Quasi-local multi-trace boundary integral formulations

Xavier Claeys (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations

In the context of time harmonic wave scattering by piecewise homogeneous penetrable objects, we present a new variant of the multi-trace boundary integral formulation, that differs from the local multi-trace approach of [Jerez-Hanckes \& Hiptmair, 2012], by the presence of regularisation terms involving boundary integral operators and localised at junctions i.e. points where at least three subdomains abut. We prove well-posedness and quasi-optimal convergence of conforming Galerkin discretisations for this new formulation, and present numerical results.

Mots clés: boundary elements; integral equations; wave scattering; multi-subdomains

Domaines: Analyse numérique [math.NA]

Xavier Claeys. Quasi-local multi-trace boundary integral formulations. Numerical Methods for Partial Differential Equations, 2015, 31 (6), pp.2043-2062. ⟨hal-01070264⟩