A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

International Journal for Numerical Methods in Engineering

Volumn 84, Issue 9, 2010, Pages 1038-1067

  Benedetti, I ^a   Aliabadi, M H ^b  

^a UNIVERSITY OF PALERMO   (Italy)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Dual boundary element method; Elastodynamics; Fast BEM solvers; Laplace transform method; Large scale computations

Indexed keywords

DUAL BOUNDARY ELEMENT METHOD; ELASTO-DYNAMICS; FAST BEM SOLVERS; LAPLACE TRANSFORM METHOD; LARGE-SCALE COMPUTATIONS;

APPROXIMATION ALGORITHMS; CRACKS; DYNAMIC ANALYSIS; LAPLACE TRANSFORMS; THREE DIMENSIONAL;

BOUNDARY ELEMENT METHOD;

EID: 78049408028     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2929     Document Type: Article

References (50)

1. Sladek J, Sladek VA. Boundary integral equation method for dynamic crack problems. Engineering Fracture Mechanics 1987; 27:269-277.
2. Gallego R, Dominguez J. Dynamic crack propagation analysis by moving singular boundary elements. Journal of Applied Mechanics, ASME 1992; 29:S158-S162.
3. Fedelinski P, Aliabadi MH, Rooke DP. A single region time domain BEM for dynamic crack problems. International Journal of Solids and Structures 1995; 32:3555-3571.
4. Zhang Ch. Transient elastodynamic antiplane crack analysis in anisotropic solids. International Journal of Solids and Structures 2000; 37:6107-6130.
5. Abascal R, Dominguez J. Dynamic response of two-dimensional foundations allowed to uplift. Computers and Geomechanics 1990; 9:113-119.
6. Mansur WJ, Carrer JAM, Siqueira EFN. Time discontinuous linear traction approximation in time-domain BEM scalar wave propagation analysis. International Journal for Numerical Methods in Engineering 1998; 42:667-683.
7. Manolis GD, Beskos DE. Boundary Element Methods in Elastodynamics. Unwin Hyman: London, 1988.
8. Dominguez J. Boundary Elements in Dynamics. Computational Mechanics Publications, Elsevier Applied Science: London, 1993.
9. Aliabadi MH. The Boundary Element Method: Applications in Solids and Structures, vol. 2. Wiley: New York, 2002.
10. Aliabadi MH. Boundary element formulations in fracture mechanics. Applied Mechanics Reviews 1997; 50(2):83-96.
11. Rungamornrat J, Mear ME. A weakly singular SGBEM for analysis of cracks in 3D anisotropic media. Computer Methods in Applied Mechanics and Engineering 2008; 197(49-50):4319-4332.
12. Aliabadi MH. A new generation of boundary element methods in fracture mechanics. International Journal of Fracture 1997; 86:91-125.
13. Fedelinski P, Aliabadi MH, Rooke DP. The Laplace transform DBEM for mixed-mode dynamic crack analysis. Computers and Structures 1996; 59(6):1021-1031.
14. Wen PH, Aliabadi MH, Rooke DP. Cracks in thee dimensions: a dynamic dual boundary element analysis. Computer Methods in Applied Mechanics and Engineering 1998; 167:139-151.
15. Wen PH, Aliabadi MH, Rooke DP. A mass-matrix formulation for three-dimensional dynamic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 1999; 173:365-374.
16. Fedelinski P, Aliabadi MH, Rooke DP. Boundary element formulations for the dynamic analysis of cracked structures. Engineering Analysis with Boundary Elements 1996; 17:45-56.
17. Wen PH, Aliabadi MH, Young A. Dual boundary element methods for three-dimensional dynamic crack problems. The Journal of Strain Analysis for Engineering Design 1999; 34(6):373-394.
18. Rokhlin H. Rapid solution of integral equations of classical potential theory. Journal of Computational Physics 1985; 60(2):187-207.
19. Hackbusch W, Nowak ZP. On the fast matrix multiplication in the boundary element method by panel clustering. Numerische Mathematik 1989; 73:207-243.
20. Tyrtyshnikov EE. Mosaic-skeleton approximations. Calcolo 1996; 33:47-57.
21. Hackbusch W. A sparse matrix arithmetic based on H-matrices. Part I: introduction to H-matrices. Computing 1999; 62:89-108.
22. Takahashi T, Nishimura N, Kobayashi S. A fast BIEM for three-dimensional elastodynamics in time domain. Engineering Analysis with Boundary Elements 2003; 27:491-506.
23. Fujiwara H. The fast multipole method for integral equations of seismic scattering problems. Geophysical Journal International 1998; 133:773-782.
24. Fujiwara H. The fast multipole method for solving integral equations three-dimensional topography and basin problems. Geophysical Journal International 2000; 140:198-210.
25. Chaillat S, Bonnet M, Semblat J-F. A multi-level fast multipole BEM for 3D elastodynamics in the frequency domain. Computer Methods in Applied Mechanics and Engineering 2008; 197:4233-4249.
26. Benedetti I, Aliabadi MH, Davi G. A fast 3D dual boundary element method based on hierarchical matrices. International Journal of Solids and Structures 2008; 45:2355-2376.
27. Benedetti I, Milazzo A, Aliabadi MH. A fast dual boundary element method for 3D anisotropic crack problems. International Journal for Numerical Methods in Engineering 2009; 80(10):1356-1378. DOI: 10.1002/nme.2666.
28. Bebendorf M. Hierarchical LU decomposition-based preconditioners for BEM. Computing 2005; 74:225-247.
29. Mi Y, Aliabadi MH. Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements 1992; 10:161-171.
30. Hackbusch W, Khoromskij BN. A sparse H-matrix arithmetic. Part II: application to multidimensional problems. Computing 2000; 64:21-47.
31. Börm S, Grasedyck L, Hackbusch W. Introduction to hierarchical matrices with applications. Engineering Analysis with Boundary Elements 2003; 27:405-422.
32. Barra LPS, Coutinho ALGA, Mansur WJ, Telles JFC. Iterative solution of BEM equations by GMRES algorithm. Computers and Structures 1992; 44(6):1249-1253.
33. Guru Prasad K, Kane JH, Keyes DE, Balakrishna C. Preconditioned Krylov solvers for BEA. International Journal for Numerical Methods in Engineering 1994; 37:1651-1672.
34. Leung CY, Walker SP. Iterative solution of large three-dimensional BEM elastostatic analyses using the GMRES technique. International Journal for Numerical Methods in Engineering 1997; 40:2227-2236.
35. Merkel M, Bulgakov V, Bialecki R, Kuhn G. Iterative solution of large-scale 3D-BEM industrial problems. Engineering Analysis with Boundary Elements 1998; 22:183-197.
36. Goreinov SA, Tyrtyshnikov EE, Zamarashkin NL. A theory of pseudoskeleton approximations. Linear Algebra and its Applications 1997; 261:1-21.
37. Bebendorf M. Approximation of boundary element matrices. Numerische Mathematik 2000; 86:565-589.
38. Bebendorf M, Rjasanow S. Adaptive low-rank approximation of collocation matrices. Computing 2003; 70:1-24.
39. Bebendorf M, Grzhibovskis R. Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation. Mathematical Methods in the Applied Sciences 2006; 29:1721-1747.
40. Grasedyck L, Hackbusch W. Construction and arithmetics of H-matrices. Computing 2003; 70:295-334.
41. Kurz S, Rain O, Rjasanow S. The adaptive cross approximation technique for the 3-D boundary element method. IEEE Transactions on Magnetics 2002; 38(2):421-424.
42. Bebendorf M. Effiziente numerische Lösung von Randintegralgleichungen unter Verwendung von Niedrigrang-Matrizen. Ph.D. Thesis, Universität Saarbrücken, dissertation.de, Verlag im Internet, 2000. ISBN 3-89825-183-7.
43. Hackbusch W, Khoromskij BN, Kriemann R. Hierarchical matrices based on weak admissibility criterion. Computing 2004; 73:207-243.
44. Grasedyck L. Adaptive recompression of H-matrices for BEM. Computing 2005; 74:205-223.
45. Saad Y, Schultz MH. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986; 7(3):856-869.
46. Durbin F. Numerical inversion of Laplace transform: an efficient improvement to Dubner and Abate's method. The Computer Journal 1974; 17(4):371-376.
47. Zhao K, Vouvakis MN, Lee JF. The adaptive cross approximation algorithm for accelerated method of moments computation of EMC problems. IEEE Transaction on Electromagnetic Compatibility 2005; 47:763-773.
48. Wen PH. Dynamic Fracture Mechanics: Displacement Discontinuity Method. Computational Mechanics Publications: Southampton, Boston, 1996.
49. Zhang YY, Shi W. Transient analysis of three-dimensional crack problems by the Laplace transformed boundary element method. Engineering Fracture Mechanics 1994; 47(5):715-722.
50. Zhong M, Zhang YY. The analysis of dynamic stress intensity factor for semi-circular surface crack using time-domain BEM formulation. Applied Mathematics and Mechanics 2001; 22(11):1344-1351.