Ocean Dynamics

, Volume 67, Issue 5, pp 639–649 | Cite as

A parallel domain decomposition algorithm for coastal ocean circulation models based on integer linear programming

Part of the following topical collections:
  1. Topical Collection on the 8th International Workshop on Modeling the Ocean (IWMO), Bologna, Italy, 7-10 June 2016


This paper presents a new parallel domain decomposition algorithm based on integer linear programming (ILP), a mathematical optimization method. To minimize the computation time of coastal ocean circulation models, the ILP decomposition algorithm divides the global domain in local domains with balanced work load according to the number of processors and avoids computations over as many as land grid cells as possible. In addition, it maintains the use of logically rectangular local domains and achieves the exact same results as traditional domain decomposition algorithms (such as Cartesian decomposition). However, the ILP decomposition algorithm may not converge to an exact solution for relatively large domains. To overcome this problem, we developed two ILP decomposition formulations. The first one (complete formulation) has no additional restriction, although it is impractical for large global domains. The second one (feasible) imposes local domains with the same dimensions and looks for the feasibility of such decomposition, which allows much larger global domains. Parallel performance of both ILP formulations is compared to a base Cartesian decomposition by simulating two cases with the newly created parallel version of the Stevens Institute of Technology’s Estuarine and Coastal Ocean Model (sECOM). Simulations with the ILP formulations run always faster than the ones with the base decomposition, and the complete formulation is better than the feasible one when it is applicable. In addition, parallel efficiency with the ILP decomposition may be greater than one.


Coastal ocean circulation model Parallel computing Domain decomposition Integer linear programming Urban ocean ECOM 



This work was partially funded by a research task agreement entered between the Trustees of the Stevens Institute of Technology and the Port Authority of New York and New Jersey, effective August 19, 2014. The authors would like to acknowledge the unwavering support of Mr. David Dodd, Vice President for Information Technology and CIO at Stevens Institute of Technology. We would also like to thank Karen Swift, Kevin Ying, Joe Formoso, David Runnels, Kurt Hockenbury, and James Cunningham, for their assistance with the Pharos Hyperscale Supercomputing Facility.


  1. Asselin R (1972) Frequency filters for time integrations. Mon Weather Rev 100:487–490CrossRefGoogle Scholar
  2. Belov G, Kartak V, Rohling H, Scheithauer G (2009) One-dimensional relaxations and lp bounds for orthogonal packing. Int Trans Oper Res 16:745–766CrossRefGoogle Scholar
  3. Bleck R (2002) An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Model 4:55–88CrossRefGoogle Scholar
  4. Blumberg AF, Georgas N (2008) Quantifying uncertainty in estuarine and coastal ocean circulation modeling. J Hydraul Eng 134:403–415CrossRefGoogle Scholar
  5. Blumberg AF, Mellor GL (1983) Diagnostic and prognostic numerical circulation studies of the South Atlantic Bight. J Geophys Res 88:4579–4592CrossRefGoogle Scholar
  6. Blumberg AF, Khan LA, St. John JP (1999) Three-dimensional hydrodynamic model of New York Harbor region. J Hydraul Eng 125:799–816CrossRefGoogle Scholar
  7. Blumberg AF, Georgas N, Yin L, Herrington TO, Orton PM (2015) Street-scale modeling of storm surge inundation along the New Jersey Hudson River Waterfront. J Atmos Ocean Tech 32:1486–1497CrossRefGoogle Scholar
  8. Bryan K, Cox M (1969) A numerical method for the study of the circulation of the world ocean. J Comput Phys 4:347–376CrossRefGoogle Scholar
  9. Capet X, Mcwilliams JC, Mokemaker MJ, Shchepetkin AF (2008) Mesoscale to submesoscale transition in the California current system. Part i: flow structure, eddy flux, and observational tests. J Phys Oceanogr 38:29–43. doi: 10.1175/2007jpo3671.1 CrossRefGoogle Scholar
  10. Chen CS, Liu HD, Beardsley RC (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. J Atmos Ocean Tech 20:159–186CrossRefGoogle Scholar
  11. Cowles GW (2008) Parallelization of the FVCOM coastal ocean model. Int J High Perform Comput Appl 22:177–193. doi: 10.1177/1094342007083804 CrossRefGoogle Scholar
  12. Dennis JM (2007) Inverse space-filling curve partitioning of a global ocean model. Parallel and Distributed Processing Symposium, 2007 IPDPS 2007 I.E. International, IEEE, pp 1–10Google Scholar
  13. Di Liberto T, Colle BA, Georgas N, Blumberg AF, Taylor AA (2011) Verification of a multimodel storm surge ensemble around New York City and Long Island for the cool season. Weather Forecast 26:922–939CrossRefGoogle Scholar
  14. Dukowicz JK, Smith RD (1994) Implicit free-surface method for the Bryan-Cox-Semtner ocean model. J Geophys Res-Oceans 99:7991–8014CrossRefGoogle Scholar
  15. Dunning I, Huchette J and Lubin M (2015) Jump: a modeling language for mathematical optimization. arXiv preprint arXiv:150801982Google Scholar
  16. Feige U (1998) A threshold of ln n for approximating set cover. Journal of the ACM (JACM) 45:634–652CrossRefGoogle Scholar
  17. Fekete SP, Schepers J (2004) A combinatorial characterization of higher-dimensional orthogonal packing. Math Oper Res 29:353–368CrossRefGoogle Scholar
  18. Flaherty JE, Loy RM, Shephard MS, Szymanski BK, Teresco JD, Ziantz LH (1997) Adaptive local refinement with Octree load balancing for the parallel solution of three-dimensional conservation laws. J Parallel Distrib Comput 47:139–152CrossRefGoogle Scholar
  19. Georgas N and Blumberg AF (2010) Establishing confidence in marine forecast systems: the design and skill assessment of the New York Harbor observation and prediction system, version 3 (NYHOPS v3). 11th International Conference in Estuarine and Coastal Modeling (ECM11) Spalding, ML, Ph D, PE, American Society of Civil Engineers, Washington, pp 660–685Google Scholar
  20. Georgas N, Blumberg AF, Herrington TO (2007) An operational coastal wave forecasting model for New Jersey and Long Island waters. Shore and Beach 75:30Google Scholar
  21. Georgas N, Blumberg AF, Bruno MS and Runnels DS (2009) Marine forecasting for the New York urban waters and harbor approaches: the design and automation of NYHOPS. 3rd International Conference on Experiments/Process/System Modelling/Simulation & Optimization Demos T Tsahalis, Ph D, University of Patras, Greece, pp 345–352Google Scholar
  22. Georgas N, Yin L, Jiang Y, Wang Y, Howell P, Saba V, Schulte J, Orton P, Wen B (2016) An open-access, multi-decadal, three-dimensional, hydrodynamic hindcast dataset for the long island sound and new york/new jersey harbor estuaries. J Mar Sci Eng 4:48CrossRefGoogle Scholar
  23. Griffies S, Gnanadesikan A, Dixon KW, Dunne J, Gerdes R, Harrison MJ, Rosati A, Russell J, Samuels BL, Spelman MJ (2005) Formulation of an ocean model for global climate simulations. Ocean Sci 1:45–79CrossRefGoogle Scholar
  24. Hendrickson B, Kolda TG (2000) Graph partitioning models for parallel computing. Parallel Comput 26:1519–1534CrossRefGoogle Scholar
  25. Hurlburt HE, Hogan PJ (2000) Impact of 1/8 degrees to 1/64 degrees resolution on gulf stream model—data comparisons in basin-scale subtropical atlantic ocean models. Dynam Atmos Oceans 32:283–329CrossRefGoogle Scholar
  26. Jones PW, Worley PH, Yoshida Y, White JB, Levesque J (2005) Practical performance portability in the parallel ocean program (pop). Concurr Comp-Pract E 17:1317–1327. doi: 10.1002/cpe.894 CrossRefGoogle Scholar
  27. Jordi A, Wang D-P (2009) Mean dynamic topography and eddy kinetic energy in the Mediterranean sea: comparison between altimetry and a 1/16 degree ocean circulation model. Ocean Model 29:137–146. doi: 10.1016/j.ocemod.2009.04.001 CrossRefGoogle Scholar
  28. Jordi A, Wang DP (2012) SbPOM: a parallel implementation of Princeton ocean model. Environ Model Softw 38:59–61. doi: 10.1016/J.Envsoft.2012.05.013 CrossRefGoogle Scholar
  29. Kerbyson DJ, Jones PW (2005) A performance model of the parallel ocean program. Int J High Perform Comput Appl 19:261–276. doi: 10.1177/1094342005056114 CrossRefGoogle Scholar
  30. Klein P, Hua BL, Lapeyre G, Capet X, Le Gentil S, Sasaki H (2008) Upper ocean turbulence from high-resolution 3d simulations. J Phys Oceanogr 38:1748–1763. doi: 10.1175/2007jpo3773.1 CrossRefGoogle Scholar
  31. Leung JY (2004) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press, Boca RatonGoogle Scholar
  32. Madala RV, Piacseki SA (1977) A semi-implicit numerical model for baroclinic oceans. J Comput Phys 23:167–178CrossRefGoogle Scholar
  33. Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997) A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J Geophys Res-Oceans 102:5753–5766CrossRefGoogle Scholar
  34. Mellor GL, Yamada T (1982) Development of a turbulent closure model for geophysical fluid problems. Rev Geophys 20:851–875CrossRefGoogle Scholar
  35. Mesyagutov M, Scheithauer G, Belov G (2012) Lp bounds in various constraint programming approaches for orthogonal packing. Comput Oper Res 39:2425–2438CrossRefGoogle Scholar
  36. Orton P, Georgas N, Blumberg A, Pullen J (2012) Detailed modeling of recent severe storm tides in estuaries of the New York city region. J Geophys Res Oceans (1978–2012) 117Google Scholar
  37. Padberg M, Rinaldi G (1991) A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev 33:60–100CrossRefGoogle Scholar
  38. Pilkington JR, Baden SB (1996) Dynamic partitioning of non-uniform structured workloads with spacefilling curves. IEEE Trans Parallel Distrib Syst 7:288–300CrossRefGoogle Scholar
  39. Saule E, Baş EÖ, Çatalyürek ÜV (2012) Load-balancing spatially located computations using rectangular partitions. J Parallel Distrib Comput 72:1201–1214CrossRefGoogle Scholar
  40. Shchepetkin AF, McWilliams JC (2005) The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Model 9:347–404. doi: 10.1016/j.ocemod.2004.08.002 CrossRefGoogle Scholar
  41. Sierksma G (2001) Linear and integer programming: theory and practice. CRC Press, Boca RatonGoogle Scholar
  42. Smagorinsky J (1963) General circulation experiments with primitive equations, i, the basic experiment. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
  43. Wang D-P, Jordi A (2011) Surface frontogenesis and thermohaline intrusion in a shelfbreak front. Ocean Model 38:161–170. doi: 10.1016/j.ocemod.2011.02.012 CrossRefGoogle Scholar
  44. Wang P, Song YT, Chao Y, Zhang HC (2005) Parallel computation of the regional ocean modeling system. Int J High Perform Comput Appl 19:375–385CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Davidson LaboratoryStevens Institute of TechnologyHobokenUSA

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