Skip to main content
SpringerLink
Log in

BEM for wave interaction with structures and low storage accelerated methods for large scale computation

  • Review Article
  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

The boundary element method (BEM) is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required calculations and storage increase rapidly with the increase of the structure scale. Thus, an accelerated method with a low storage is desirable for the wave interaction with a very large structure. A systematic review is given in this paper for the BEM for solving the problem of the wave interaction with a large scale structure. Various integral equations are derived based on different Green functions, the advantages and disadvantages of different discretization schemes of the integral equations by the constant panels, the higher order elements, and the spline functions are discussed. For the higher order element discretization method, the special concerns are given to the numerical calculations of the single-layer potential, the double layer potential and the solid angle coefficients. For a large scale computation problem such as the wave interaction with a very large structure or a large number of bodies, the BEMs with the FMM and pFFT accelerations are discussed, respectively, including the principles of the FMM and the pFFT, and their implementations in various integral equations with different Green functions. Finally, some potential applications of the acceleration methods for problems with large scale computations in the ocean and coastal engineering are introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li Y. C., Teng B. Wave action on marine structures [M]. Beijing, China: China Ocean Press, 2015 (in Chinese).

    Google Scholar 

  2. Hess J. L., Smith A. M. O. Calculation of non-lifting potential flow about arbitrary three-dimensional bodies [J]. Journal of Ship Research, 1964, 8: 22–44.

    Google Scholar 

  3. Faltinsen O. M., Michelsen F. C. The effect of large structures in waves at zero Froude number [C]. Proceedings Dynamics of Marine Vehicles and Structures in Waves. London, UK, 1974, 99–114.

    Google Scholar 

  4. Garrison C. J. Hydrodynamic loading of large volume offshore structure: Three-dimensional source distribution method (Zienkiewicz O. C. et al. Numerical methods in offshore engineering) [M]. Chichester, UK: Wiley, 1979.

    Google Scholar 

  5. Liu Y. H., Kim C. H., Kim M. H. The computation of mean drift forces and wave run-up by higher-order boundary element method [C]. The First International Offshore and Polar Engineering Conference. Edinburgh, UK, 1991, 476–481.

    Google Scholar 

  6. Liu Y. H., Kim C. H., Lu X. S. Comparison of higher-order boundary element and constant panel methods for hydrodynamic loadings [J]. International Journal of Offshore and Polar Engineering, 1991, 1(1): 8–17.

    Google Scholar 

  7. Eatock Taylor R., Chau F. P. Wave diffraction-some developments in linear and non-linear theory [C]. Proceedings of the 10th International Conference on Offshore Mechanics and Arctic Engineering. Stavanger, Norway, 1991.

    Google Scholar 

  8. Teng B., Eatock Taylor R. New higher order boundary element method for wave diffraction/radiation [J]. Applied Ocean Research, 1995, 17(2): 71–77.

    Article  Google Scholar 

  9. He G. H., Chen K. M., Zhang J. S. et al. Iterative Rankine HOBEM analysis of hull-form effects in forwards-speed diffraction problem [J]. Journal of Hydrodynamics, 2017, 29(2): 226–234.

    Article  Google Scholar 

  10. Xi C., Zhu R. C., Ma C. et al. Computation of linear and nonlinear ship waves by higher-order boundary element method [J]. Ocean Engineering, 2016, 114: 142–153.

    Article  Google Scholar 

  11. Maniar H. D. A three dimensional higher order panel method based on B-splines [D]. Doctoral Thesis, Cambirdge, MA, USA: Massachusetts Institute of Technology, 1995.

    Google Scholar 

  12. Teng B., Bai W. A B-spline based BEM and its application in predicting wave forces on 3D bodies [J]. China Ocean Engineering, 1999, 13(3): 257–264.

    Google Scholar 

  13. Newman J. N., Maniar H. D., Lee C. H. Analysis of wave effects for very large floating structures [C]. The International Workshop on Very Large Floating Structures (VLFS’96). Hayama, Japan, 1996, 135–142.

    Google Scholar 

  14. Ohkusu M., Nanba Y. Analysis of hydroelastic behavior of a large floating platform of thin plate configuration in waves [C]. The International Workshop on Very Large Floating Structures (VLFS’96). Hayama, Japan, 1996, 143–148.

    Google Scholar 

  15. Liu Y. Z., Cui W. C., Wu Y. S. Hydroelasticity of VLFS [C]. Proceedings of the 17th National Conference on Hydrodynamics and the 6th National Congress on Hydrodynamics. Hong Kong, China, 2003, 76–89 (in Chinese).

    Google Scholar 

  16. Wu Y. S., Zou M. S., Tian C. et al. Theory and application of coupled fluid-structure interaction of ships in waves and ocean acoustic environment [J]. Journal of Hydrodynamics, 2016, 28(6): 923–936.

    Article  Google Scholar 

  17. Falnes J., Hals J. Heaving buoys, point absorbers and arrays [J]. Philosophical Transactions of the Royal Society, A, 2012, 370(1959): 246–277.

    Article  Google Scholar 

  18. Nihous G. C. Wave power extraction by arbitrary arrays of non-diffracting oscillating water columns [J]. Ocean Engineering, 2012, 51: 94–105.

    Article  Google Scholar 

  19. Rokhlin V. Rapid solution of integral equations of classical potential theory [J]. Journal of Computational Physics, 1985, 60(2): 187–207.

    Article  MathSciNet  Google Scholar 

  20. Greengard L., Rokhlin V. A fast algorithm for particle simulations [J]. Journal of Computational Physics, 1987, 73(2): 325–348.

    Article  MathSciNet  Google Scholar 

  21. Greengard L. The rapid evaluation of potential fields in particle systems [M]. Cambridge, MA, USA: MIT Press, 1988.

    MATH  Google Scholar 

  22. Korsmeyer F. T., Phillips J. R., Nabors K. et al. Some empirical results on using multipole-accelerated iterative methods to solve 3-D potential integral equations [C]. Proceedings: Parallel Numerical Algorithms: Proceedings of an ICASE/LaRC Workshop. Hampton, VA, USA, 1995.

    Google Scholar 

  23. Nabors K., Phillips J. R. Korsmeyer F. T. et al. Multipole and Precorrected-FFT accelerated iterative methods for solving surface integral formulations of three-dimensional Laplace problems (Domain-based parallelism and problem decomposition methods in science and engineering) [M]. Philadelphia, USA: Society for Industrial and Applied Mathematics, 1995.

    MATH  Google Scholar 

  24. Phillips J. R., White J. K. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures [J]. IEEE Transactions on Computer-Aided Design, 1997, 16(10): 1059–1072.

    Article  Google Scholar 

  25. Nygaard J. O., Grue J. Wavelet methods for the solution of wave-body problems [J]. Journal of Engineering Mathe-matics, 1998, 38(3): 323–354.

    Article  MathSciNet  Google Scholar 

  26. John F. On the motion of floating bodies. I [J]. Communications on Pure Applied Mathematics, 1949, 2(1): 13–57.

    Article  MathSciNet  Google Scholar 

  27. John F. On the motion of floating bodies. II [J]. Communications on Pure Applied Mathematics, 1950, 3(1): 45–101.

    Article  MathSciNet  Google Scholar 

  28. Wehausen J. V., Laitone E. V. Surface waves [M]. Berlin, Germany: Springer-Verlag, 1960, 9: 446–778.

    Google Scholar 

  29. Li H. B., Han G. M., Mang H. A. A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method [J]. International Journal of Numerical Methods in Engineering, 1985, 21(11): 2071–2098.

    Article  MathSciNet  Google Scholar 

  30. Teng B., Gou Y., Ning D. Z. A higher-order BEM for wave action with structures-direct computation of free term coefficient and CPV integral [J]. Acta Oceanologica Sinica, 2006, 28(1): 132–138.

    Google Scholar 

  31. Teng B. Theory of wave interaction with structures and its application [M]. Beijing, China: China Ocean Press, 2010, 549–565 (in Chinese).

    Google Scholar 

  32. Montic V. A new formula for the C-matrix in the Somi-gliana identity [J]. Journal of Elasticity, 1993, 33(3): 191–201.

    Article  MathSciNet  Google Scholar 

  33. Nabors K., WHITE J. K. Multipole-accelerated capacitance extraction algorithms for 3-D structures with multiple dielectrics [J]. IEEE Transactions Circuits and Systems I: Fundamental Theory and Applications, 1992, 39(12): 946–954.

    Article  Google Scholar 

  34. Watanabe O., Hayami K. A fast solver for the boundary element method using multipole expansion [C]. Proceedings 4th BEM Technology Conference (BTEC94), JASCOME. Tokyo, Japan, 1994, 39–44 (in Japanese).

    Google Scholar 

  35. Nishida T., Hayami K. Application of the fast multipole method to the 3-D BEM analysis of electron guns [C]. Proceedings of the 19th International Boundary Element Conference held in Rome. Rome, Italy, 1997, 613–622.

    MATH  Google Scholar 

  36. Nie Z. P., Hu J., Yao H. Y. et al. The fast multipole method for vector analysis of scattering from 3-dimen-sional objects with complex structure [J]. Acta Electronica Sinica, 1999, 27(6): 104–109.

    Google Scholar 

  37. Nishimura N., Yoshida K., Kobayashi S. A fast multipole boundary integral equation method for crack problems in 3D [J]. Engineering Analysis with Boundary Elements, 1999, 23(1): 97–105.

    Article  Google Scholar 

  38. Gomez J. E., POWER H. A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number [J]. Engineering Analysis with Boundary Elements, 1997, 19(1): 17–31.

    Article  Google Scholar 

  39. Teng B., Chen B. A multipole expansion method for current diffraction from bodies [C]. Proceeding of the Fourth International Conference on Fluid Mechanics. Dalian, China, 2004.

    Google Scholar 

  40. Teng B., Ning D. Z., Gou Y. A fast multipole boundary element method for three-dimensional potential flow problems [J]. Atca Oceanologica Sinica, 2004, 23(4): 747–756.

    Google Scholar 

  41. Ning D. Z., Teng B., Geng B. L. Application of the accelerated desingularized BEM in water wave problems [C]. ISOPE’2005. Seoul, Korea, 2005.

    Google Scholar 

  42. Utsunomiya T., Watanabe E., Nishimura N. Fast multipole algorithm for wave diffraction/radition problems and its application to VLFS in variable water depth and topography [C]. Proceedings of the 12th International Conference on Offshore Mechanics and Arctic Engineering. Rio de Janeiro, Brazil, 2001.

    Google Scholar 

  43. Utsunomiya T., Watanabe E. Accelerates higher order boundary element method for wave diffraction/radiation problems and its applications [C]. The 12th International Offshore and Polar Engineering Conference. Kitakyushu, Japan, 2002, 3: 305–312

    Google Scholar 

  44. Utsunomiya T., Watanabe E. Wave response analysis of hybrid-type VLFS by accelerated BEM [C]. Hydroela-sticity in Marine Technology. Oxford, UK, 2003, 297–303.

    Google Scholar 

  45. Teng B., Gou Y. Fast multipole expansion method and its application in bem for wave diffraction and radiation [C]. The 16th International Offshore and Polar Engineering Conference. San Francisco, USA, 2006, 3: 318–325.

    Google Scholar 

  46. Mei C. C., Stiassnie M., Yue D. K. P. Theory and applications of ocean surface waves, Part 1: Linear aspects [M]. Singapore: World Scientific, 2005.

    MATH  Google Scholar 

  47. Yan H., Liu Y. An efficient high-order boundary element method for nonlinear wave–wave and wave-body interactions [J]. Journal of Computational Physics, 2011, 230(2): 402–424.

    Article  MathSciNet  Google Scholar 

  48. Korsmeyer F. T., Phillips J. R., White J. K. Procorrected-FFT algorithm for accelerating surface wave problem [C]. IWWWFB. Hamburg, Germany, 1996.

    Google Scholar 

  49. Korsmeyer F. T., Klemas T., White J. K. et al. Fast hydro-dynamic analysis of large offshore structures [C]. The 9th International Offshore and Polar Engineering Conference. Brest, France, 1999. I: 27–34.

    Google Scholar 

  50. Kring D., Korsmeyer F. T., Singer J. et al. Analyzing mobile offshore bases using accelerated boundary-element methods [J]. Marine Structures, 2000, 13(4–5): 301–313.

    Article  Google Scholar 

  51. Newman J. N., LEE C. H. Boundary-element methods in offshore structure analysis [J]. Journal of Offshore Mechanics and Arctic Engineering, 2002, 124(2): 81–89.

    Article  Google Scholar 

  52. Dai Y. Z., Song J. Z., Zeng J. et al. An Application of the precorrected-FFT method to the analysis of wave-body interaction [J]. Journal of Hydrodynamics, Ser. A, 2004, 19(3): 361–369 (in Chinese).

    Google Scholar 

  53. Dai Y. Z., Qin C. W., Huang X. P. Hydroelastic analysis of large offshore structures based on the precorrected-FFT method [J]. Journal of Yanshan University, 2004, 28(2): 150–154 (in Chinese).

    Google Scholar 

  54. Jiang S. C., Teng B., Gou Y. et al. Applications of pre-corrected-FFT method to higher-order boundary element method for wave-body problem [J]. Acta Oceanologica Sinica, 2011, 33(3): 38–46.

    Google Scholar 

  55. Song Z. J., TENG B. Removing irregular frequency in the pre-corrected FFT method for wave-structues interaction [J]. Chinese Journal of Hydrodynamics, 2016, 31(4): 489–495 (in Chinese).

    Google Scholar 

  56. Newman J. N. The approximation of free-surface Green functions [C]. The 4th International Conference on Numerical Ship Hydrodynamics. Washington DC, USA, 1985.

    Google Scholar 

  57. Wu C., Watanabe E., Utsunomiya T. An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate [J]. Applied Ocean Research, 1995, 17(5): 301–310.

    Article  Google Scholar 

  58. Sahoo T., Yip T. L., Chwang A. T. On the interaction of surface waves with a semi-infinite elastic plate [C]. The 10th International Offshore and Polar Engineering Conference. Seattle, USA, 2000, 3: 594–589.

    Google Scholar 

  59. Teng B., Cheng L., Liu S. X. et al. Modified eigenfunction expression methods for interaction of water waves with a semi-infinite elastic plate [J]. Applied Ocean Research, 2001, 23(6): 357–368.

    Article  Google Scholar 

  60. Xu F., Lu D. Q. An Optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate [J]. Journal of Hydrodynamics, 2009, 21(4): 526–530.

    Article  Google Scholar 

  61. Squire V. A., Dugan J. P., Wadhanms P. et al. Ocean waves and sea ice [J]. Annual Review of Fluid Mechanics, 1995, 27: 115–168.

    Article  MathSciNet  Google Scholar 

  62. Maeda H., Masuda K., Miyajima S. et al. Hydroelastic responses of pontoon type very large floating offshore structure [J]. Journal of the Society Naval Architects of Japan, 1995, 178: 203–212.

    Article  Google Scholar 

  63. Wu Y. S., Cui W. C. Advances in the three-dimensional hydroelasticity of ships [J]. Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment, 2009, 223(3): 331–348.

    Article  Google Scholar 

  64. Tian C., Wu Y. S., Chen Y. Q. Numerical predictions on the hydroelastic responses of a large bulker in waves [C]. The 5th International Conference on Hydroelasticity in Marine Technology. Southampton, UK, 2009, 333-346.

  65. Newman J. N. Wave effects on deformable bodies [J]. Applied Ocean Research, 1994, 16(1): 47–59.

    Article  Google Scholar 

  66. Eatock Tayloy R. Wet or dry modes in linear hydroela-sticity–why modes? [C]. Hydroelasticity in Marine Technology, Oxford, UK, 2003, 239–250.

    Google Scholar 

  67. Maniar H. D., Newman J. N. Wave diffraction by a long array of cylinders [J]. Journal of Fluid Mechanics, 1997, 339: 309–330.

    Article  MathSciNet  Google Scholar 

  68. Spring B. H., Monkneyer P. L. Interaction of plane waves with vertical cylinders [C]. The 14th International Conference on Coastal Engineering. Copenhagen, Denmark, 1974, 1828–1845.

    Google Scholar 

  69. Linton C. M., Evans D. V. The interaction of waves with arrays of vertical circular cylinders [J]. Journal of Fluid Mechanics, 1990, 215: 549–569

    Article  MathSciNet  Google Scholar 

  70. Kagemoto H., Yue D. K. P. Interactions among multiple three dimensional bodies in water waves: an exact algebraic method [J]. Journal of Fluid Mechanics, 1986, 166: 189–209.

    Article  Google Scholar 

  71. Göteman M., Engström J., Eriksson M. et al. Interaction distance for scattered and radiated waves in large wave energy parks [C]. The 30th International Workshop on Water Waves and Floating Bodies. Bristol, UK, 2015.

    Google Scholar 

  72. Longuet-higgins M. S., Cokelet C. D. The deformation of steep surface waves on water: I. A numerical method of computation [J]. Proceedings of the Royal Society of London, 1976, 350(1660), 1–26.

    Article  MathSciNet  Google Scholar 

  73. Yan C., Liu Y. Z. Numerical calculation of nonlinear wave diffraction [J]. Journal of Hydrodynamics, Ser. A, 1991, 6(2): 10–15 (in Chinese).

    Google Scholar 

  74. Bai W., Eatock Taylor R. Fully nonlinear simulation of wave interaction with fixed and floating flares structures [J]. Ocean Engineering, 2009, 36(3–4): 223–236.

    Article  Google Scholar 

  75. Isaacson M., Cheung K. F. Time-domain second-order wave diffraction in three dimension [J]. Jounal of Waterway Port Coastal and Ocean Engineering, 1992, 118(5): 496–516.

    Article  Google Scholar 

  76. Bai W., Teng B. Second-order wave diffraction around 3-D bodies by a time-domain method [J]. China Ocean Engineering, 2001, 15(1): 73–85.

    Google Scholar 

  77. Teng B., Ning D. Z. Application of a fast multipole BIEM for flow diffraction from a 3D body [J]. China Ocean Engineering, 2004, 18(2): 291–298.

    Google Scholar 

  78. Yan H., Liu Y. An efficient high-order boundary element method for nonlinear wave–wave and wave-body interactions [J]. Journal of Computational Physics, 2011, 230(2): 402–424.

    Article  MathSciNet  Google Scholar 

  79. Teng B., Gao S. Coupling of normal and hypersingular integral equations in wave-structure interaction problems [C]. Proceeding of the 31th International Workshop on Water Waves and Floating Bodies. Plymouth, USA, 2016.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116023, China

    Bin Teng  (滕斌) & Ying Gou  (勾莹)

Authors
  1. Bin Teng  (滕斌)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Gou  (勾莹)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Teng  (滕斌).

Additional information

Prof. Bin Teng is now working in the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology. He received his Ph. D. from Dalian University of Technology in 1989, and worked as a post-doctoral research assistant in Oxford University, UK from December of 1990 to January of 1993. He received the Research Founding for Distinguished Youths in 2000, and the title of the Specially Appointed Professor in “Changjiang Scholars Programme” of Education Ministry of China in 2001. He also a Chief Scientist of a National Key Basic Research Development Program (973 Program) Project of China. He is also an associate editor of “Journal of Hydrodynamics”, and board members of “Journal of Dalian University of Technology”, “Journal of Marine Science and Application”, and “Applied Ocean Research”.

Prof. Bin Teng works on offshore and coastal hydrodynamics, including the computation of wave loads on structures, hydro-elastic analysis of very large structures, analysis of wave interaction with multiple bodies, coupling analysis of deep water platforms with risers and mooring lines, and simulation of ship berthing in harbor. He has established the second and third order wave force models in the frequency domain, and the second order and the fully nonlinear wave force models in the time-domain with higher order boundary element method.

Project supported by the National Natural Science Foundation of China (Grant Nos. 51379032, 51490672 and 51479026).

Biography: Bin Teng (1958-), Male, Ph. D., Professor

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teng, B., Gou, Y. BEM for wave interaction with structures and low storage accelerated methods for large scale computation. J Hydrodyn 29, 748–762 (2017). https://doi.org/10.1016/S1001-6058(16)60786-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1001-6058(16)60786-2

Key words

Search

Navigation