Comptes Rendus
Multi-directional and multi-time step absorbing layer for unbounded domain
Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 539-557.

Variant techniques are proposed for reproducing the elastic wave propagation in an unbounded medium such as the infinite elements, the absorbing boundary conditions or the perfect matched layers. Here, a simplified approach is adopted by considering absorbing layers characterized by the viscous Rayleigh matrix as studied by Semblat et al. [16] and Rajagopal et al. [14]. Here, further improvements to this procedure are provided. First, we start by establishing the strong form for the elastic wave propagation in a medium characterized by the Rayleigh matrix. This strong form will be used for deriving optimal conditions for damping out in the most efficient way the incident waves while minimizing the spurious reflected waves at the interface between the domain of interest and the Rayleigh damping layer. A procedure for designing the absorbing layer is proposed by targeting a performance criterion expressed in terms of logarithmic decrement of the wave amplitude in the layer thickness. Second, the GC subdomain coupling method, proposed by Combescure and Gravouil [9], is introduced for enabling the choice of any Newmark time integration schemes associated with different time steps depending on subdomains. When wave propagation is predicted by an explicit time integrator, the subdomain strategy is of great interest because it enables a different time integrator for the absorbing layer to be adopted. An external coupling software, based on the GC method, is used to carry out multi=time step explicit/implicit co-computations, making interact in time an explicit FE code (Europlexus) for the domain of interest, with an implicit FE code (Cast3m) handling the absorbing boundary layers. The efficiency of the approach is shown in 1D and 2D elastic wave propagation problems.

Published online:
DOI: 10.1016/j.crme.2014.05.007
Keywords: Unbounded medium, Absorbing layer, Subdomain coupling, Heterogeneous time integrators, Multi time steps

Eliass Zafati 1; Michaël Brun 1; Irini Djeran-Maigre 1; Florent Prunier 1

1 Université de Lyon, INSA-Lyon, LGCIE, 34, rue des Arts, 69621 Villeurbanne cedex, France
     author = {Eliass Zafati and Micha\"el Brun and Irini Djeran-Maigre and Florent Prunier},
     title = {Multi-directional and multi-time step absorbing layer for unbounded domain},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {539--557},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2014},
     doi = {10.1016/j.crme.2014.05.007},
     language = {en},
AU  - Eliass Zafati
AU  - Michaël Brun
AU  - Irini Djeran-Maigre
AU  - Florent Prunier
TI  - Multi-directional and multi-time step absorbing layer for unbounded domain
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 539
EP  - 557
VL  - 342
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2014.05.007
LA  - en
ID  - CRMECA_2014__342_9_539_0
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%0 Journal Article
%A Eliass Zafati
%A Michaël Brun
%A Irini Djeran-Maigre
%A Florent Prunier
%T Multi-directional and multi-time step absorbing layer for unbounded domain
%J Comptes Rendus. Mécanique
%D 2014
%P 539-557
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%F CRMECA_2014__342_9_539_0
Eliass Zafati; Michaël Brun; Irini Djeran-Maigre; Florent Prunier. Multi-directional and multi-time step absorbing layer for unbounded domain. Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 539-557. doi : 10.1016/j.crme.2014.05.007.

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