Mathematical Algorithms for Multidimensional Inverse Scattering Problems in Inhomogeneous Medium.

• Main Author: Klibanov, Michael V.
• Other Authors: NORTH CAROLINA UNIV AT CHARLOTTE DEPT OF MATHEMATICS
• Format: Text
• Language: English
• Published: 1992
• Subjects: Numerical Mathematics; *ALGORITHMS; *INVERSE SCATTERING; *APPLIED MATHEMATICS; ACOUSTICS; BIOLOGY; CONVERGENCE; DIFFUSION; ELECTROMAGNETIC PROPERTIES; MATERIALS; MEDIA; NAVY; OCEANS; PHASE; RATES; SEA ICE; SEMICONDUCTORS; THEORY; TOMOGRAPHY; X RAYS; MARINE BIOLOGY; *Inhomogeneity; *Noninvasive testing; Sea ice
• Online Access: http://www.dtic.mil/docs/citations/ADA266440; http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA266440

Multidimensional inverse scattering problems (ISP) in inhomogeneous media have important and extensive applications in many areas of interest to the NAVY. Among them are ocean acoustics, electromagnetic properties of sea ice, oceanic biology, and non-invasive testing of some materials, including semiconductors. From mathematical point of view the numerical methods must be based on robust and efficient mathematical algorithms. The development of such algorithms with rapid convergence rates is a challenging task in the theory of multidimensional ISP. In fact, ISPs represent an alternative to the conventional X-ray tomography. The major difficulty of the ISPs is that waves propagate in different (unknown) directions rather than just along straight lines, as it is in the case with X-ray tomography. Thus another term for ISPs is diffusion tomography . We have been working on theoretical studies and computational testing of numerical methods for Inverse Scattering Problems (ISP). Our main efforts have been concentrated on 3-Dimensional ISP. A more minor effort was devoted to 1-D phaseless ISP, that is ISP without phase information.