Making Efficient High-Fidelity Acoustic Analysis A Reality!

 

Further information on the BEM and FMM can be found in the following references.

   

Books On the FMM and Fast Multipole BEM

Review/Tutorial Articles On the FMM and Fast Multipole BEM

  • N. Nishimura, "Fast multipole accelerated boundary integral equation methods," Applied Mechanics Reviews, 55, No. 4 (July), 299-324 (2002).
  • Y. J. Liu and N. Nishimura, "The fast multipole boundary element method for potential problems: a tutorial," Engineering Analysis with Boundary Elements, 30, No. 5, 371-381 (2006).

Papers On the FMM and Fast Multipole BEM for Helmholtz Equations/Acoustic Problems

  • V. Rokhlin, "Diagonal forms of translation operators for the Helmholtz equation in three dimensions," Appl. Comput. Harmon. Anal., 1, No.1, 82-93 (1993).
  • M. Epton and B. Dembart, "Multipole translation theory for the three dimensional Laplace and Helmholtz equations," SIAM J Sci Comput, 16, No. 865-897 (1995).
  • L. Greengard, J. Huang, V. Rokhlin, and S. Wandzura, "Accelerating fast multipole methods for the Helmholtz equation at low frequencies," IEEE Comput. Sci. Eng., 5, No.3, 32-38 (1998).
  • S. Koc and W. C. Chew, "Calculation of acoustical scattering from a cluster of scatterers," J. Acoust. Soc. Am., 103, No.2, 721-734 (1998).
  • K. Yoshida, "Applications of Fast Multipole Method to Boundary Integral Equation Method", Ph.D. Dissertation, Department of Global Environment Engineering, Kyoto University (2001).
  • E. Darve and P. Havé, "Efficient fast multipole method for low-frequency scattering," Journal of Computational Physics, 197, No. 1, 341-363 (2004).
  • H. Cheng, W. Y. Crutchfield, Z. Gimbutas, L. F. Greengard, J. F. Ethridge, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao, "A wideband fast multipole method for the Helmholtz equation in three dimensions," Journal of Computational Physics, 216, No. 1, 300-325 (2006).
  • L. Shen and Y. J. Liu, "An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation," Computational Mechanics, 40, No. 3, 461-472 (2007).
  • Y. J. Liu, L. Shen and M. Bapat, "Development of the Fast Multipole Boundary Element Method for Acoustic Wave Problems," in: Recent Advances in the Boundary Element Methods, edited by G. Manolis and D. Polyzos (Springer-Verlag, Berlin, 2009).
  • M. S. Bapat, L. Shen and Y. J. Liu, "Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems,"  Engineering Analysis with Boundary Elements, 33, Nos. 8-9, 1113-1123 (2009).

Books On the BEM

  • C. A. Brebbia and J. Dominguez, Boundary Elements - An Introductory Course (McGraw-Hill, New York, 1989).
  • P. K. Banerjee, The Boundary Element Methods in Engineering, 2nd ed (McGraw-Hill, New York, 1994). 
  • J. H. Kane, Boundary Element Analysis in Engineering Continuum Mechanics (Prentice Hall, Englewood Cliffs, NJ, 1994). 
  • M. Bonnet, Boundary Integral Equation Methods for Solids and Fluids (Wiley, Chichester, 1995).
  • T. W. Wu, ed. Boundary Element Acoustics: Fundamentals and Computer Codes, (WIT Press, Southampton, 2000).
  • L. C. Wrobel, The Boundary Element Method - Vol.1 Applications in Thermo-Fluids and Acoustics (Wiley,  Chichester,  2002). 
  • M. H. Aliabadi, The Boundary Element Method - Vol.2 Applications in Solids and Structures (Wiley, Chichester, 2002). 
  • S. Mukherjee and Y. X. Mukherjee, Boundary Methods: Elements, Contours, and Nodes (CRC, Boca Raton, 2005).

Papers On BIE and Conventional BEM for Wave Problems

  • H. A. Schenck, "Improved integral formulation for acoustic radiation problems," J. Acoust. Soc. Am., 44, No. 41-58 (1968).
  • A. J. Burton and G. F. Miller, "The application of integral equation methods to the numerical solution of some exterior boundary-value problems," Proc. R. Soc. Lond. A, 323, No. 201-210 (1971).
  • F. J. Rizzo, D. J. Shippy, and M. Rezayat, "A boundary integral equation method for radiation and scattering of elastic waves in three dimensions," International Journal for Numerical Methods in Engineering, 21, No. 115-129 (1985).
  • A. F. Seybert, B. Soenarko, F. J. Rizzo, and D. J. Shippy, "An advanced computational method for radiation and scattering of acoustic waves in three dimensions," J. Acoust. Soc. Am., 77, No. 2, 362-368 (1985).
  • M. Rezayat, D. J. Shippy, and F. J. Rizzo, "On time-harmonic elastic-wave analysis by the boundary element method for moderate to high frequencies," Computer Methods in Applied Mechanics and Engineering, 55, No. 349-367 (1986).
  • A. F. Seybert and T. K. Rengarajan, "The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations," J. Acoust. Soc. Am., 81, No. 1299-1306 (1987). 
  • A. F. Seybert, T. W. Wu, and X. F. Wu, "Radiation and scattering of acoustic waves from elastic solids and shells using the boundary element method," J. Acoust. Soc. Am., 84, No. 5, 1906-1912 (1988). 
  • A. F. Seybert, C. Y. R. Cheng, and T. W. Wu, "The solution of coupled interior/exterior acoustic problems using the boundary element method," J. Acoust. Soc. Am., 88, No. 1612-1618 (1990).
  • G. Krishnasamy, T. J. Rudolphi, L. W. Schmerr, and F. J. Rizzo, "Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering," Journal of Applied Mechanics, 57, No. 404-414 (1990).
  • Y. J. Liu, "Development and applications of hypersingular boundary integral equations for 3-D acoustics and elastodynamics," Ph.D. Dissertation, Department of Theoretical and Applied Mechanics, The University of Illinois at Urbana-Champaign (UIUC) (November 1991, Advisor: Professor Frank J. Rizzo).
  • Y. J. Liu and F. J. Rizzo, "Application of Overhauser C(1) continuous boundary elements to `hypersingular' BIE for 3-D acoustic wave problems", in: eds. C. A. Brebbia and G. S. Gipson, Boundary Elements XIII (Computation Mechanics Publications, Tulsa, OK, 1991) 957-966.
  • G. Krishnasamy, F. J. Rizzo, and Y. J. Liu, "Scattering of acoustic and elastic waves by crack-like objects: the role of hypersingular integral equations", in: eds. D. O. Thompson and D. E. Chimenti, Review of Progress in Quantitative Nondestructive Evaluation (Plenum Press, Brunswick, Maine, 1991).
  • Y. J. Liu and F. J. Rizzo, "A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems," Computer Methods in Applied Mechanics and Engineering, 96, No. 271-287 (1992).
  • Y. J. Liu and F. J. Rizzo, "Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions," Computer Methods in Applied Mechanics and Engineering, 107, No. 131-144 (1993).
  • Y. J. Liu, D. M. Zhang, and F. J. Rizzo, "Nearly singular and hypersingular integrals in the boundary element method", in: eds. C. A. Brebbia and J. J. Rencis, Boundary Elements XV (Computational Mechanics Publications, Worcester, MA, 1993) 453-468.
  • G. Krishnasamy, F. J. Rizzo, and Y. J. Liu, "Boundary integral equations for thin bodies," International Journal for Numerical Methods in Engineering, 37, No. 107-121 (1994). 
  • J. C. Chao, Y. J. Liu, F. J. Rizzo, and et al., "Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions," IEEE Trans. on Antennas and Propagat, 43, No. 12, 1416-1422 (1995).
  • J. C. Chao, F. J. Rizzo, I. Elshafiey, Y. J. Liu, and et al., "General formulation for light scattering by a dielectric body near a perfectly conducting surface," J. Optical Society of America A, 13, No. 2 (February), 338-344 (1996).
  • J. C. Chao, F. J. Rizzo, I. El-Shafiey, Y. J. Liu, and et al., "A general formulation for light scattering by dielectric bodies near a perfectly conducting surface," J. Optical Society of America A, 13, No. 2, 338-344 (1996).
  • Y. J. Liu and F. J. Rizzo, "Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation," J. Acoust. Soc. Am.,  102 (2), No. Pt.1, August, 926-932 (1997).
  • Y. J. Liu and S. H. Chen, "A new form of the hypersingular boundary integral equation for 3-D acoustics and its implementation with C0 boundary elements," Computer Methods in Applied Mechanics and Engineering, 173, No. 3-4, 375-386 (1999).
  • S. H. Chen and Y. J. Liu, "A unified boundary element method for the analysis of sound and shell-like structure interactions. I. Formulation and verification," J. Acoust. Soc. Am., 103, No. 3, 1247-1254 (1999).
  • S. H. Chen, Y. J. Liu, and X. Y. Dou, "A unified boundary element method for the analysis of sound and shell-like structure interactions. II. Efficient solution techniques," J. Acoust. Soc. Am., 108, No. 6, 2738-2745 (2000).

 

Note: Reprints (in pdf files) of Dr. Y. J. Liu's papers listed above can be found at his academic website:  http://urbana.mie.uc.edu/yliu/Publications/