Mathematical and numerical study of transient wave scattering by obstacles with a new class of arlequin coupling

Abstract

In this work, we extend the Arlequin method, a multiscale and multimodel framework based on overlapping domains and energy partitions for reliable modeling and flexible simulation of transient problems of wave scattering by obstacles. The main contribution is the derivation and analysis of new variants of the coupling operators. The constructed finite element and finite difference discretizations allow for solving wave propagation problems while using nonconforming and overlapping meshes for the background propagating medium and a local patch surrounding the obstacle, respectively. This provides a method with great flexibility and a low computational cost. The method is proved to be stable in terms of both space discrtization-an inf-sup condition is established-and time discretization-conservation of discrte energy is proved. 1 dimensional and 2 dimensional numerical results confirm the good perfomance of the overall discretization scheme.