A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation

Journal of the Acoustical Society of America

Volumn 125, Issue 1, 2009, Pages 191-205

  Gumerov, Nail A ^a,b   Duraiswami, Ramani ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b Fantalgo LLC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENTS; BOUNDARY SHAPES; BOUNDARY VALUES; CONVERGENCE CRITERION; DOMAIN SIZES; FAST MULTIPOLE; FAST MULTIPOLE METHOD (FMM); HELMHOLTZ; PRECONDITIONER; WAVE NUMBERS;

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERRORS; HELMHOLTZ EQUATION; MATHEMATICAL OPERATORS; THREE DIMENSIONAL;

BOUNDARY ELEMENT METHOD;

EID: 58649105751     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.3021297     Document Type: Article

References (29)

1. L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems (MIT, Cambridge, MA, 1988).
2. N. Nishimura, " Fast multipole accelerated boundary integral equation methods.," Appl. Mech. Rev. 55, 299-324 (2002).
3. M. Fischer, " The fast multipole boundary element method and its application to structure-acoustic field interaction.," Ph.D. dissertation, Institut A für Mechanik der Universität Stuttgart (2004).
4. M. Fischer, U. Gauger, and L. Gaul, " A multipole Galerkin boundary element method for acoustics.," Eng. Anal. Boundary Elem. 28, 155-162 (2004).
5. T. Sakuma and Y. Yasuda, " Fast multipole boundary element method for large-scale steady-state sound field analysis, Part I: Setup and validation.," Acust. Acta Acust. 88, 513-525 (2002).
6. S. Schneider, " Application of fast methods for acoustic scattering and radiation problems.," J. Comput. Acoust. 11, 387-401 (2003).
7. 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.," Comput. Mech. 40, 461-472 (2007).
8. Y. Yasuda and T. Sakuma, " Fast multipole boundary element method for large-scale steady-state sound field analysis, Part II: Examination of numerical items.," Acust. Acta Acust. 89, 28-38 (2003).
9. Y. Yasuda and T. Sakuma, " An effective setting of hierarchical cell structure for the fast multipole boundary element method.," J. Comput. Acoust. 13, 47-70 (2005).
10. M. S. Tong, W. C. Chew, and M. J. White, " Multilevel fast multipole algorithm for acoustic wave scattering by truncated ground with trenches.," J. Acoust. Soc. Am. 123, 2513-2521 (2008).
11. B. Chandrasekhar and S. M. Rao, " Acoustic scattering from rigid bodies of arbitrary shape-double layer formulation.," J. Acoust. Soc. Am. 115, 1926-1933 (2004).
12. N. A. Gumerov and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Elsevier, Oxford, UK, 2004).
13. N. A. Gumerov and R. Duraiswami, " Recursions for the computation of multipole translation and rotation coefficients for the 3-D Helmholtz equation.," SIAM J. Sci. Comput. (USA) 25, 1344-1381 (2003).
14. E. Darve and P. Hav́, " Efficient fast multipole method for low-frequency scattering.," J. Comput. Phys. 197, 341-363 (2004).
15. L. Greengrard, J. Huang, V. Rokhlin, and S. Wandzura, " Accelerating fast multipole methods for the Helmholtz equation at low frequencies.," IEEE Comput. Sci. Eng. 5, 32-38 (1998).
16. V. Rokhlin, " Diagonal forms of translation operators for the Helmholtz equation in three dimensions.," Appl. Comput. Harmon. Anal. 1, 82-93 (1993).
17. 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.," J. Comput. Phys. 216, 300-325 (2006).
18. Fast and Efficient Algorithms in Computational Electromagnetics, edited by, W. C. Chew, J. M. Jin, E. Michelssen, and, J. Song, (Artech House, Boston, 2001).
19. Y. Saad, " A flexible inner-outer preconditioned GMRES algorithm.," SIAM J. Sci. Comput. (USA) 14, 461-469 (1993).
20. A. J. Burton and G. F. Miller, " The application of the integral equation methods to the numerical solution of some exterior boundary-value problems.," Proc. R. Soc. London, Ser. A 323, 201-210 (1971).
21. L. H. Chen and J. Zhou, Boundary Element Methods (Academic, New York, 1992).
22. S. Kirkup, " The boundary element method in acoustics.," http://www.boundary-element-method.com/acoustics/index.htm (Last viewed December 30, 2007).
23. Y. Saad and M. H. Schultz, " GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems.," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
24. N. A. Gumerov and R. Duraiswami, " Computation of scattering from clusters of spheres using the fast multiple method.," J. Acoust. Soc. Am. 117, 1744-1761 (2005).
25. E. Darve, " The fast multipole method (I): Error analysis and asymptotic complexity.," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 38, 98-128 (2000).
26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC, 1964).
27. J. R. Driscoll and D. M. Healy, Jr., " Computing Fourier transforms and convolutions on the 2-sphere.," Adv. Appl. Math. 15, 202-250 (1994).
28. E. Lutz, A. R. Ingraffea, and L. J. Gray, " Use of 'simple solutions' for boundary integral equation methods in elasticity and fracture analysis.," Int. J. Numer. Methods Eng. 35, 1737-1751 (1992).
29. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1998).