Averaged Steklov Eigenvalues, Inside-Outside Duality and Application to Inverse Scattering
Abstract
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.
Fields of Study & Subjects
Numerical methods in inverse problems
Electromagnetic Scattering and Analysis
Microwave Imaging and Scattering Analysis
Publication details
- Journal / source
- SIAM Journal on Applied Mathematics
- Volume
- 86
- Issue
- 3
- Pages
- 961–984
- Publication date
- 27 May 2026
- Language
- EN