A boundary condition in Padé series for frequency-domain solution of wave propagation in unbounded domains

International Journal for Numerical Methods in Engineering

Volumn 69, Issue 11, 2007, Pages 2330-2358

  Song, Chongmin ^a   Bazyar, Mohammad Hossein ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Absorbing boundary; Pad series; Scaled boundary finite element method; Transmitting boundary; Unbounded domain; Wave propagation

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; STIFFNESS MATRIX;

DYNAMIC STIFFNESS MATRIX; ELASTIC VECTOR WAVES; SCALAR WAVES; UNBOUNDED DOMAIN;

ELASTIC WAVES;

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELASTIC WAVES; FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; STIFFNESS MATRIX;

EID: 33947113523     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1852     Document Type: Article

References (57)

1. Sommerfeld A. Partial Differential Equations in Physics (Chapter 28). Academic Press: New York, 1949.
2. Geers TL (ed.). Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains. Kluwer Academic Publishers: Dordrecht, 1997.
3. Gazetas G. Analysis of machine foundation vibrations: state of the art. Soil Dynamics and Earthquake Engineering 1983; 2:2-42.
4. Wolf JP. A comparison of time-domain transmitting boundaries. Earthquake Engineering and Structural Dynamics 1986; 14:655-673.
5. Kausel E. Local transmitting boundaries. Journal of Engineering Mechanics (ASCE) 1988; 114:1011-1027.
6. Givoli D. High-order non-reflecting boundary conditions: a review. Wave Motion 2004; 39:319-326.
7. Wolf JP. Dynamic Soil-Structure Interaction. Prentice-Hall: Englewood Cliffs, NJ, 1985.
8. Wolf JP. Soil-Structure-Interaction Analysis in Time Domain. Prentice-Hall: Englewood Cliffs, NJ, 1988.
9. Wolf JP, Song Ch. Finite-Element Modelling of Unbounded Media. Wiley: Chichester, 1996.
10. Beskos DE. Boundary element methods in dynamic analysis. Applied Mechanics Reviews (ASME) 1987; 40:1-23.
11. Beskos DE. Boundary element methods in dynamic analysis: Part II (1986-1996). Applied Mechanics Reviews (ASME) 1997; 50:149-197.
12. Dominguez J. Boundary Elements in Dynamics. Computational Mechanics: Southampton, 1993.
13. Hall WS, Oliveto G. Boundary Element Methods for Soil-Structure Interaction. Kluwer Academic Publishers: Dordrecht, 2003.
14. Lysmer J. Lumped mass method for Rayleigh waves. Bulletin of the Seismological Society of America 1970; 43:17-34.
15. Kausel E. Dynamic point sources in laminated media via the thin-layer method. International Journal of Solids and Structures 1999; 36:4725-4742.
16. Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media. Journal of Engineering Mechanics (ASCE) 1969; 95:859-877.
17. Smith WD. A nonreflecting plane boundary for wave propagation problems. Journal of Computational Physics 1974; 15:492-503.
18. Cundall PA, Kunar RR, Carpenter PC, Marti J. Solution of infinite dynamic problems by finite modelling in the time domain. In Proceedings of the 2nd International Conference on Applied Numerical Modelling, Madrid, Spain, 1974; 339-351.
19. Engquist B, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation 1977; 31:629-651.
20. Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bulletin of the Seismological Society of America 1977; 67:1529-1540.
21. Underwood P, Geers TL. Doubly asymptotic boundary-element analysis of dynamic soil-structure interaction. International Journal of Solids and Structures 1981; 17:687-697.
22. Nicolas-Vullierme B. A contribution to doubly asymptotic approximation: an operator top-down approach. Journal of Vibration and Acoustics (ASME) 1991; 113:409-415.
23. Liao ZP, Wong HL. A transmitting boundary for the numerical simulation of elastic wave propagation. Soil Dynamics and Earthquake Engineering 1984; 3:174-183.
24. Keys RG. Absorbing boundary conditions for acoustic media. Geophysics 1985; 50:892-902.
25. Higdon RL. Absorbing boundary conditions for acoustic and elastic waves in stratified media. Journal of Computational Physics 1992; 101:386-418.
26. Krenk S. Unified formulation of radiation conditions for the wave equations. International Journal for Numerical Methods in Engineering 2002; 53:275-295.
27. Bayliss A, Turkel E. Radiation boundary conditions for wave-like equations. Communications on Pure and Applied Mathematics 1980; 33:707-725.
28. Bayliss A, Gunzburger M, Turkel E. Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM Journal on Applied Mathematics 1982; 42:430-451.
29. Wolf JP, Song Ch. Doubly asymptotic multi-directional transmitting boundary for dynamic unbounded medium-structure-interaction analysis. Earthquake Engineering and Structural Dynamics 1995; 24:175-188.
30. Kellezi K. Local transmitting boundaries for transient elastic analysis. Soil Dynamics and Earthquake 2000; 19:533-547.
31. Bettes P. Infinite Elements. Penshaw Press: Sunderland, U.K., 1992.
32. Astley R. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. International Journal for Numerical Methods in Engineering 2000; 49:951-976.
33. Israeli M, Orszag S. Approximation of radiation boundary conditions. Journal of Computational Physics 1981; 41:115-135.
34. Song Ch, Wolf JP. Dynamic stiffness of unbounded medium based on damping-solvent extraction. Earthquake Engineering and Structural Dynamics 1994; 23:169-181.
35. Berenger JP. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 1994; 114:185-200.
36. Hagstrom T, Hariharan S. A formulation of asymptotic and exact boundary conditions using local operators. Applied Numerical Mathematics 1998; 27:403-416.
37. Guddati M, Tassoulas J. Continued-fraction absorbing boundary conditions for the wave equations. Journal of Computational Acoustics 2000; 8:139-156.
38. Paronesso A, Wolf JP. Global lumped-parameter model with physical representation for unbounded medium. Earthquake Engineering and Structural Dynamics 1995; 24:637-654.
39. Ruge P, Trinks C, Witte S. Time-domain analysis of unbounded media using mixed-variable. Earthquake Engineering and Structural Dynamics 2001; 30:899-925.
40. Paronesso A, Wolf JP. Recursive evaluation of interaction forces and property matrices from unit-impulse response functions of unbounded medium based on balancing approximation. Earthquake Engineering and Structural Dynamics 1998; 27:609-618.
41. Yan JY, Zhang CH, Jin F. A coupling procedure of FE and SBFE for soil-structure interaction in the time domain. International Journal for Numerical Methods in Engineering 2004; 59:1453-1471.
42. Song Ch. Dynamic analysis of unbounded domains by a reduced set of base functions. Computer Methods in Applied Mechanics and Engineering 2006; 195:4075-4094.
43. Song Ch, Wolf JP. The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics. Computer Methods in Applied Mechanics and Engineering 1997; 147:329-355.
44. Zhang X, Wegner JL, Haddow JB. Three-dimensional dynamic soil-structure interaction analysis in the time domain. Earthquake Engineering and Structural Dynamics 1999; 28:1501-1524.
45. Wegner JL, Zhang X. Free-vibration analysis of a three-dimensional soil-structure system. Earthquake Engineering and Structural Dynamics 2001; 30:43-57.
46. Ekevid T, Wiberg NE. Wave propagation related to high-speed train: a scaled boundary FE-approach for unbounded domains. Computer Methods in Applied Mechanics and Engineering 2002; 191:3947-3964.
47. Genes MC, Kocak S. Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/ scaled boundary finite element model. International Journal for Numerical Methods in Engineering 2005; 62:798-823.
48. Fan SC, Li SM, Yu GY. Dynamic fluid-structure interaction analysis using boundary finite element method-finite element method. Journal of Applied Mechanics (ASME) 2005; 72:591-598.
49. Wegner J, Yao M, Zhang X. Dynamic wave-soil-structure interaction analysis in the time domain. Computers and Structures 2005; 83:2206-2214.
50. Ekevid T, Lane H, Wiberg NE. Adaptive solid wave propagation-influences of boundary conditions in high-speed train applications. Computer Methods in Applied Mechanics and Engineering 2006; 195:236-250.
51. Bazyar MH, Song Ch. Time-harmonic response of non-homogeneous elastic unbounded domains using the scaled boundary finite-element method. Earthquake Engineering and Structural Dynamics 2006; 35:357-383.
52. Wolf JP, Song Ch. The scaled boundary finite-element mediod - a primer: derivations. Computers and Structures 2000; 78:191-210.
53. Press WH, A TS, Vetterling WT, Flannery BP. Numerical Recipes in Fortran (2nd edn). Cambridge University Press: Cambridge, MA, 1992.
54. Bender CM, Orszag SA. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill: Singapore, 1978.
55. Harari I, Djellouli R. Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scatting. Journal of Applied Numerical Mathematics 2004; 50:15-47.
56. Song Ch. Weighted block-orthogonal base functions for static analysis of unbounded domains. In Proceedings of the 6th World Congress on Computational Mechanics, Beijing, China, 5-10 September 2004; 615-620.
57. Lehoucq RB, Sorensen DC, Yang C. ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM: PA, 1998.