Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

Volumn , Issue , 2005, Pages

  Gumerov, Nail A ^a   Duraiswami, Ramani ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85013789628     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-08-044371-3.X5000-5     Document Type: Book

References (69)

1. Allen J.B., Berkley D.A. Method for simulating small-room acoustics. J. Acoust. Soc. Am. 1979, 65:943-950.
2. Algazi V.R., Duda R.O., Duraiswami R., Gumerov N.A., Tang Z. Approximating the head-related transfer function using simple geometric models of the head and torso. J. Acoust. Soc. Am. 2002, 112:2053-2701.
3. Alpert B.K., Rokhlin V. A fast algorithm for the evaluation of Legendre expansions. SIAM J. Sci. Stat. Comput. 1991, 12:158-179.
4. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions 1964, National Bureau of Standards, Washington, DC.
5. Atkinson F.V. On Sommerfield's radiation condition. Phil. Mag. Ser. 7 1949, 40:645-651.
6. Cheng H., Greengard L., Rokhlin V. A fast adaptive multipole algorithm in three dimensions. J. Comput. Phys. 1999, 155:468-498.
7. Chew W.C. Waves and Fields in Inhomogeneous Media 1990, Van Nostrand Reinhold, New York.
8. Chew W.C. Recurrence relations for three-dimensional scalar addition theorem. J. Electromagn. Waves Appl. 1992, 6(2):133-142.
9. Choi C.H., Ivanic J., Gordon M.S., Ruedenberg K. Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion. J. Chem. Phys. 1999, 111:8825-8831.
10. Colton D., Kress R. Inverse Acoustic and Electromagnetic Scattering Theory 1998, Springer, Berlin. 2nd ed.
11. Cooley J.W., Tukey J.W. An algorithm for the machine calculation of complex Fourier series. Math. Comput. 1965, 19:297-301.
12. Cormen T.H., Leiserson C.E., Rivest R.L. Introduction to Algorithms 1990, MIT Press, Cambridge, MA.
13. Chew W.C., Michielssen E., Song J.M., Jin J.M. Fast and Efficient Algorithms in Computational Electromagnetics 2001, Artech House, Boston, MA.
14. Coifman R., Rokhlin V., Wandzura S. The fast multipole method: A pedestrian prescription. IEEE Trans. Antennas Propagat. 1993, 35:7-12.
15. Darve E. The fast multipole method I: Error analysis and asymptotic complexity. SIAM J. Numer. Anal. 2000, 38:98-128.
16. Dongarra J.J., Sullivan F. The top 10 algorithms. Comput. Sci. Eng. 2000, 2:22-23.
17. Dutt A., Gu M., Rokhlin V. Fast algorithms for polynomial interpolation, integration and differentiation. SIAM J. Numer. Anal. 1996, 33:1689-1711.
18. Duraiswami R., Gumerov N.A., Zotkin D.N., Davis L.S. Efficient evaluation of reverberant sound fields. Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics 2001, 203-206.
19. Driscoll J.R., Healy D.M. Computing Fourier transforms and convolution on the sphere. Adv. Appl. Math. 1994, 15:202-250.
20. Epton M.A., Dembart B. Multipole translation theory for the three-dimensional Laplace and Helmholtz equations. SIAM J. Sci. Comput. 1995, 16:865-897.
21. Elliott W.D., Board J.A. Fast Fourier transform accelerated fast multipole algorithm. SIAM J. Sci. Comput. 1996, 17:398-415.
22. Wigner G.E. Gruppentheorie und ihre Anwendung auf die Quanten-mechanik der Atomspektren 1931, Vieweg, Wiesbaden, Germany.
23. Filippi P., Habault D., Lefevre J.P., Bergassoli A. Acoustics, basic physics, theory and methods 1999, Academic Press, London.
24. Greengard L., Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 1987, 73:325-348.
25. Greengard L., Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 1997, 135:280-292.
26. Gumerov N.A., Duraiswami R. fast, exact, and stable computation of multipole translation and rotation coefficients for the 3-D Helmholtz equation. Technical Report 2001-44 2001, University of Maryland, Institute for Advanced Computer Studies.
27. Gumerov N.A., Duraiswami R. Modeling the effect of a nearby boundary on the HRTF. Proceedings. (ICASSP'01). IEEE International Conference on Acoustics, Speech, and Signal Proceesing 2001, Vol. 5:3337-3340.
28. Gumerov N.A., Duraiswami R. Computation of scattering from n spheres using multipole reexpansion. J. Acoust. Soc. Am. 2002, 112:2688-2701.
29. Gumerov N.A., Duraiswami R., Borovikov Y.A. Data structures, optimal choice of parameters, and complexity results for generalized fast multipole methods in d dimensions. Technical Report CS-TR-4458 2003, Version available as University of Maryland UMIACS-TR-2003-28, CS-TR-4458, University of Maryland Institute for Advanced Computer Studies.
30. Gumerov N.A., Duraiswami R., Tang Z. Numerical study of the influence of the torso on the HRTF. Proceedings. (ICASSP'02). IEEE International Conference on Acoustics, Speech, and Signal Processing 2002, Vol. 2:1965-1968.
31. Golun G., Van Loan C. Matrix Computations 1989, Johns Hopkins University Press, Baltimore, MD. 2nd ed.
32. Hanish S. A Treatise on Acoustical Radiation 1981, Naval Research Laboratory, Washington, DC.
33. Ivanic J., Ruedenberg K. Rotation matrices for real spherical harmonics. Direct determination by recursion. J. Chem. Phys. 1996, 100:6342-6347.
34. Jackson J.D. Classical Electrodynamics 1975, Wiley, New York.
35. Jakob-Chien R., Alpert B.K. A fast spherical filter with uniform resolution. J. Comput. Phys. 1997, 136:580-584.
36. Jaeger H.M., Nagel S.R. Physics of granular states. Science 1992, 255:1524.
37. Koc S., Chew W.C. Calculation of acoustical scattering from a cluster of scatterers. J. Acoust. Soc. Am. 1998, 103:721-734.
38. Kelly C.T. Iterative Methods for Linear and Nonlinear Equations 1995, SIAM, Philadelphia, PA.
39. Kostelec P.J., Maslen D.K., Healy D.M., Rockmore D.N. Computational harmonic analysis for tensor fields on the two-sphere. J. Comput. Phys. 2000, 162(2):514-535.
40. Koc S., Song J., Chew W.C. Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem. SIAM J. Numer. Anal. 1999, 36:906-921.
41. Kurzweil R. The Age of Spiritual Machines: When Computers Exceed Human Intelligence 1999, Penguin, Baltimore, MD.
42. Landau L.D., Lifshitz E.M. Electrodynamics of Continuous Media, volume 8 of Course of Theoretical Physics 1960, Pergamon Press, New York.
43. Landau L.D., Lifshitz E.M. Fluid Mechanics. Course of Theoretical Physics 1975, Pergamon Press, New York.
44. Moore G. Cramming more components onto integrated circuits. Electronics 1965, 38:8.
45. Morse P.M., Feshbach H. Methods of Theoretical Physics 1953, Vol. 1. McGraw-Hill, New York.
46. Morse P.M., Ingard K.U. Theoretical Acoustics 1968, Princeton University Press, Princeton, NJ.
47. Moler C., Van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 1978, 20:801-836.
48. Mohlenkamp M.J. A fast transform for spherical harmonics. J. Fourier Anal. Appl. 1999, 2:159-184.
49. Orenstein J.A., Merret T.H. A class of data structures for associative searching. Proceedings of the Third ACM SIGAT-SIGMOD Symposium on Principles of Database Systems 1984, 181-190.
50. Peano G. Sur une courbe qui remplit toute une aire plaine. Math. Annalen 1890, 36:157-160.
51. Rahola J. Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems. BIT 1996, 36:333-358.
52. Strutt (Lord Rayleight) J.W. On the acoustic shadow of a sphere. Phil. Trans. R. Soc. Lond. Ser. A 1904, 203:87-89.
53. Rokhlin V. Diagonal form of translation operators for the Helmholtz equation in three dimensions. Appl. Comput. Harmon. Anal. 1993, 1:82-93.
54. Saad Y. Numerical Methods for Large Eigenvalue Problems 1992, Halstead Press, New York.
55. Saad Y. Iterative Methods for Sparse Linear Systems 2003, SIAM, Philadelphia, PA. 2nd ed.
56. Saad Y. A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 1993, 14(2):461-469.
57. Samet H. Applications of Spatial Data Structures 1990, Addison-Wesley, Reading, MA.
58. Samet H. The Design and Analysis of Spatial Data Structures 1994, Addison-Wesley, Reading, MA.
59. Suda R., Takami M. A fast spherical harmonics transform algorithm. Math. Comput. 2002, 71(238):703-715.
60. Stein S. Addition theorems for spherical wave functions. Quart. Appl. Math. 1961, 19:15-24.
61. Tang Z. Fast transforms based on structured matrices with applications to the fast multipole method. PhD Thesis 2003, University of Maryland, College Park, MD.
62. Taylor M. Cubature for the sphere and the discrete spherical harmonic transform. SIAM J. Numer. Anal. 1995, 32:667-670.
63. Tang Z., Duraiswami R., Gumerov N.A. Fast algorithms to compute matrix vector products for Pascal matrices. Technical Report 2004, University of Maryland, College Park, MD.
64. Kailath T., Sayed A.H. Fast Reliable Algorithms for Matrices with Structure 1999, SIAM, Philadelphia, PA.
65. Varsalovich D.A., Moskalev A.N., Khersonskii V.K. Quantum Theory of Angular Momentum 1988, World Scientific, Singapore.
66. Olshevsky V., Shokrollahi A. A superfast algorithm for confluent rational tangential interpolation problem via matrix-vector multiplication for confluent Cauchy-like matrices. Structured Matrices in Mathematics, Computer Science, and Engineering I 2001, Vol. 280:67-78. AMS, Providence, RI.
67. Watson G.N. A Treatise on the Theory of Bessel Functions 1958, Cambridge University Press, Cambridge.
68. Wilcox C.H. A generalization of theorems of Rellich and Atkinson. Proc. Am. Math. Soc. 1956, 7:271-276.
69. Yarvin N., Rokhlin V. A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics. J. Comput. Phys. 1998, 147(594):609.