A Linearized Boundary Control Method for the Acoustic Inverse Boundary Value Problem

Abstract

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.

19 pages, 9 figures

References in corpus (2)

• Spacetime finite element methods for control problems subject to the wave equation
• Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map