Carpio Rodríguez, Ana MaríaRapún Banzo, María Luisa2023-06-202023-06-2020080075-8434https://hdl.handle.net/20.500.14352/49859Topological derivative methods are used to solve constrained optimization reformulations of inverse scattering problems. The constraints take the form of Helmholtz or elasticity problems with different boundary conditions at the interface between the surrounding medium and the scatterers. Formulae for the topological derivatives are found by first computing shape derivatives and then performing suitable asymptotic expansions in domains with vanishing holes. We discuss integral methods for the numerical approximation of the scatterers using topological derivatives and implement a fast iterative procedure to improve the description of their number, size, location and shape.engjournal articlehttp://www.springerlink.com/content/q47k22718j526414/fulltext.pdfhttp://www.springerlink.comrestricted access517.9Inverse obstacle scatteringBoundary inegral-equationsLevel set methodsTransmission problemsHelmholtz-equationAnisotropic elasticitySampling methodTomographyWavesOptimizationEcuaciones diferenciales1202.07 Ecuaciones en Diferencias