Boundary integral equations of time harmonic wave scattering at complex structures

Xavier Claeys 1
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris
Abstract : The first chapter will be a brief recapitulation of well known results concerning layer potentials in the context of wave propagation in harmonic regime. In Chapter 2, we give an overview of the Rumsey reaction principle that is the most popular boundary integral formulation for multi-subdomain scattering, and we present a new alternative integral formulation that seems to be the first boundary integral formulation of the second kind for multi-subdomain scattering in geometrical configurations involving junction points. Chapter 3 is dedicated to the multi-trace formalism which is a completely new approach to boundary integral formulation of multi-subdomain scattering: we briefly describe the local multi-trace formulation, and describe in detail the derivation of the global multi-trace formulation developed by us, as well as its sparsified counterpart that we dubbed quasi-local multi-trace formulation. In Chapter 4 we present a new functional framework adapted to well-posed boundary integral equations for scattering by particular types of object dubbed multi-screens as they take the form of arbitrary arrangements of thin panels of impenetrable material. In Chapter 5 we describe several works on asymptotic modelling in the context wave propagation in harmonic regime. The last chapter presents research perspectives.
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Xavier Claeys. Boundary integral equations of time harmonic wave scattering at complex structures. Numerical Analysis [math.NA]. Université Pierre et Marie Curie (UPMC Paris 6), 2016. ⟨tel-01357729⟩

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