Equivalent Boundary Conditions for Heterogeneous Acoustic Media

Manuela Longoni de Castro, Julien Diaz, Victor Perón

Abstract


In this work, we have worked on possibilities to model artificial boundaries needed in the simulation of wave propagation in acoustic heterogeneous media.  Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. Two possibilities were studied and compared in computational tests: the use of absorbing boundary conditions on an artificial boundary in the atmosphere layer and the elimination of the atmosphere layer using an equivalent boundary condition that mimics the propagation of waves through the atmosphere.

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References


B. Alpert, L. Greengard, and T. Hagstrom, “Rapid evaluation of nonreflect-

ing boundary kernels for time-domain wave propagation,” SIAM Journal

on Numerical Analysis, vol. 37, no. 4, pp. 1138–1164, 2000.

T. Hagstrom and S. Hariharan, “A formulation of asymptotic and exact

boundary conditions using local operators,” Appl. Numer. Math., vol. 27,

pp. 403–416, 1998.

B. Alpert, L. Greengard, and T. Hagstrom, “Nonreflecting boundary con-

ditions for the time-dependent wave equation,” Journal of Computational

Physics, vol. 180, no. 1, pp. 270–296, 2002.

M. J. Grote and J. B. Keller, “Exact nonreflecting boundary conditions for

the time dependent wave equation,” SIAM Journal on Applied Mathematics

, vol. 55, no. 2, pp. 280–297, 1995.

J. P. B´erenger, “A perfectly matched layer for the absorption of electro-

magnetic waves,” J. Comput. Phys., vol. 114, pp. 185–200, 1994.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium

for the truncation of fdtd lattices,” Antennas and Propagation, IEEE

Transactions on, vol. 44, no. 12, pp. 1630–1639, 1996.

F. Collino and C. Tsogka, “Application of the perfectly matched absorbing

layer model to the linear elastodynamic problem in anisotropic heteroge-

neous media,” Geophysics, vol. 66, no. 1, pp. 294–307, 2001.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched

anisotropic absorber for use as an absorbing boundary condition,” Antennas

and Propagation, IEEE Transactions on, vol. 43, no. 12, pp. 1460–1463,

S. Abarbanel and D. Gottlieb, “A mathematical analysis of the pml

method,” Journal of Computational Physics, vol. 134, no. 2, pp. 357–363,

D. Givoli and B. Neta, “High-order nonreflecting boundary scheme for time-

dependent waves,” J. Comput. Phys., vol. 186, pp. 24 – 46, Mar 2003.

R. Higdon, “Numerical absorbing boundary conditions for the wave equa-

tion,” Math. Comp., vol. 49, pp. 65–90, 1987.

T. Hagstrom and T. Warburton, “A new auxiliary variable formulation

of high-order local radiation boundary conditions: corner compatibility

conditions and extensions to first-order systems,” Wave motion, vol. 39,

pp. 327 – 338, Apr 2004.

D. Givoli, “High-order local non-reflecting boundary conditions: a review,”

Wave Motion, vol. 39, no. 4, pp. 319–326, 2004.

T. Hagstrom, T. Warburton, and D. Givoli, “Radiation boundary con-

ditions for time-dependent waves based on complete plane wave expan-

sions,” Journal of Computational and Applied Mathematics, vol. 234, no. 6,

pp. 1988–1995, 2010.

T. Hagstrom, M. L. De Castro, D. Givoli, and D. Tzemach, “Local high-

order absorbing boundary conditions for time-dependent waves in guides,”

Journal of Computational Acoustics, vol. 15, no. 01, pp. 1–22, 2007.

D. Givoli, T. Hagstrom, and I. Patlashenko, “Finite element formulation

with high-order absorbing boundary conditions for time-dependent waves,”

Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 29,

pp. 3666–3690, 2006.

T. Hagstrom and T. Warburton, “A new auxiliary variable formulation

of high-order local radiation boundary conditions: corner compatibility

conditions and extensions to first-order systems,” Wave Motion, vol. 39,

no. 4, pp. 327–338, 2004.

A. Bendali and K. Lemrabet, “The effect of a thin coating on the scattering

of a time-harmonic wave for the helmholtz equation,” SIAM Journal on

Applied Mathematics, vol. 56, no. 6, pp. 1664–1693, 1996.

B. Engquist and J.-C. N´ed´elec, “Effective boundary conditions for acoustic

and electromagnetic scattering in thin layers,” Technical Report of CMAP

, Centre de Math´ematiques Appliqu´ees, 1993.

T. B. Senior and J. L. Volakis, Approximate boundary conditions in electromagnetics

, vol. 41. Iet, 1995.

O. D. Lafitte, “Diffraction in the high frequency regime by a thin layer

of dielectric material i: The equivalent impedance boundary condition,”

SIAM Journal on Applied Mathematics, vol. 59, no. 3, pp. 1028–1052, 1998.

T. Hagstrom, M. L. De Castro, D. Givoli, and D. Tzemach, “Local high-

order absorbing boundary conditions for time-dependent waves in guides,”

Journal of Computational Acoustics, vol. 15, no. 01, pp. 1–22, 2007.

C. Agut and J. Diaz, “Stability analysis of the interior penalty discon-

tinuous galerkin method for the wave equation,” ESAIM: Mathematical

Modelling and Numerical Analysis, vol. 1, no. 1, 2010.

V. P´eron, “Equivalent Boundary Conditions for an Elasto-Acoustic Prob-

lem with a Thin Layer,” Rapport de recherche RR-8163, INRIA, Nov. 2012.




DOI: https://doi.org/10.5540/tema.2014.015.03.0301

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