An eigenvalue decomposition method to construct absorbing boundary conditions for acoustic and elastic wave equations

Dong, Liangguo; She, De-Ping; L, Guan; Ma, Zaitian

doi:10.1088/1742-2132/2/3/003

Cited by 7 publications

(1 citation statement)

References 23 publications

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“…They have been adapted to numerical techniques as different as finite differences, finite elements and spectral elements in order to reduce reflections at the outer boundaries of the computational domain and efficiently simulate unbounded media at the local or regional scale. Damping layers or 'sponge zones' (Cerjan et al 1985;Sochacki et al 1987), paraxial conditions (Clayton & Engquist 1977;Engquist & Majda 1977;Stacey 1988;Higdon 1991;Quarteroni et al 1998), optimized conditions (Peng & Töksoz 1995), the eigenvalue decomposition method (Dong et al 2005), continued fraction absorbing conditions (Guddati & Lim 2006), exact absorbing conditions on a spherical contour (Grote 2000) or asymptotic local or non-local operators (Givoli 1991;Hagstrom & Hariharan 1998) have been introduced. However, the local conditions generate spurious low frequency energy reflected back into the main domain at all angles of incidence, sponge layers require a prohibitive number of gridpoints to be relatively efficient, and paraxial conditions do not efficiently absorb waves reaching the boundaries at grazing incidence and can become unstable in some cases, for instance for a high value of Poisson's ratio.…”

Section: Introductionmentioning

confidence: 99%

An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation

Martin¹,

Komatitsch

2009

Geophysical Journal International

155

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S U M M A R YIn the context of the simulation of wave propagation, the perfectly matched layer (PML) absorbing boundary layer has proven to be efficient to absorb non-grazing incidence waves. However, the classical discrete PML cannot efficiently absorb waves reaching the absorbing layer at grazing incidence. This is observed, for instance, in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In order to improve the PML efficiency at grazing incidence we derive an unsplit convolutional PML (CPML) for a fourth-order staggered finite-difference numerical scheme applied to the 3-D viscoelastic seismic wave equation. The time marching equations of the standard linear solid mechanisms used do not need to be split and only the memory variables associated with velocity derivatives are stored at each time step. This is important in the case of more than one damping mechanism. Memory storage is reduced by more than 70 per cent in the PML regions in 3-D simulations compared to split PMLs optimized at grazing incidence. We validate the technique based on a benchmark performed in a thin mesh slice.

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