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A General Computational Formalism for Networks of Structured Grids

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Abstract

Extended Cellular Automata (XCA) represent one of the most known parallel computational paradigm for the modeling and simulation of complex systems on stenciled structured grids. However, the formalism does not perfectly lend itself to the modeling of multiple automata were two or more models co-evolve by interchanging information and by synchronizing during the dynamic evolution of the system. Here we propose the Extended Cellular Automata Network (XCAN) formalism, an extension of the original XCA paradigm in which different automata are described by means of a graph, with vertices representing automata and inter-relations modeled by a set of edges. The formalism is applied to the modeling of a theoretical 2D/3D coupled system, where space/time variance and synchronization aspects are pointed out.

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Notes

  1. 1.

    The vinoAC acronym does not explicitly appear in the text.

References

  1. Aidun, C., Clausen, J.: Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andersson, B., et al.: Computational Fluid Dynamics for Engineers. Cambridge University Press, Cambridge (2011). https://doi.org/10.1017/CBO9781139093590

    Book  Google Scholar 

  3. Belli, G., et al.: A unified model for the optimal management of electrical and thermal equipment of a prosumer in a DR environment. IEEE Trans. Smart Grid 10(2), 1791–1800 (2019). https://doi.org/10.1109/TSG.2017.2778021

    Article  Google Scholar 

  4. Burks, A.W.: Programming and the theory of automata. In: Burks, A.W. (ed.) Essays on Cellular Automata, chap. 2, pp. 65–83. University of Illinois Press, Urbana (1970)

    Google Scholar 

  5. Calidonna, C.R., Naddeo, A., Trunfio, G.A., Di Gregorio, S.: CANv2: a hybrid CA model by micro and macro-dynamics examples. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds.) ACRI 2010. LNCS, vol. 6350, pp. 128–137. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15979-4_13

    Chapter  Google Scholar 

  6. Cervarolo, G., Mendicino, G., Senatore, A.: A coupled ecohydrological-three-dimensional unsaturated flow model describing energy, H2O and CO2 fluxes. Ecohydrology 3(2), 205–225 (2010)

    Google Scholar 

  7. Cicirelli, F., Furfaro, A., Giordano, A., Nigro, L.: An agent infrastructure for distributed simulations over HLA and a case study using unmanned aerial vehicles. In: 40th Annual Simulation Symposium (ANSS 2007), pp. 231–238, March 2007. https://doi.org/10.1109/ANSS.2007.10

  8. Cicirelli, F., Giordano, A., Nigro, L.: Distributed simulation of situated multi-agent systems. In: 2011 IEEE/ACM 15th International Symposium on Distributed Simulation and Real Time Applications, pp. 28–35, September 2011. https://doi.org/10.1109/DS-RT.2011.11

  9. Cicirelli, F., Forestiero, A., Giordano, A., Mastroianni, C.: Transparent and efficient parallelization of swarm algorithms. ACM Trans. Auton. Adapt. Syst. (TAAS) 11(2), 14 (2016)

    Google Scholar 

  10. Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Crisci, G.M., et al.: Predicting the impact of lava flows at Mount Etna. Italy. J. Geophys. Res. Solid Earth 115(B4), 1–14 (2010)

    Google Scholar 

  12. D’Ambrosio, D., et al.: The open computing abstraction layer for parallel complex systems modeling on many-core systems. J. Parallel Distrib. Comput. 121, 53–70 (2018). https://doi.org/10.1016/j.jpdc.2018.07.005

    Article  Google Scholar 

  13. D’Ambrosio, D., Rongo, R., Spataro, W., Trunfio, G.A.: Meta-model assisted evolutionary optimization of cellular automata: an application to the SCIARA model. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2011. LNCS, vol. 7204, pp. 533–542. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31500-8_55

    Chapter  Google Scholar 

  14. D’Ambrosio, D., Rongo, R., Spataro, W., Trunfio, G.A.: Optimizing cellular automata through a meta-model assisted memetic algorithm. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012. LNCS, vol. 7492, pp. 317–326. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32964-7_32

    Chapter  Google Scholar 

  15. Dattilo, G., Spezzano, G.: Simulation of a cellular landslide model with CAMELOT on high performance computers. Parallel Comput. 29(10), 1403–1418 (2003)

    Article  Google Scholar 

  16. De Rango, A., Napoli, P., D’Ambrosio, D., Spataro, W., Di Renzo, A., Di Maio, F.: Structured grid-based parallel simulation of a simple DEM model on heterogeneous systems. In: 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), pp. 588–595, March 2018. https://doi.org/10.1109/PDP2018.2018.00099

  17. Deng, X., Min, Y., Mao, M., Liu, H., Tu, G., Zhang, H.: Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids. J. Comput. Phys. 239, 90–111 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Filippone, G., Spataro, W., D’Ambrosio, D., Spataro, D., Marocco, D., Trunfio, G.: CUDA dynamic active thread list strategy to accelerate debris flow simulations. In: Proceedings - 23rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing, PDP 2015, pp. 316–320 (2015)

    Google Scholar 

  19. Filippone, G., D’Ambrosio, D., Marocco, D., Spataro, W.: Morphological coevolution for fluid dynamical-related risk mitigation. ACM Trans. Model. Comput. Simul. (TOMACS) 26(3), 18 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Folino, G., Mendicino, G., Senatore, A., Spezzano, G., Straface, S.: A model based on cellular automata for the parallel simulation of 3D unsaturated flow. Parallel Comput. 32(5), 357–376 (2006)

    Article  MathSciNet  Google Scholar 

  21. Frish, U., Hasslacher, B., Pomeau, Y.: Lattice gas automata for the Navier–Stokes equation. Phys. Rev. Lett. 56(14), 1505–1508 (1986)

    Article  Google Scholar 

  22. Fujimoto, R.M.: Parallel and Distribution Simulation Systems, 1st edn. Wiley, New York (1999)

    Google Scholar 

  23. Cervarolo, G., Mendicino, G., Senatore, A.: Coupled vegetation and soil moisture dynamics modeling in heterogeneous and sloping terrains. Vadose Zone J. 10, 206–225 (2011)

    Article  Google Scholar 

  24. Giordano, A., De Rango, A., D’Ambrosio, D., Rongo, R., Spataro, W.: Strategies for parallel execution of cellular automata in distributed memory architectures. In: 2019 27th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP), pp. 406–413, February 2019. https://doi.org/10.1109/EMPDP.2019.8671639

  25. Giordano, A., et al.: Parallel execution of cellular automata through space partitioning: the landslide simulation Sciddicas3-Hex case study. In: 2017 25th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), pp. 505–510, March 2017. https://doi.org/10.1109/PDP.2017.84

  26. Di Gregorio, S., Serra, R.: An empirical method for modelling and simulating some complex macroscopic phenomena by cellular automata. Future Gen. Comput. Syst. 16, 259–271 (1999)

    Article  Google Scholar 

  27. Higuera, F., Jimenez, J.: Boltzmann approach to lattice gas simulations. Europhys. Lett. 9(7), 663–668 (1989)

    Article  Google Scholar 

  28. Jammy, S., Mudalige, G., Reguly, I., Sandham, N., Giles, M.: Block-structured compressible Navier–Stokes solution using the OPS high-level abstraction. Int. J. Comput. Fluid Dyn. 30(6), 450–454 (2016)

    Article  MathSciNet  Google Scholar 

  29. Langton, C.: Computation at the edge of chaos: phase transition and emergent computation. Physica D 42, 12–37 (1990)

    Article  MathSciNet  Google Scholar 

  30. Lucà, F., D’Ambrosio, D., Robustelli, G., Rongo, R., Spataro, W.: Integrating geomorphology, statistic and numerical simulations for landslide invasion hazard scenarios mapping: an example in the Sorrento Peninsula (Italy). Comput. Geosci. 67(1811), 163–172 (2014)

    Article  Google Scholar 

  31. McNamara, G., Zanetti, G.: Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 61, 2332–2335 (1988)

    Article  Google Scholar 

  32. Mendicino, G., Pedace, J., Senatore, A.: Stability of an overland flow scheme in the framework of a fully coupled eco-hydrological model based on the macroscopic cellular automata approach. Commun. Nonlinear Sci. Numer. Simul. 21(1–3), 128–146 (2015)

    Article  Google Scholar 

  33. Mendicino, G., Senatore, A., Spezzano, G., Straface, S.: Three-dimensional unsaturated flow modeling using cellular automata. Water Resour. Res. 42(11), W11419 (2006)

    Article  Google Scholar 

  34. von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Champaign (1966)

    Google Scholar 

  35. Ninagawa, S.: Dynamics of universal computation and 1/f noise in elementary cellular automata. Chaos Solitons Fractals 70(1), 42–48 (2015)

    Article  MATH  Google Scholar 

  36. Oliverio, M., Spataro, W., D’Ambrosio, D., Rongo, R., Spingola, G., Trunfio, G.: OpenMP parallelization of the SCIARA cellular automata lava flow model: performance analysis on shared-memory computers. Procedia Comput. Sci. 4, 271–280 (2011)

    Article  Google Scholar 

  37. De Rango, A., Spataro, D., Spataro, W., D’Ambrosio, D.: A first multi-GPU/multi-node implementation of the open computing abstraction layer. J. Comput. Sci. 32, 115–124 (2019). https://doi.org/10.1016/j.jocs.2018.09.012

    Article  Google Scholar 

  38. Reguly, I., et al.: Acceleration of a full-scale industrial CFD application with OP2. IEEE Trans. Parallel Distrib. Syst. 27(5), 1265–1278 (2016). https://doi.org/10.1109/TPDS.2015.2453972

    Article  Google Scholar 

  39. Reguly, I., Mudalige, G., Giles, M., Curran, D., McIntosh-Smith, S.: The OPS domain specific abstraction for multi-block structured grid computations. In: Proceedings of WOLFHPC 2014: 4th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing - Held in Conjunction with SC 2014: The International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 58–67 (2014). https://doi.org/10.1109/WOLFHPC.2014.7

  40. Spataro, D., D’Ambrosio, D., Filippone, G., Rongo, R., Spataro, W., Marocco, D.: The new SCIARA-fv3 numerical model and acceleration by GPGPU strategies. Int. J. High Perform. Comput. Appl. 31(2), 163–176 (2017). https://doi.org/10.1177/1094342015584520

    Article  Google Scholar 

  41. Spingola, G., D’Ambrosio, D., Spataro, W., Rongo, R., Zito, G.: Modeling complex natural phenomena with the libAuToti cellular automata library: an example of application to lava flows simulation. In: PDPTA - International Conference on Parallel and Distributed Processing Techniques and Applications, pp. 277–283 (2008)

    Google Scholar 

  42. Thatcher, J.W.: Universality in the von Neumann cellular model. In: Burks, A.W. (ed.) Essays on Cellular Automata, chap. 5, pp. 132–186. University of Illinois Press, Urbana (1970)

    Google Scholar 

  43. Tie, B.: Some comparisons and analyses of time or space discontinuous Galerkin methods applied to elastic wave propagation in anisotropic and heterogeneous media. Adv. Model. Simul. Eng. Sci. 6(1) (2019). https://doi.org/10.1186/s40323-019-0127-x

  44. Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)

    MATH  Google Scholar 

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Correspondence to Donato D’Ambrosio .

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D’Ambrosio, D. et al. (2020). A General Computational Formalism for Networks of Structured Grids. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11973. Springer, Cham. https://doi.org/10.1007/978-3-030-39081-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-39081-5_22

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