Solveur itératif pour des problèmes stochastiques d’interaction sol-structure
Keywords:
BEM-FEM coupling, iterative method, preconditioner, polynomial chaos, Karhunen- Loeve expansionAbstract
This paper deals with the modeling and the numerical simulation of wave propagation in a random media with sol structure interaction. When the random physical soil properties are restricted to a bounded sub-domain, a coupled finite elements and boundary elements method is proposed to perform Monte Carlo simulations. A iterative solver with an common preconditionner for all simulations is built using a polynomial chaos expansion. It is shown, that this preconditionner related to the Dyson equation on the mean field leads to uniform acceleration of the convergence.
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References
[AUB 92] AUBRY D., CLOUTEAU D., A subdomain approach to dynamic soil-structure interaction,
vol. pp. 251–272, Nantes : Ouest Editions/AFPS, 1992.
[BAR 95] DE BARROS F., LUCO J., « Identification of foundation impedance functions and
soil properties from vibration tests of the Hualien containment model », Soil Dyn. Earthquake
Engrg., vol. 14, 1995, p. 229–248.
[CLO 75] CLOUGH R., PENZIEN J., Dynamics of structures, New York : McGraw-Hill, 1975.
[CLO 90] CLOUTEAU D., « Propagation d’ondes dans les milieux hétérogènes, Application à
la tenue d’ouvrages sous séismes », PhD thesis, Ecole Centrale Paris, 1990.
[CLO 01] CLOUTEAU D., AUBRY D., Computational soil-structure Interaction, Kluwer,
[GHA 91] GHANEM, SPANOS, Stochastic finite elements : a spectral approach, New York :
Springer Verlag, 1991.
[HAO 99] HAO H., ZHANG S., « Spatial ground motion effect on relative displacement of
adjacent building structures », Earthquake Engrg. Struct. Dyn., vol. 28, 1999, p. 333–349.
[ISH 78] ISHIMARU A., Wave propagation and scattering in random media, Oxford University
Press, 1978.
[SAA 86] SAAD Y., SCHULTZ M., « GMRES : A generalized minimal residual algorithm for
solving nonsymetric linear systems », SIAM Journal on Scientific and Statistical Computing,
vol. 7, 1986, p. 856-869.
[SAV 99] SAVIN E., « Effet de la variabilité du sol et du champ incident en interaction sismique
sol-structure », PhD thesis, Ecole Centrale Paris, 1999.
[SAV 02] SAVIN E., CLOUTEAU D., « Coupling a bounded domain and an unbounded heterogeneous
domain for elastic wave propagation in three-dimensional random media », Int.
J. Num. Meth. in Eng, vol. 24, 2002, p. 607-630.
[SHE 98] SHENG P., Introduction to wave scattering, localization and mesoscopic phenomena,
Academic Press, 1998.
[TAL 94] LE TALLEC P., Domain decomposition methods in computational mechanics, Noth-
Holland, 1994.