The inverse problem of detecting the shape and location of a rigid scatterer fully embedded in a halfplane based solely on surficial measurements of the scatterer's response to illumination by plane waves, is solved numerically in the frequency domain, using integral equations within the general framework of PDE-constrained optimization. Two different, but closely related, physical problems are considered: first, scatterers embedded in the soil where SH waves are used for detection, and secondly, scatterers embedded in an acoustic fluid, where pressure waves are used for detection. The elastic case of SH waves gives rise to a traction-free surface and an associated Neumann condition, whereas the acoustic case gives rise to a pressure-free surface and a Dirichlet condition, respectively. The measurement stations are sparsely located on the free surface and depending on the physical problem, either displacements are measured (SH case), or fluid velocities (or pressure gradients) are recorded (acoustic case). Localizing and detecting the shape of the scatterer entails matching the observed response to the response resulting from the scatterer's assumed location and shape. There arises a misfit minimization problem that is tackled using a PDE-constrained optimization approach, which, in turn, results in state, adjoint, and control problems, necessary for the satisfaction of the first- order optimality conditions. Boundary integral equations are used throughout, whereas operations over moving interfaces that arise naturally during the iterative search process, are treated using the apparatus of total differentiation.To alleviate inherent difficulties with solution multiplicity, amplitude-based misfits and continuation schemes are used. Numerical results, attesting to the efficacy of the methodology in detecting shapes and localizing scatterers, are discussed. / text

Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-06-29T15:51:42Z No. of bitstreams: 0 / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-07-03T15:49:10Z (GMT) No. of bitstreams: 0 / Made available in DSpace on 2018-07-03T15:49:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-03-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho será proposto um método de acoplamento iterativo de interface com um esquema de subcycling no tempo eficiente e preciso. Este será aplicado a pro-blemas do tipo sólido-fluido discretizados, respectivamente, pelos métodos dos elementos finitos clássico (MEF) e espectral (MEFE). Adicionalmente, será proposta uma melhoria no esquema de subcycling, de modo que para convergir não sejam necessários métodos de relaxação. Aplicando o MEFE em subdomínios com geometrias pouco distorcidas, pode-se usufruir da alta precisão numérica com baixo custo de armazenamento oferecidos pelo método ao mesmo tempo em que é possível aplicar o MEF aos subdomínios com geometrias complexas, acrescentando versatilidade ao método. Diferentes exemplos nu-méricos são apresentados e analisados para demonstrar a precisão e a potencialidade das formulações numéricas propostas. / In this work, an iterative interface coupling method with an efficient and precise time subcycling scheme is proposed. It is applied to solid-fluid type problems discretized respectively by classical finite element method (FEM) and spectral finite element method (SFEM), additionally, an improvement in the subcycling scheme is proposed so as not to require relaxation methods to converge. Applying the SFEM in subdomains with low distorted geometries one can take advantage of the high numerical precision with low cost of storage offered by the method, while it is possible to apply the FEM in subdomains with complex geometries, adding versatility to the method. Many numerical examples are presented and analyzed here to show the accuracy and potentiality of the proposed numerical formulations.