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Quasi-local multi-trace boundary integral formulations

Xavier Claeys 1, 2 
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
Abstract : 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.
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Xavier Claeys. Quasi-local multi-trace boundary integral formulations. Numerical Methods for Partial Differential Equations, Wiley, 2015, 31 (6), pp.2043-2062. ⟨hal-01070264⟩

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