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A Parallel Implementation of ALE Moving Mesh Technique for FSI Problems using OpenMP

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Abstract

This paper investigates a high performance implementation of an Arbitrary Lagrangian Eulerian moving mesh technique on shared memory systems using OpenMP environment. Moving mesh techniques are considered an integral part of a wider class of fluid mechanics problems that involve moving and deforming spatial domains, namely, free-surface flows and Fluid Structure Interaction (FSI). The moving mesh technique adopted in this work is based on the notion of nodes relocation, subjected to a certain evolution as well as constraint conditions. A conjugate gradient method augmented with preconditioning is employed for solution of the resulting system of equations. The proposed algorithm, initially, reorders the mesh using an efficient divide and conquer approach and then parallelizes the ALE moving mesh scheme. Numerical simulations are conducted on the multicore AMD Opteron and Intel Xeon processors, and unstructured triangular and tetrahedral meshes are used for the 2D and 3D problems. The quality of generated meshes is checked by comparing the element Jacobians in the reference and current meshes, and by keeping track of the change in the interior angles in triangles and tetrahedrons. Overall, 51 and 72% efficiencies in terms of speedup are achieved for both the parallel mesh reordering and ALE moving mesh algorithms, respectively.

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References

  1. Li R., Tang T., Zhang P.: A moving mesh finite element algorithm for singular problems in two and three space dimensions. J. Comput. Phys. 177, 365–393 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tang, T.:, Moving mesh methods for computational fluid dynamics. In: Shi, Z.C., Chen, Z., Tang, T., Yu, D. (eds.) Recent Advances in Adaptive Computations (Providence USA), Contemporary Mathematics, vol. 383, pp. 141–174. American Mathematical Society, Zhejiang University, Hangzhou, China (2005)

  3. Bhanabhagwanwala, M.: A Mesh Pre-Processing Scheme for Moving Boundary Flows and a Novel Graphics Post-Processor for DGM, MS. Thesis, Mechanical Engineeering, University of Illinois at Chicago (2004)

  4. Perot J.B., Nallapati R.: A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows. J. Comput. Phys. 184(1), 192–214 (2003)

    Article  MATH  Google Scholar 

  5. Tourigny Y., Hülsemann F.: A new moving mesh algorithm for the finite element solution of variational problems. SIAM J. Numer. Anal. 35, 1416–1438 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Donea J.: Arbitrary Lagrangian-Eulerian finite element methods. In: Belytschko, T., Hughes, T.J.R. (eds) Computational Methods for Transient Analysis, pp. 473–516. North-Holland, Amsterdam (1983)

    Google Scholar 

  7. Hughes T.J.R., Liu W.K., Zimmerman T.K.: Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29, 329–349 (1984)

    Article  Google Scholar 

  8. Masud A., Hughes T.J.R.: A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems. Comput. Methods Appl. Mech. Eng. 146, 91–126 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Masud A., Bhanabhagwanwala M., Khurram R.A.: An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction. Comput. Fluids 36, 77–91 (2005)

    Article  Google Scholar 

  10. Kanchi H., Masud A.: A 3D adaptive mesh moving scheme. Int. J. Numer. Methods Fluids 54(4), 21–34 (2007)

    MathSciNet  Google Scholar 

  11. Johnson A.A., Tezduyar T.E.: Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput. Methods Appl. Mech. Eng. 119(1–2), 73–94 (1994)

    Article  MATH  Google Scholar 

  12. Johnson A.A., Tezduyar T.E.: Advanced mesh generation and update methods for 3D flow simulations. Comput. Mech. 23, 130–143 (1999)

    Article  MATH  Google Scholar 

  13. Farhat C., Geuzaine P.: Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Comput. Methods Appl. Mech. Eng. 193(39–41), 4073–4095 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Masud A.: Effects of mesh motion on the stability and convergence of ALE based formulations for moving boundary flows. Comput. Mech. 38(4), 430–439 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Khurram R.A, Masud A.: A multiscale/stabilized formulation of the incompressible Navier-Stokes equations for moving boundary flows and fluid-structure interaction. Comput. Mech. 38(4), 403–416 (2006)

    Article  MATH  Google Scholar 

  16. Calderer R., Masud A.: A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. Comput. Mech. 46, 185–197 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Flaherty J.E., Loy R.M., Shephard M.S., Szymanski B.K., Teresco J.D., Ziantz L.H.: Adaptive local refinement with Octree load-balancing for the parallel solution of three-dimensional conservation laws. J. Parallel Distrib. Comput. 47, 139–152 (1998)

    Article  Google Scholar 

  18. Mitchell W.F.: A refinement-tree based partitioning method for dynamic load balancing with adaptively refined grids. J. Parallel Distrib. Comput. 67(4), 417–429 (2007)

    Article  MATH  Google Scholar 

  19. Balman, M.: Tetrahedral mesh refinement in distributed environments. In: Proceedings Supercomputing’93, pp. 497–504. IEEE, Aug. (2006)

  20. Walshaw C., Cross M.: Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM J. Sci. Comput. 22(1), 63–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Karypis, G.: Multi-constraint mesh partitioning for contact/impact computations. In: Proceedings Supercomputing’03, pp. 497–504. IEEE Computer Society, Washington, DC, USA (2003)

  22. Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. In: Proceedings ICPP, pp. 113–122 (1995)

  23. Karypis G., Kumar V.: Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48, 96–129 (1998)

    Article  Google Scholar 

  24. Gupta A.: Fast and effective algorithms for graph partitioning and sparse-matrix ordering. IBM J. Res. Develop. 41, 171–183 (1996)

    Article  Google Scholar 

  25. Frazer W.D., McKellar A.C.: Samplesort: a sampling approach to minimal storage tree sorting. J. ACM 17, 496–507 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  26. Chen J.C.: Efficient sample sort and the average case analysis of PEsort. Theoret. Comput. Sci. 369, 44–66 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. The OpenMP API specification for parallel programming. www.openmp.org

  28. Diaz J., Petit J., Serna M.: A Survey of graph layout problems. ACM Comput. Surveys 34(3), 313–356 (2002)

    Article  Google Scholar 

  29. Lai Y.L., Williams K.: On bandwidth for the tensor product of paths and cycles. Discrete Appl. Math. 73(2), 133–141 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  30. George P.L.: Automatic Mesh Generation: Application to Finite Element Methods. Wiley, New York (1991)

    MATH  Google Scholar 

  31. Sadeghi S., Mashadi M.M.: A new semi-automatic method for node numbering in a finite element mesh. Comput. Struct. 58, 183–187 (1996)

    Article  MATH  Google Scholar 

  32. Hughes T.J.R., Ferencz R.M., Hallquist J.O.: Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients. Comput. Methods Appl. Mech. Eng. 61(2), 215–248 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  33. Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms, pp. 145–164. 2nd edn. Printice-Hall of India, New Delhi (2003)

    Google Scholar 

  34. Hussain, M., Ahmad, M., Abid, M., Khokhar, A.: Implementation of 2D parallel ALE mesh generation technique in FSI problems using OpenMP. In: Proceedings FIT’09. Abbottabad, Pakistan, no. 18, December (2009)

  35. Wilkinson B., Allen M.: Parallel Programming—Techniques and Applications and Parallel Computers, pp. 145–164. 2nd edn. Printice-Hall of India, New Delhi (2003)

    Google Scholar 

  36. Grama A.Y., Gupta A., Kumar V.: Isoefficiency: measuring the scalability of parallel algorithms and architectures. IEEE Parallel Distrib. Technol 1(3), 12–21 (1993)

    Article  Google Scholar 

  37. Belytschko T., Liu W.K., Moran B.: Nonlinear Finite Elements for Continua and Structures. Wiley, New York (2006)

    Google Scholar 

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Authors and Affiliations

  1. FCSE, GIK Institute, Topi, Pakistan

    Masroor Hussain & Mushtaq Ahmad

  2. FME, GIK Institute, Topi, Pakistan

    Muhammad Abid

  3. University of Illinois at Chicago, Chicago, IL, USA

    Ashfaq Khokhar

  4. University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA

    Arif Masud

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  1. Masroor Hussain
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  2. Muhammad Abid
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  4. Ashfaq Khokhar
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  5. Arif Masud
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Correspondence to Masroor Hussain.

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Hussain, M., Abid, M., Ahmad, M. et al. A Parallel Implementation of ALE Moving Mesh Technique for FSI Problems using OpenMP. Int J Parallel Prog 39, 717–745 (2011). https://doi.org/10.1007/s10766-011-0168-3

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  • DOI: https://doi.org/10.1007/s10766-011-0168-3

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