Globally Convergent Methods for Solving Coefficient Inverse Problems for Time Dependent Maxwell Equations
Final rept. 15 Sep 2011-15 Sep 2014
NORTH CAROLINA UNIV AT CHARLOTTE DEPT OF MATHEMATICS AND STATISTICS
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This is an interdisciplinary project. The main results of the project are 1. The analytical proof of the global convergence property using a sophisticated mathematical apparatus. 2. The development of a sophisticated analytical apparatus for establishing the relaxation property of the adaptivity technique. 3. Numerical implementations of resulting algorithms. 4. Numerical verifications of resulting algorithms on computationally simulated data. 5. Assembling an experimental apparatus in Microwave Laboratory of University of North Carolina at Charlotte. 6. Verification of the globally convergent numerical method on backscattering experimental data for targets standing in air. Targets mimic explosives. 7. Verification of the globally convergent numerical method on backscattering experimental data for targets buried in the ground. This case is much more complicated than the case of targets in air. 8. An experimental and numerical reconstruction evidence of the super resolution phenomenon. 9. Addressing a need of the Army via successful work with experimental data collected by the Forward Looking Radar of US Army Research Laboratory ARL. The globally convergent method of this project was used. 10. Transfer of a ready-to-use software to ARL resulting from item 9. This software works with the real data of the Forward Looking Radar of ARL. 11. The use of experimental data of item 9 for a comparison of performances of the globally convergent numerical method of this project and the classical Krein equation method. It was established that while the first method works well, the second one fails for these data.
- Numerical Mathematics
- Miscellaneous Detection and Detectors