An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation

Computational Mechanics

Volumn 40, Issue 3, 2007, Pages 461-472

  Shen, L ^a   Liu, Y J ^a  

^a University of Cincinnati   (United States)

Author keywords

Boundary element method; Burton Miller formulation; Fast multipole method; Helmholtz equation

Indexed keywords

BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; COMPUTATIONAL EFFICIENCY; HELMHOLTZ EQUATION; PROBLEM SOLVING; THREE DIMENSIONAL;

BURTON-MILLER FORMULATION; FAST MULTIPOLE METHOD (FMM); GENERALIZED MINIMAL RESIDUAL (GMRES);

ACOUSTIC WAVE PROPAGATION;

EID: 34250874558     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0121-2     Document Type: Article

References (52)

1. Brebbia CA, Dominguez, J (1989) Boundary elements - an introductory course. McGraw Hill, New York
2. Banerjee PK (1994) The boundary element methods in engineering. McGraw-Hill, New York
3. Copley LG (1967) Integral equation method for radiation from vibrating bodies. J Acoust Soc Am 41:807-810
4. Schenck HA (1968) Improved integral formulation for acoustic radiation problems. J Acoust Soc Am 44:41-58
5. Burton AJ, Miller GF (1971) The application of the integral equation methods to the numerical solution of some exterior boundary-value problems. In: Proceedings of the Royal Society of London, Series A, Math Phys Sci 323(1553):201-210
6. Meyer WL, Bell WA, Zinn BT (1978) Boundary integral solutions of three dimensional acoustic radiation problems. J Sound Vib 59(2):245-262
7. Terai T (1980) On calculation of sound fields around three dimensional objects by integral equation methods. J Sound Vib 69(1):71-100
8. Gentle JE (1998) Gaussian elimination. In Numerical linear algebra for applications in statistics. Springer, Berlin Heidelberg New York, pp 87-91
9. Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Statist Comput 7:856-869
10. Sonneveld P (1989) GGS: a fast Lanczos-type solver for nonsymmetric linear systems. STAM J Sci Statist Comput 10:36-52
11. Beylkin G, Coifman A, Rokhlin V (1991) Fast wavelet transforms and numerical algorithms I. Comm Pure Appl Math XLIV:141-183
12. Hackbusch W (1999) A sparse matrix arithmetic based on Hmatrices I. Introduction to H-matrices. Computing 62(2):89-108
13. Golub G, Loan CV (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, Baltimore
14. Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73:325-348
15. Rokhlin V (1988) A fast algorithm for the discrete Laplace transformation. J Complex 4(1):12-32
16. White CA, Head-Gordon M (1994) Derivation and efficient implementation of the fast multipole method. J Chem Phys 101(8):6593-6605
17. White CA, et al. (1994) The continues fast multipole method. Chem Phys Lett 230(1-2):8-16
18. White CA, Head-Gordon M (1996) Rotating around the quartic angular momentum barrier in fast multipole method calculations. J Chem Phys 105(12):5061-5067
19. Beatson R, Greengard L (1996) A short course on fast multipole methods. In: Ainsworth M, et al. (eds) Wavelets, multilevel methods and elliptic PDEs. Oxford University Press, pp 1-37
20. Cheng H, Greengard L, Rokhlin V (1999) A fast adaptive multipole algorithm in three dimensions. J Comput Phys 155(1):468-498
21. Rokhlin V (1990) Rapid solution of integral equations of scattering theory in two dimensions. J Comput Phys 86(2):414-439
22. Engheta N, et al. (1992) The fast multipole method (FMM) for electromagnetic scattering problems. IEEE Trans Ant Propag 40(6):634-641
23. Rokhlin V (1993) Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Appl Comput Harmon Anal 1(1):82-93
24. Coifman R, Rokhlin V, Wandzura S (1993) The fast multipole method for the wave equation: a pedestrian prescription. IEEE Ant Propagat Mag 35(3):7-12
25. Lu C, Chew W (1993) Fast algorithm for solving hybrid integral equations. IEE Proceedings-H 140(6):455-460
26. Wagner R, Chew W (1994) A ray-propagation fast multipole algorithm. Microwave Opt Technol Lett 7:435-438
27. Epton M, Dembart B (1995) Multipole translation theory for the three dimensional Laplace and Helmholtz equations. SIAM J Sci Comput 16:865-897
28. Rahola J (1996) Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems. BIT 36:333-358
29. Chen YH, Chew WC, Zeroug S (1997) Fast multipole method as an efficient solver for 2D elastic wave surface integral equations. Comput Mech 20(6):495-506
30. Song J, Lu C-C, Chew WC (1997) Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans Ant Propag 45 (10): 1488-1493
31. Koc S, Chew WC (1998) Calculation of acoustical scattering from a cluster of scatterers. J Acoust Soc Am 103(2):721-734
32. Gyure MF, Stalzer MA (1998) A prescription for the multilevel Helmholtz FMM. IEEE Comput Sei Eng 5(3): 39-47
33. GreengardL,etal(1998) Accelerating fast multipole methods for the Helmholtz equation at low frequencies. IEEE Comput Sci Eng 5(3):32-38
34. Tournour MA, Atalla N (1999) Efficient evaluation of the acoustic radiation using multipole expansion. Int J Numer Methods Eng 46(6):825-837
35. Darve E (2000) The fast multipole method: Numerical implementation. J Comput Phys 160(1):195-240
36. Gumerov NA, Duraiswami R (2003) Recursions for the computation of multipole translation and rotation coefficients for the 3-D Helmholtz equation. SIAM J Sci Comput 25(4):1344-1381
37. Darve E, Have P (2004) Efficient fast multipole method follow-frequency scattering. J Comput Phys 197(1):341-363
38. Fischer M, Gauger U, Gaul L (2004) A multipole Galerkin boundary element method for acoustics. Eng Anal Bound Elem 28(2):1.55-162
39. Chen JT, Chen KH (2004) Applications of the dual integral formulation in conjunction with fast multipole method in large-scale problems for 2D exterior acoustics. Eng Anal Bound Elem 28(6):685-709
40. Chew WC (1992) Recurrence relations for three-dimensional scalar and addition theorem. J Electromagn Waves Appl 6:133-142
41. Nishimura N (2002) Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55(4):299-324
42. Chen J, Hong H-K (1999) Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl Mech Rev 52(1):17-33
43. Guiggiani M (1998) Formulation and numerical treatment of boundary integral equations with hypersingular kernels. In: Sladek V, Sladek J (eds) Singular integrals in boundary element methods. Computational Mechanics Publications, Boston
44. Krishnasamy GL, et al. (1990) Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. J Appl Mech 57:404-414
45. Liu YJ, Rizzo FJ (1992) A weakly singular form of the hypersingular boundary integral equation applied to 3D acoustic wave problems. Comput Methods Appl Mech Eng 96: 271-287
46. Yang SA (2002) Evaluation of 2D Green's boundary formula and its normal derivative using Legendre polynomials, with an application to acoustic scattering problems. Int J Numer Methods Eng 53:905-927
47. Shen L, Liu YJ (2006) An adaptive fast multipole boundary element method for three-dimensional potential problems. Comput Mech (in press)
48. Kress R (1985) Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering. Q J Mech Appl Math 38:323-341
49. Yoshida K-i (2001) Applications of fast multipole method to boundary integral equation method. Department of Global Environment Engineering, Kyoto University
50. Nishida T, Hayami K (1997) Application of the fast multipole method to the 3D BEM analysis of electron guns. In: Marchettia M, Brebbia CA, Aliabadi MH (eds) Boundary elements XIX. Computational Mechanics Publications, Boston, pp 613-622
51. Chen K, Harris PJ (2001) Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz equation. Appl Numer Math 36(4):475-489
52. Seybert AF, Wu TW (1989) Modified Helmholtz integral equation for bodies sitting on an infinite plane. J Acoust Soc Am 85(1):19-23