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Parallel Structured Adaptive Mesh Refinement

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Parallel Computing

Parallel structured adaptive mesh refinement is a technique for efficient utilization of computational resources. It reduces the computational effort and memory requirements needed for numerical simulation of complex phenomena, described by partial differential equations. Structured adaptive mesh refinement (SAMR) is applied in simulations where the domain is divided into logically rectangular patches, where each patch is discretized with a structured mesh. The purpose of adaptive mesh refinement is to automatically adapt the mesh to the resolution required to epresent important features of the simulated phenomenon in different subdomains. In a parallel computing context, an important consequence of the adaptation is that the dynamically changing resolution leads to a dynamically changing work load, data volume, and communication pattern at run-time. This calls for dynamic load balancing and has implications for data placement as well as parallelization granularity.

This chapter gives an overview of structured adaptive mesh refinement approaches. After a brief introductory survey of SAMR techniques and software packages, the main part of the chapter addresses various issues related to implementation of SAMR on parallel computers. In particular programming models, data placement and load balancing are discussed, for shared memory as well as distributed memory platforms. Various approaches and algorithms are presented. The appropriate choice of dynamic load balancing algorithm, data placement strategy, programming model, etc., depends on both the application state and the computer platform. There is no single best alternative under all circumstances. Consequently, the chapter ends with an account of ongoing research where the objective is to equip SAMR-based simulation software with additional adaptivity, e.g., automatic selection of load balancing algorithms and automatic decision about level of parallelization granularity using a hybrid MPI/OpenMP programming model.

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References

  1. E. Steinthorsson, D. Modiano, Advanced methodology for simulation of complex flows using structured grid systems, Tech. Rep. 95-28, ICOMP, NASA Lewis Research Center, Cleveland, OH (1995).

    Google Scholar 

  2. L. Ferm, P. Lötstedt, P. Sjöberg, Conservative solution of the Fokker–Planck equation for stochastic chemical reactions, BIT 46 (2006) 561–583.

    Article  Google Scholar 

  3. M. J. Berger, J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics 53 (1984) 484–512.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. J. Berger, P. Colella, Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics 82 (1989) 64–84.

    Article  MATH  Google Scholar 

  5. M. J. Berger, Data structures for adaptive grid generation, SIAM Journal on Scientific and Statistical Computing 7 (1986) 904–916.

    Article  MATH  Google Scholar 

  6. J. Dreher, R. Grauer, Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws, Parallel Computing 31 (2005) 913–932.

    Article  MathSciNet  Google Scholar 

  7. L. Ferm, P. Lötstedt, Blockwise adaptive grids with multigrid acceleration for compressible flow, AIAA J. 37 (1999) 121–123.

    Article  Google Scholar 

  8. P. Lötstedt, S. Söderberg, Parallel solution of hyperbolic pdes with space-time adaptivity, in: D. H. R. Vilsmeier, F. Benkhaldour (Ed.), Finite Volumes for Complex Applications II, Hermes Science, Paris, 1999, pp. 769–776.

    Google Scholar 

  9. P. Lötstedt, S. Söderberg, A. Ramage, L. Hemmingsson-Frändén, Implicit solution of hyperbolic equations with space-time adaptivity, BIT 42 (2002) 128–153.

    Article  Google Scholar 

  10. P. MacNeice et al, PARAMESH: A parallel adaptive mesh refinement community toolkit, Computer Physics Communications 126 (2000) 330–354.

    Article  MATH  Google Scholar 

  11. K. G. Powell et al., A solution-adaptive upwind scheme for ideal magnetohydrodynamics, Journal of Computational Physics 154 (1999) 284–309.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. A. Trompert, Local uniform grid refinement for time-dependent partial differential equations, Ph.D. thesis, University of Amsterdam (1994).

    Google Scholar 

  13. Z. Lan, V. E. Taylor, G. Bryan, A novel dynamic load balancing scheme for parallel systems, Journal of Parallel and Distributed Computing 62 (2002) 1763–1781.

    Article  MATH  Google Scholar 

  14. P. Colella, D. T. Graves, N. D. Keen, T. J. Ligocki, D. F.Martin, P.W. McCorquodale, D. Modiano, P. O. Schwartz, T. D. Sternberg, B. V. Straalen, Chombo software package for AMR applications: Design document, Available at the Chombo website: http://seesar.lbl.gov/ANAG/chombo/ (September 2008).

  15. R. Deiterding, Parallel adaptive simulation of multi-dimensional detonation structures, Ph.D. thesis, Brandenburgische Technische Universität Cottbus (2003).

    Google Scholar 

  16. R. Deiterding, Detonation structure simulation with AMROC, in: L. Y. et. al. (Ed.), High Performance Computing and Communications, No. 3726 in Lecture Notes in Computer Science, Springer, Berlin Heidelberg, (2005), pp. 916–927.

    Google Scholar 

  17. M. Parashar, J. Browne, System engineering for high performance computing software: The HDDA/DAGH infrastructure for implementation of parallel structured adaptive mesh refinement, in: Structured Adaptive Mesh Refinement Grid Methods, Volume 117 of IMA Volumes in Mathematics and its Applications, Springer-Verlag, Berlin (2000), pp. 1–18.

    Google Scholar 

  18. C. Rendleman, V. Beckner, M. Lijewski, W. Crutchfield, J. Bell, Parallelization of structured, hierarchical adaptive mesh refinement algorithms, Computing and Visualization in Science 3 (2000) 147–157.

    Article  MATH  Google Scholar 

  19. A. Wissink, R. Hornung, S. Kohn, S. Smith, N. Elliott, Large scale parallel structured AMR calculations using the SAMRAI framework, in: Proceedings of Supercomputing 2001, Denver, USA, (2001).

    Google Scholar 

  20. M. Berger, R. LeVeque, Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems, SIAM Journal of Numerical Analysis 35 (1998) 2298–2316.

    Article  MATH  MathSciNet  Google Scholar 

  21. R. Blikberg, T. Sørevik, Load balancing and OpenMP implementation of nested parallelism, Parallel Computing 31 (2005) 984–998.

    Article  Google Scholar 

  22. L. Bebreu, C. Vouland, E. Blayo, AGRIF: Adaptive grid refinement in Fortran, Computers and Geosciences 34 (2008) 8–13.

    Article  Google Scholar 

  23. M. J. Berger, I. Rigoutsos, An algorithm for point clustering and grid generation, IEEE Transactions on Systems, Man and Cybernetics 21 (1991) 1278–1286.

    Article  Google Scholar 

  24. J. Pilkington, S. Baden, Dynamic partitioning of non-uniform structured workloads with spacefilling curves, IEEE Transactions on Parallel and Distributed Systems 7 (3) (1996) 288– 300.

    Article  Google Scholar 

  25. J. Rantakokko, Partitioning strategies for structured multiblock grids, Parallel Computing 26 (12) (2000) 1161–1680.

    Article  MathSciNet  Google Scholar 

  26. M. Thuné, Partitioning strategies for composite grids, Parallel Algorithms and Applications 11 (1997) 325–348.

    MathSciNet  Google Scholar 

  27. D. Balsara, C. Norton, Highly parallel structured adaptive mesh refinement using languagebased approaches, Journal of parallel computing 27 (2001) 37–70.

    Article  MATH  Google Scholar 

  28. R. D. Hornung, S. Kohn, The SAMRAI homepage, structured adaptive mesh refinement applications infrastructure, http://www.llnl.gov/CASC/SAMRAI/.

  29. J. J. Quirk, A parallel adaptive grid algorithm for computational shock hydrodynamics, Applied Numerical Mathematics 20 (1996) 427–453.

    Article  MATH  MathSciNet  Google Scholar 

  30. M. Parashar, J. C. Browne, On partitioning dynamic adaptive grid hierarchies, presented at HICSS-29 (1996).

    Google Scholar 

  31. J. Steensland, Efficient partitioning of dynamic structured grid hierarchies, Ph.D. thesis, Uppsala University (2002).

    Google Scholar 

  32. Z. Lan, V. Taylor, G. Bryan, Dynamic load balancing of SAMR applications on distributed systems, in: Proceedings of Supercomputing 2001, (2001).

    Google Scholar 

  33. M. Thuné, Straightforward partitioning of composite grids for explicit difference methods, Parallel Computing 17 (1991) 665–672.

    Article  MATH  MathSciNet  Google Scholar 

  34. H. Johansson, A. Vakili, A patch-based partitioner for parallel SAMR applications, accepted for publication in the proceedings of the IASTED International Conference on Parallel and Distributed Computing and Systems, November 2008.

    Google Scholar 

  35. J. Berger, S. Bokhari, A partitioning strategy for non-uniform problems onmultiprocessors, IEEE Transactions on Computers 85 (1987) 570–580.

    Article  Google Scholar 

  36. S. H. Bokhari, T. W. Crockett, D. M. Nicol, Binary dissection: Variants & applications, Tech. Rep. ICASE Report No. 97-29, NASA Langley Research Center, Hampton, VA (1997).

    Google Scholar 

  37. J. Rantakokko, Strategies for parallel variational data assimilation, Parallel Computing 23 (1997) 2017–2039.

    Article  MATH  Google Scholar 

  38. J. Rantakokko, A framework for partitioning structured grids with inhomogeneous workload, Parallel Algorithms and Applications 13 (1998) 135–152.

    MATH  MathSciNet  Google Scholar 

  39. C.-W. Ou, S. Ranka, Parallel remapping algorithms for adaptive problems, Journal of Parallel and Distributed Computing 42 (1997) 109–121.

    Article  Google Scholar 

  40. J. Steensland, Dynamic structured grid hierarchy partitioners using inverse space-filling curves, Tech. Rep. 2001-002, Uppsala University, Department of Information Technology, Uppsala, Sweden (2001).

    Google Scholar 

  41. J. Steensland, M. Thuné, S. Chandra, M. Parashar, Towards an adaptive meta-partitioner for parallel SAMR applications, in: Proceedings of the IASTED International Conference on Parallel and Distributed Computing Systems, Las Vegas, (2000), pp. 425–430.

    Google Scholar 

  42. J. Steensland, S. Söderberg, M. Thuné, Comparison of dynamic load balancing techniques for a parallel SAMR algorithm, in: T. Sørevik, F. Manne, R. Moe, A. H. Gebremedhin (Eds.), Applied Parallel Computing—New Paradigms for HPC in Industry and Academia, Springer-Verlag, Heidelberg, (2001), pp. 160–169, (Lecture Notes in Computer Science, Vol. 1947).

    Chapter  Google Scholar 

  43. E. N. Houstis et al., PYTHIA-II: A knowledge/database system for managing performance data and recommending scientific software, ACM TOMS 26 (2000) 227–253.

    Article  MATH  Google Scholar 

  44. N. Ramakrishnan, C. J. Ribbens, Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes, ACM TOMS 26 (2000) 254–273.

    Article  MATH  Google Scholar 

  45. S. Chandra, Armada: A framework for adaptive application-sensitive runtime management of dynamic applications, Master’s Thesis, Graduate School, Rutgers University, NJ (2002).

    Google Scholar 

  46. J. Rantakokko, Comparison of parallelization models for structured adaptive mesh refinement, in: M. Danelutto, D. Laforcena, M. Vanneschi (Eds.), Lecture Notes in Computer Science 3149, Springer-Verlag, Heidelberg (2004), pp. 615–623.

    Google Scholar 

  47. M. Nordén, H. Löf, J. Rantakokko, S. Holmgren, Geographical locality and dynamic data migration for OpenMP implementations of adaptive PDE solvers, in: Lecture Notes in Computer Science 4315, (2008), pp. 382–393.

    Article  Google Scholar 

  48. J. Rantakokko, An integrated decomposition and partitioning approach for irregular blockstructured applications, in: J. Romlin et al. (Ed.), Proceedings of the IEEE International Parallel and Distributed Processing Symposium, IPDPS 2000, Springer–Verlag, Berlin, (2000), pp. 485–496, Lecture Notes in Computer Science, Vol. 1800.

    Google Scholar 

  49. T. Wilhelmsson et al., Increasing resolution and forecast length with a parallel ocean model, in: Proceedings of the Second EuroGOOS International Conference, (1999).

    Google Scholar 

  50. T. Wilhelmsson, J. Schüle, Running an operational baltic sea model on the T3E, in: Proceedings of the Fifth European SGI/Cray MPP Workshop, Cineca, Bologna, (1999).

    Google Scholar 

  51. J. Rantakokko, A dynamic MPI-OpenMP model for structured adaptive mesh refinement, Parallel Processing Letters 15 (2005) 37–47.

    Article  MathSciNet  Google Scholar 

  52. H. Johansson, Performance characterization and evaluation of parallel PDE solvers, Licentiate Thesis 2006-010, Department of Information Technology, Uppsala University (2006).

    Google Scholar 

  53. H. Johansson, Design and implementation of a dynamic and adaptive meta-partitioner for parallel SAMR grid hierarchies;, Technical Report 2008-017, Department of Information Technology, Uppsala University (2008).

    Google Scholar 

  54. The Common Component Architechture, http://www.cca-forum.org/.

  55. L. Li, B. Norris, H. Johansson, L. C. McInnes, J. Ray, Component infrastructure for managing performance data and runtime adaptation of parallel applications, accepted for publication in the Proceedings of PARA2008, Trondheim, Norway, 2008.

    Google Scholar 

  56. J. O. Kephart, D.M. Chess, The vision of autonomic computing, IEEE Computer 36 (1) (2003) 41–50.

    Google Scholar 

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Sweden

    Jarmo Rantakokko & Michael Thuné

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  1. Jarmo Rantakokko
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  2. Michael Thuné
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Correspondence to Jarmo Rantakokko .

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Editors and Affiliations

  1. Dept. Communication Systems, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

    Roman Trobec

  2. Department of Computer Sciences, University of Salzburg, Jakob–Haringer Str. 2, 5020 Salzburg, Austria

    Marián Vajteršic  & Peter Zinterhof  & 

  3. Mathematical Institute Department of Informatics, Slovak Academy of Sciences, Dúbravská 9, 840 00 Bratislava, Slovakia

    Marián Vajteršic

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Rantakokko, J., Thuné, M. (2009). Parallel Structured Adaptive Mesh Refinement. In: Trobec, R., Vajteršic, M., Zinterhof, P. (eds) Parallel Computing. Springer, London. https://doi.org/10.1007/978-1-84882-409-6_5

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  • DOI: https://doi.org/10.1007/978-1-84882-409-6_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-408-9

  • Online ISBN: 978-1-84882-409-6

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