Application of hierarchical matrices to boundary element methods for elastodynamics based on Green's functions for a horizontally layered halfspace

Engineering Analysis with Boundary Elements

Volumn 37, Issue 12, 2013, Pages 1745-1758

  Coulier, P ^a   Francois S ^a   Lombaert, G ^a   Degrande, G ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Boundary element method; Elastodynamics; H matrices; Halfspace Green's functions; Railway induced vibrations

Indexed keywords

DYNAMIC SOIL-STRUCTURE INTERACTION; ELASTO-DYNAMICS; H-MATRICES; HALF-SPACE; HIERARCHICAL MATRICES; INDUCED VIBRATIONS; LARGE-SCALE PROBLEM; LAYERED HALF SPACES;

GEOMETRY; GREEN'S FUNCTION; WAVE PROPAGATION;

BOUNDARY ELEMENT METHOD;

EID: 84887065899     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2013.09.009     Document Type: Article

References (62)

1. J.-F. Semblat, A. Duval, and P. Dangla Seismic site effects in a deep alluvial basin numerical analysis by the boundary element method Computers and Geotechnics 29 7 2002 573 585 (Pubitemid 34825313)
2. G. Lombaert, G. Degrande, and D. Clouteau Numerical modelling of free field traffic induced vibrations Soil Dynamics and Earthquake Engineering 19 7 2000 473 488
3. D. Beskos, T. Krauthammer, and I. Vardoulakis Dynamic soil-structure interaction 1984 A.A. Balkema
4. V. Rokhlin Rapid solution of integral equations of classical potential theory Journal of Computational Physics 60 1985 187 207
5. W. Hackbusch, and Z. Nowak On the fast matrix multiplication in the boundary element method by panel clustering Numerische Mathematik 54 1989 463 491
6. W. Hackbusch A sparse matrix arithmetic based on H-matrices. Part I introduction to H-matrices Computing 62 2 1999 89 108
7. N. Nishimura Fast multipole accelerated boundary integral equation methods Applied Mechanics Reviews 22 2002 175 181
8. H. Fujiwara The fast multipole method for solving integral equations of three-dimensional topography and basin problems Geophysical Journal International 140 1 2000 198 210 (Pubitemid 30147597)
9. S. Chaillat, M. Bonnet, and J.-F. Semblat A new fast multi-domain BEM to model seismic wave propagation and amplification in 3D geological structures Geophysical Journal International 177 2009 509 531
10. E. Grasso, S. Chaillat, M. Bonnet, and J.-F. Semblat Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics Engineering Analysis with Boundary Elements 36 5 2012 744 758
11. Chaillat S, Bonnet M. Formulation and fast evaluation of the multipole expansions of the elastic half-space fundamental solutions. In: 8th European solid mechanics conference, Graz, Austria, July 2012.
12. S. Rjasanow, and O. Steinbach The fast solution of boundary integral equations (mathematical and analytical techniques with applications to engineering) 2007 Springer-Verlag New York
13. M. Bebendorf Hierarchical matrices a means to efficiently solve elliptic boundary value problems 1st ed. 2008 Springer Publishing Company
14. L. Banjai, and W. Hackbusch Hierarchical matrix techniques for low- and high-frequency Helmholtz problems IMA Journal of Numerical Analysis 28 1 2008 46 79
15. J. Ostrowski, Z. Andjelić, M. Bebendorf, B. Cranganu-Cretu, and J. Smajić Fast BEM-solution of Laplace problems with H-matrices and ACA IEEE Transactions on Magnetics 42 4 2006 627 630
16. M. Bebendorf, and R. Grzhibovskis Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation Mathematical Methods in the Applied Sciences 29 14 2006 1721 1747 (Pubitemid 44343131)
17. F. Maerten Adaptive cross-approximation applied to the solution of system of equations and post-processing for 3D elastostatic problems using the boundary element method Engineering Analysis with Boundary Elements 34 5 2010 483 491
18. M. Messner, and M. Schanz An accelerated symmetric time-domain boundary element formulation for elasticity Engineering Analysis with Boundary Elements 34 11 2010 944 955
19. I. Benedetti, and M. Aliabadi A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems International Journal for Numerical Methods in Engineering 84 9 2010 1038 1067
20. A. Milazzo, I. Benedetti, and M. Aliabadi Hierarchical fast BEM for anisotropic time-harmonic 3-D elastodynamics Computers and Structures 96-97 2012 9 24
21. F. Rizzo, and D. Shippy An application of the correspondence principle of linear viscoelasticity theory SIAM Journal on Applied Mathematics 21 2 1971 321 330
22. L. Wheeler, and E. Sternberg Some theorems in classical elastodynamics Archive for Rational Mechanics and Analysis 31 1968 51 90
23. J. Domínguez Boundary elements in dynamics 1993 Computational Mechanics Publications and Elsevier Applied Science Southampton, UK
24. M. Bonnet Boundary integral equation methods for solids and fluids 1995 John Wiley and Sons Chichester, UK
25. F. Rizzo, D. Shippy, and M. Rezayat A boundary integral equation method for radiation and scattering International Journal for Numerical Methods in Engineering 21 1985 115 129
26. D. Aubry, and D. Clouteau A regularized boundary element method for stratified media G. Cohen, L. Halpern, P. Joly, Proceedings of the first international conference on mathematical and numerical aspects of wave propagation phenomena 1991 SIAM Philadelphia, Strasbourg, France 660 668
27. E. Kausel, and J. Roësset Stiffness matrices for layered soils Bulletin of the Seismological Society of America 71 6 1981 1743 1761
28. M. Schevenels, S. François, and G. Degrande EDT An ElastoDynamics Toolbox for MATLAB Computers & Geosciences 35 8 2009 1752 1754
29. J. Talman Numerical Fourier and Bessel transforms in logarithmic variables Journal of Computational Physics 29 1 1978 35 48
30. Schevenels M. The impact of uncertain dynamic soil characteristics on the prediction of ground vibrations [Ph.D. thesis]. Department of Civil Engineering, KU Leuven; 2007.
31. E. Pan Static Green's functions in multilayered half spaces Applied Mathematical Modelling 21 8 1997 509 521 (Pubitemid 127420451)
32. W. Thomson Transmission of elastic waves through a stratified solid medium Journal of Applied Physics 21 1950 89 93
33. N. Haskell The dispersion of surface waves on multilayered media Bulletin of the Seismological Society of America 73 1953 17 43
34. J. Dunkin Computation of modal solutions in layered, elastic media at high frequencies Bulletin of the Seismological Society of America 55 2 1965 335 358
35. J. Luco, and R. Apsel On the Green's functions for a layered half-space. Part I Bulletin of the Seismological Society of America 4 1983 909 929
36. R. Apsel, and J. Luco On the Green's functions for a layered half-space. Part II Bulletin of the Seismological Society of America 73 4 1983 931 951
37. E. Kausel Fundamental solutions in elastodynamics a compendium 2006 Cambridge University Press New York
38. L. Grasedyck, and W. Hackbusch Construction and arithmetics of H-matrices Computing 70 2003 295 334
39. S. Börm, L. Grasedyck, and W. Hackbusch Introduction to hierarchical matrices with applications Engineering Analysis with Boundary Elements 27 5 2003 405 422
40. A. George Nested dissection of a regular finite element mesh SIAM Journal on Numerical Analysis 10 1973 345 363
41. L. Grasedyck, R. Kriemann, and S. Le Borne Domain decomposition based H-LU preconditioning Numerische Mathematik 112 4 2009 565 600
42. M. Bebendorf Approximation of boundary element matrices Numerische Mathematik 86 2000 565 589
43. M. Bebendorf, and S. Rjasanow Adaptive low-rank approximation of collocation matrices Computing 70 2003 1 24
44. L. Grasedyck Adaptive recompression of H-matrices for BEM Computing 74 3 2005 205 223
45. M. Bebendorf, and S. Kunis Recompression techniques for adaptive cross approximation Journal of Integral Equations and Applications 21 3 2009 331 357
46. G. Golub, and C. Van Loan Matrix computations 3rd ed. 1996 John Hopkins University Press Baltimore, MD
47. Y. Saad, and M. Schultz GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM Journal on Scientific and Statistical Computing 7 3 1986 856 869
48. François S, Schevenels M, Degrande G. BEMFUN: MATLAB toolbox for boundary elements in elastodynamics. Version 2.1 Build 16, User's guide BWM-2009-26, Department of Civil Engineering, KU Leuven, December 2009.
49. G. Gazetas Analysis of machine foundation vibrations state of the art Soil Dynamics and Earthquake Engineering 2 1 1983 2 42
50. M. Bebendorf Hierarchical LU decomposition based preconditioners for BEM Computing 74 2005 225 247 (Pubitemid 40682765)
51. A. Sohrabi-Bidar, M. Kamalian, and M.K. Jafari Time-domain BEM for three-dimensional site response analysis of topographic structures International Journal for Numerical Methods in Engineering 79 12 2009 1467 1492
52. F. Sánchez-Sesma Diffraction of elastic waves by three-dimensional surface irregularities Bulletin of the Seismological Society of America 73 6 1983 1621 1636
53. E. Reinoso, L. Wrobel, and H. Power Three-dimensional scattering of seismic waves from topographical structures Soil Dynamics and Earthquake Engineering 16 1 1997 41 61
54. S. Chaillat, M. Bonnet, and J.-F. Semblat A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain Computer Methods in Applied Mechanics and Engineering 197 49-50 2008 4233 4249
55. D. Aubry, and D. Clouteau A subdomain approach to dynamic soil-structure interaction V. Davidovici, R. Clough, Recent advances in earthquake engineering and structural dynamics, Ouest editions/AFPS, Nantes 1992 251 272
56. D. Aubry, D. Clouteau, and G. Bonnet Modelling of wave propagation due to fixed or mobile dynamic sources N. Chouw, G. Schmid, Workshop wave '94, wave propagation and reduction of vibrations 1994 Ruhr Universität Bochum Germany 109 121
57. D. Clouteau, and D. Aubry Modification of the ground motion in dense urban areas Journal of Computational Acoustics 9 4 2001 1659 1675 (Pubitemid 33575118)
58. M. Kham, J.-F. Semblat, P.-Y. Bard, and P. Dangla Seismic city-site interaction main governing phemomena through simplified numerical models Bulletin of the Seismological Society of America 96 5 2006 1934 1951 (Pubitemid 44613013)
59. G. Lombaert, and D. Clouteau The resonant multiple wave scattering in the seismic response of a city Waves in Random and Complex Media 16 3 2006 205 230 (Pubitemid 44210340)
60. G. Lombaert, G. Degrande, J. Kogut, and S. François The experimental validation of a numerical model for the prediction of railway induced vibrations Journal of Sound and Vibration 297 3-5 2006 512 535
61. S. François, C. Karg, W. Haegeman, and G. Degrande A numerical model for foundation settlements due to deformation accumulation in granular soils under repeated small amplitude dynamic loading International Journal for Numerical and Analytical Methods in Geomechanics 34 3 2010 273 296
62. X. Sheng, C. Jones, and D. Thompson A theoretical model for ground vibration from trains generated by vertical track irregularities Journal of Sound and Vibration 272 3-5 2004 937 965