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Marc Bonnet (POEMS group, ENSTA Paris, France).
Title: An iterative domain decomposition coupling approach for transient acoustic-elastic scattering.
Hosts: Jason Kaye, Shravan Veerapaneni.
In this work, motivated by an ongoing collaboration with naval industry, we address the transient scattering of waves propagating in an unbounded fluid medium (treated as linearly acoustic) surrounding a submerged elastic solid. We establish data-to-solution mappings for which the continuous transient acoustic-elastic scattering problem is well-posed. Our main goal is then to develop an iterative domain decomposition that acts globally on the whole finite time analysis duration, consistently with the aim of using a convolution quadrature-based integral equation formulation for the unbounded acoustic medium. We then show that available solvability mappings for Dirichlet or Neumann transient problems in each medium rule out coupling iterations based on Dirichlet or Neumann initial-boundary value problems in each domain. In view of this, we propose coupling iterations based on impedance (Robin) boundary conditions (RR iterations), and establish their convergence for the continuous coupled problem. We implemented a proof-of-concept version of this approach, where the acoustic Robin problems are solved by means of boundary integral equations and a convolution quadrature method while solid motions are computed using conventional finite elements and time-stepping methods. Through several numerical examples, the proposed iterative coupling approach is validated against an analytical reference solution, its convergence demonstrated and some features (such as the use of relaxation) illustrated. Finally, we discuss an important extension of the RR iterations whereby the coupling interface is moved inside the fluid domain. This is a joint work with Stephanie Chaillat (CNRS, POEMS) and Alice Nassor (PhD student, defended Dec. 2023).