2014
DOI: 10.1002/nme.4780
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Time‐domain hybrid formulations for wave simulations in three‐dimensional PML‐truncated heterogeneous media

Abstract: SUMMARYWe are concerned with the numerical simulation of wave motion in arbitrarily heterogeneous, elastic, perfectly‐matched‐layer‐(PML)‐truncated media. We extend in three dimensions a recently developed two‐dimensional formulation, by treating the PML via an unsplit‐field, but mixed‐field, displacement‐stress formulation, which is then coupled to a standard displacement‐only formulation for the interior domain, thus leading to a computationally cost‐efficient hybrid scheme. The hybrid treatment leads to, at… Show more

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Cited by 83 publications
(70 citation statements)
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“…The PML technique was introduced in 1994 by Berenger for electromagnetism [92], and later has been extended to other fields such as acoustics [93] and other elastic waves [94,95,96]. PML elements perfectly match the impedance of the material of study, so that waves enter in PML without reflections (at least in theory; in practice, studies have shown that some numerical reflections occur, mostly due to insufficient numbers of element per wavelength employed in the model [97]).…”
Section: Cylindrically Focused Air-coupled Transmittermentioning
confidence: 99%
“…The PML technique was introduced in 1994 by Berenger for electromagnetism [92], and later has been extended to other fields such as acoustics [93] and other elastic waves [94,95,96]. PML elements perfectly match the impedance of the material of study, so that waves enter in PML without reflections (at least in theory; in practice, studies have shown that some numerical reflections occur, mostly due to insufficient numbers of element per wavelength employed in the model [97]).…”
Section: Cylindrically Focused Air-coupled Transmittermentioning
confidence: 99%
“…We are concerned with stress wave propagation in a three‐dimensional, heterogeneous, elastic halfspace containing a target inclusion. In order to obtain a finite computational model, we truncate the domain of interest ( normalΩreg=normalΩnormalanormalΩnormalb) using hybrid PMLs (Ω PML ) . Note that in Figure , Ω a represents the target inclusion and Ω b represents the heterogeneous elastic solid surrounding the target inclusion.…”
Section: The Forward Problemmentioning
confidence: 99%
“…From the frequency-domain equations of Basu and Chopra, Kucukcoban and Kallivokas derived an unsplit mixed approach of the PML, by retaining the displacement and stress fields as unknowns in the time domain [17]. Next, in order to couple their PML to a displacement-only field formulation in the physical interior domain, the authors extended their PML to a mixed hybrid approach [18,19].…”
Section: Introductionmentioning
confidence: 98%
“…The main benefit is a higher versatility and numerical efficiency of the PML which can be implemented using a more appropriate time integrator associated with a larger time step than the one employed in the soil medium imposed by the CFL condition for ensuring the algorithm stability [20]. The proposed PMLs can be viewed as a hybrid and asynchronous PML version because different time integrators can be adopted as in the work of Kucukcoban and Kallivokas [18,19], with the adding desirable properties of dealing with different time scales in the same dynamic simulation. Moreover, the proposed approach enables the number of unknowns to be reduced in comparison to the previous mixed displacement-stress formulation.…”
Section: Introductionmentioning
confidence: 99%