Mathematical and numerical study of transient wave scattering by obstacles with the Arlequin Method

Jorge Albella Martínez (1) , Hachmi Ben Dhia (2) , Sébastien Imperiale (3, 4) , Jerónimo Rodríguez (1)

1 USC - Universidade de Santiago de Compostela [Spain]
2 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
4 Université Paris-Saclay

In this work we extend the Arlequin method to overlapping domain decomposition technique for transient wave equation scattering by obstacles. The main contribution of this work is to construct and analyze from the continuous level up to the fully discrete level some variants of the Arlequin method. The constructed discretizations allow to solve wave propagation problems while using non-conforming and overlapping meshes for the background propagating medium and the surrounding of the obstacle respectively. Hence we obtain a flexible and stable method in terms of the space discretization-an inf-sup condition is proven-while the stability of the time discretization is ensured by energy identities.

Mots clés: Domain Decomposition; Stability Analysis; Wave propagation

Domaines: Analyse numérique [math.NA]

Jorge Albella Martínez, Hachmi Ben Dhia, Sébastien Imperiale, Jerónimo Rodríguez. Mathematical and numerical study of transient wave scattering by obstacles with the Arlequin Method. SIAM Journal on Numerical Analysis, inPress, ⟨10.1137/19M1263959⟩. ⟨hal-01898420⟩