Year: 2026
Type: article
Abstract: . We introduce a new family of artificial backgrounds corresponding to averaged impedance boundary conditions formulated in an abstract framework. These backgrounds are used to define a finite number of averaged Steklov eigenvalues, which are associated with inverse scattering problems from inhomogeneous media. We prove that these special eigenvalues can be determined from full-aperture, fixed-frequency far fields using the inside-outside duality method. We then numerically demonstrate how this method can be used to reconstruct averaged values of the refractive index.
DOI: 10.1137/25m1743806
Institutions: Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique et Energétique, Électricité de France (France), Unité de Mathématiques Appliquées, IDEFIX: Solution d'Equations Differentielles pour l'Imagerie et la physique, Institut national de recherche en sciences et technologies du numérique, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, École Nationale Supérieure de Techniques Avancées Paris
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406786249