methods for Navier–Stokes Equations , New York : Springer Verlag . Springer Series in Computational Mathematics
  • Guermond , J.L. and Shen , J. 2003 . A new class of truly consistent splitting schemes for incompressible flows . Journal of Computational Physics , 192 ( 1 ) : 262 – 276 .
  • Guermond , L. and Quartapelle , L. 1998 . On stability and convergence of projection methods based on pressure Poisson equation . International Journal for Numerical Methods in Fluids , 26 ( 9 ) : 1039 – 1053 .
  • John , V. 2002 . Higher order finite element methods and multigrid solvers in a benchmark problem for the 3d Navier–Stokes equations . International Journal for Numerical Methods in Fluids 2002 , 40 : 775 – 778 .
  • Pironneau , O. 1989 . Finite Element Methods for Fluids , New York : John Wiley Sons .
  • Prohl , A. 1997 . Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier–Stokes Equations , Stuttgart : BG Teubner .
  • Rannacher , R. 1991 . “ On chorin's projection method for the incompressible Navier–Stokes equations ” . Edited by: Heywood , J.G. , Masuda , K. , Rautmann , R. and Solonnikov , S.A. Vol. 1530
  • Süli , E. 1988 . Convergence and nonlinear stability of the Lagrange–Galerkin method for the Navier–Stokes equations . Numerical Mathematics , 53 : 459 – 483 .
  • Schafer , M. and Turek , S. 1996 . “ Benchmark computations of laminar flow around a cylinder ” . In Flow Simulation with High-Performance Computation II , Edited by: Hirschel , E.H. 547 – 566 . Braunschweig : Vieweg . 52
  • Verfürth , R. 1993 . “ A posteriori error estimators and adaptive mesh-refinement techniques for the Navier–Stokes equations ” . In Incompressible CFD—Trends and Advances Edited by: Gunzburger , M.D. and Nicolaides , R.A. 447 – 477 .
  • Verfürth , R. 2005 . Robust a posteriori error estimates for non-stationary convection-diffusion equations . SIAM Journal on Numerical Analysis , 43 ( 4 ) : 1783 – 1802 .
  • Vankan , J. 1988 . A second order accurate pressure—correction scheme for viscous incompressible flows . SIAM Journal on Scientific and Statistical Computing , 7 : 870 – 891 .
  • Walshaw , C. , Cross , M. and Everett , M.G. 1997 . Parallel dynamic graph partitioning for adaptive unstructured meshes . Journal of Parallel Distributed Computing , : 102 – 108 .
  • Zhang, S., 1988, Technical report, Research Report no. 88020, Dept. of Math., Pennstate Univ. Multi-level iterative techniques.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.