Convexification of restricted Dirichlet-to-Neumann map
Abstract
By our definition, “restricted Dirichlet-to-Neumann (DN) map” means that the Dirichlet and Neumann boundary data for a coefficient inverse problem (CIP) are generated by a point source running along an interval of a straight line. On the other hand, the conventional DN data can be generated, at least sometimes, by a point source running along a hypersurface. CIPs with restricted DN data are non-overdetermined in the n-dimensional case, with n ≥ 2 {n\geq 2} . We develop, in a unified way, a general and radically new numerical concept for CIPs with restricted DN data for a broad class of PDEs of second order, such as, e.g., elliptic, parabolic and hyperbolic ones. Namely, using Carleman weight functions, we construct globally convergent numerical methods. Hölder stability and uniqueness are also proved. The price we pay for these features is a well-acceptable one in the numerical analysis, that is, we truncate a certain Fourier-like series with respect to some functions depending only on the position of the point source. At least three applications are imaging of land mines, crosswell imaging and electrical impedance tomography.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 05, 2017
- Source ID
- 10.1515/jiip-2017-0067
Entities
People
- Michael Klibanov
Organizations
- Army Research Office
- Office of Naval Research
- United States Army Research Laboratory