Application of the fast multipole boundary element method to underwater acoustic scattering

References

• Amini, S. & Profit, A. T. J. 2003, “Multi-level Fast Multipole Solution of the Scattering Problem”, Engineering Analysis with Boundary Elements, Vol. 27, pp. 547–564.
   Google Scholar
• Bonnet, M. 2001, “Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems”, Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Lecture Notes in Computational Science and Engineering, Babuska, I., Ciarlet, P. G. & Miyoshi, T. (editors), Springer, Vol. 19, pp. 253–270.
   Google Scholar
• Brunner, D., Junge, M. & Gaul, L. 2009, “A comparison of FE-BE coupling schemes for large-scale problems with fluid-structure interaction”, International Journal for Numerical Methods in Engineering, No. 77, pp. 664–688.
   Google Scholar
• Brunner, D., Of, G., Junge, , M., Steinbach, O. & Gaul, L. 2010, “A fast BE-FE Coupling scheme for partly immersed bodies”, International Journal for Numerical Methods in Engineering, Vol. 81, No. 1, pp. 28–47.
   Google Scholar
• Burton, A. J. & Miller, G. F. 1971, “The application of integral equation methods to the numerical solution of some exterior boundary-value problems”, Proceedings of the Royal Society of London, No. 323, pp. 201–210.
   Google Scholar
• Chaillat, S., Bonnet, M. & Semblat, J. F. 2008, “A multilevel fast multipole BEM for 3-D elastodynamics in the frequency domain”, Computational Methods in Applied Mechanics and Engineering, No. 198, pp. 4233–4249.
   Google Scholar
• Chaillat, S., Bonnet, M. & Semblat, J. F. 2007, “A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain”, Comptes Rendus Mecanique, No. 337, pp. 714–719.
   Google Scholar
• Chaillat, S., Bonnet, M. & Semblat, J. F. 2009, “A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures”, Geophysical Journal International, Vol. 177, pp. 509–531.
   Google Scholar
• Cheng, H., Crutchfield, W. Y., Gimbutas, Z., Greengard, L. S., Ethridge, J. F., Juang, J., Rokhlin, V., Yarvin, N. & Zhao, J. 2006, “A wideband fast multipole method for the Helmholtz equation in three dimensions”, Journal of Computational Physics, Vol. 216, pp. 300–325.
   Google Scholar
• Coifamn, R., Rokhlin, V. & Wandzura, S. 1993, “The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription”, IEEE Antennas and Propagation Magazine, Vol. 35, No. 3, pp. 7–12.
   Google Scholar
• Epton, M. A. & Dembart, B. 1995, “Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations”, SIAM Journal of Scientific Computing, Vol. 16, No. 4, pp. 865–897.
   Google Scholar
• Fischer, M. & Gaul, L. 2005, “Fast BEM-FEM mortar coupling for acoustic-structure interaction”, International Journal for Numerical Methods in Engineering, No. 62, pp. 1677–1690.
   Google Scholar
• Fujiwara, H. 2000, “A fast multipole method for solving integral equations of three-dimensional topography and basin problems”, Geophysical Journal International, Vol. 140, pp. 198–210.
   Google Scholar
• Gaul, L., Kogl, M. & Wagner, M. 2003, Boundary Element Methods for Engineers and Scientists: An Introductory Course with Advanced Topics, SpringerVerlag, Berlin.
   Google Scholar
• Gaul, L., Brunner, D. & Junge, M. 2009, “Simulation of Elastic Scattering with a Coupled FMBE-FE Approach”, Recent Advances in Boundary Element Methods, Manolis, G. D. & Polyzos, D. (editors), Springer, Netherlands, pp. 131–145.
   Google Scholar
• Greengard, L. & Rokhlin, V. 1987, “A Fast Algorithm for Particle Simulations”, Journal of Computational Physics, Vol. 135, No. 2, pp. 280–292.
   Google Scholar
• Greengard, L., Huang, J., Rokhlin, V. & Wandzura, S. 1998, “Accelerating Fast Multipole Methods for the Helmholtz equation at Low Frequencies”, IEEE Computational Science and Engineering, Vol. 5, No. 3, pp. 32–38.
   Google Scholar
• Gumerov, N. A. & Duraiswami, R. 2004, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions: A Volume in the Elsevier Series in Electromagnetism, Elsevier, Oxford.
   Google Scholar
• Gumerov, N. A. & Duraiswami, R. 2009, “A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation”, The Journal of the Acoustical Society of America, Vol. 125, No. 1, pp. 191–205.
   Google Scholar
• Gumerov, N. A., Duraiswami, R. & Barovikov, E. 2003, “Data Structures, Optimal Choice in Parameters, and Complexity Results for Generalised Multilevel Fast Multipole Methods in d Dimensions”, Technical Report, Perceptual Interfaces and Reality Laboratory, University of Maryland.
   Google Scholar
• Junger, M. C. & Feit, D. 1993, Sound, Structures, and Their Interaction, Acoustical Society of America.
   Google Scholar
• Koc, S. & Chew, W. C. 1998, “Calculation of acoustical scattering from a group of scatters”, The Journal of the Acoustical Society of America, Vol. 103, No. 2, pp. 721–734.
   Google Scholar
• Liu, Y. 2009, Fast Multipole Boundary Element Method: Theory and Applications in Engineering, Cambridge University Press, New York.
   Google Scholar
• Lu, C. & Chew, W. C. 1994, “A multilevel algorithm for solving a boundary integral equation of wave scattering”, Microwave and Optical Technology Letters, Vol. 7, No. 10, pp. 466–470.
   Google Scholar
• Marburg, S. & Schneider, S. 2003, “Performance of iterative solvers for acoustic problems. Part I. Solvers and effect of diagonal preconditioning”, Engineering Analysis with Boundary Elements, No. 27, pp. 725–750.
   Google Scholar
• Masumoto, T., Gunawan, A., Oshima, T., Yasuda, Y. & Sakuma, T. 2008, “Coupling analysis between FMBEM-based acoustic and modal-based structural models”, Proceedings of the 37 th International Congress and Exposition on Noise Control Engineering, Shanghai, China, 26–29 October.
   Google Scholar
• Nell, C. W. & Gilroy, L. E. 2003, “An Improved BASIS Model for the BeTSSi Submarine”, Technical Report, Defence Research and Development Canada, DRDC Atlantic TR 2003–199.
   Google Scholar
• Nishimura, N. 2002, “Fast Multipole Accelerated Boundary Integral Equation Methods”, Applied Mechanics Reviews, Vol. 55, No. 4, pp. 299–324.
   Google Scholar
• Reddy, J. N. 2004, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, New York.
   Google Scholar
• Rokhlin, V. 1990, “Rapid Solution of Integral Equations of Scattering Theory in Two Dimensions”, Journal of Computational Physics, Vol. 86, No. 2, pp. 414–439.
   Google Scholar
• Rokhlin, V. 1992, “Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions”, Technical Report, Yale University Department of Computer Science, YALEU/DCS/RR-894.
   Google Scholar
• Schneider, S. 2008, “FE/FMBE Coupling to model fluid-structure interaction”, International Journal for Numerical Methods in Engineering, No. 76, pp. 21372156.
   Google Scholar
• Scuderi, L. 2008, “On the computation of nearly singular integrals in 3D BEM collocation”, International Journal for Numerical Methods in Engineering, No. 74, pp. 1733–1770.
   Google Scholar
• Wu, T. W. 2000, “The Helmholtz integral equation”, Boundary Element Acoustics: Fundamentals and Computer Codes, Wu, T. (editor), Advances in Boundary Elements Series, WIT Press, Great Britain.
   Google Scholar
• Xiao, H. & Chen, Z. 2007, “Numerical experiments of preconditioned Krylov subspace methods solving the dense non-symmetric systems arising from BEM”, Engineering Analysis with Boundary Elements, Vol. 31, pp. 1013–1023.
   Google Scholar