Stability assessment of a unified variational boundary integral method applicable to thin scatterers and scatterers with corners (Q1912067)

We assess the stability, especially at and near critical frequencies, of a new unified, stable, symmetric, domain finite element and boundary integral methodology for solving time-harmonic interface problems for scatterers of arbitrary shape. The validity of this energy-based variational procedure for rigid and penetrable smooth scatterers, including the existence, uniqueness and optimal convergence of the corresponding numerical approximations, has been proved rigorously in the context of fluid-structure interaction problems. The emphasis here is on investigating the applicability of this procedure to the case of scatterers with corners, using square and thin rectangular two-dimensional rigid obstacles as prototypes.