Combined far-field operators in electromagnetic inverse scattering theory

Mathematical Methods in the Applied Sciences

Volumn 26, Issue 5, 2003, Pages 413-429

  Cakoni, Fioralba ^a   Colton, David ^a   Kress R ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

Electromagnetic inverse scattering; Linear sampling method

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE POLARIZATION; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

ELECTROMAGNETIC INVERSE SCATTERING THEORY; LINEAR SAMPLING METHOD;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0037465759     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.360     Document Type: Article

References (24)

1. Cakoni F, Colton D. On the mathematical basis of the linear sampling method, to appear.
2. Cakoni F, Colton D, Monk P. The electromagnetic inverse scattering problem for partially coated Lipschitz domains, to appear.
3. Colton D, Kirsch A. A simple method for solving inverse scattering problems in the resonance region. Inverse Problems 1996; 12:383-393.
4. Colton D, Piana M, Potthast R. A simple method using Morozov's discrepancy principle for solving inverse scattering problems. Inverse Problems 1997; 13:1477-1493.
5. Kirsch A. Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 1998; 14:1489-1512.
6. Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory (2nd edn). Springer: Berlin, 1998.
7. Colton D, Kirsch A. The use of polarization effects in electromagnetic inverse scattering problems. Mathematical Methods in the Applied Sciences 1992; 15:1-10.
8. Colton D, Monk P. The scattering of electromagnetic wave by a perfectly conducting infinite cylinder. Mathematical Methods in the Applied Sciences 1990; 12:503-518.
9. Colton D, Kress R. On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Mathematical Methods in the Applied Sciences 2001; 24:1289-1303.
10. Colton D, Sleeman BD. An approximation property of importance in inverse scattering theory. Proceedings of the Edinburgh Mathematical Society 2001; 42:449-454.
11. Muniz W. Ph.D. Thesis, Department of Mathematical Sciences, University of Delaware, in preparation.
12. Brandfass M, Lanterman AD, Warnick KF. A comparison of the Colton-Kirsch inverse scattering methods with linearized tomographic inverse scattering. Inverse Problems 2001; 17:1797-1816.
13. McLean W. Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press: Cambridge, 2000.
14. Hähner P. On the uniqueness of the shape of a penetrable, anisotropic obstacle. Journal of Computational and Applied Mathematics 2000; 116:167-180.
15. Cakoni F, Colton D, Monk P. The direct and inverse scattering problems for partially coated obstacles. Inverse Problems 2001; 17:1997-2015.
16. Ochs RL. A version of Runge's theorem for the Helmholtz equation with applications to scattering theory. Proceedings of the Edinburgh Mathematical Society 1989; 32:107-119.
17. Colton D, Piana M. The simple method for solving the electromagnetic inverse scattering problem: the case of TE polarized waves. Inverse Problems 1998; 14:597-614.
18. Monk P. Finite Element Methods for Maxwell's Equations. Oxford University Press: Oxford, 2002.
19. Cessenat M. Mathematical Methods in Electromagnetism. World Scientific: Singapore, 1996.
20. Buffa A, Ciarlet Jr. P. On traces for functional spaces related to Maxwell's equations. Part I: an integration by parts formula in Lipschitz polyhedra. Mathematical Methods in the Applied Sciences 2001; 24:9-30.
21. Kirsch A, Monk P. A finite element method for approximating electromagnetic scattering from a conducting object. Numerische Mathematik, to appear.
22. Kress R. Electromagnetic wave scattering. In Scattering, Pike R, Sabatier P (eds). Academic Press: New Yok, 2001, 175-210.
23. 2 Dirichlet boundary conditions. Methoden und Verfahren der Mathematischen Physik 1991; 37:85-96.
24. Colton D, Kress R. Integral Equation Methods in Scattering Theory. Wiley: New York, 1983.