Determination of the modified exterior Steklov eigenvalues via the reciprocity gap method (Q6664860)

The authors consider a class of new eigenvalue problems arising in inverse acoustic scattering theory for inhomogeneous media with measured data inside a cavity. Precisely, the so-called modified exterior Steklov eigenvalues might serve as potential target signatures in nondestructive testing. Hence, the authors investigate how they can be determined from measured Cauchy data of the total field on some manifolds inside the cavity using interior point sources. This is achieved by exploiting the reciprocity gap method which is based on linear boundary integral equations. The authors show that the blow-up behavior of the approximate solution to this integral equation can then be used to characterize the modified exterior Steklov eigenvalues. Based on this, an algorithm is presented to determine those eigenvalues. Extensive numerical results are given in two-dimensions and show the applicability to determine them, hence complementing the given theory.