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Stable methods for solving the inverse scattering problem for a cylinder

Published online by Cambridge University Press:  14 November 2011

David Colton  and
Andreas Kirsch
David Colton
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19711, U.S.A.
Andreas Kirsch
Affiliation:
Lehrstühle für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, West Germany
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Synopsis

It is shown that the inverse scattering problem for an infinite cylinder can be stabilized by assuming a priori that the unknown boundary of the cylindrical cross section lies in a compact family of continuously differentiable simple closed curves. A constructive method for determining the shape of this boundary is given under the assumption that an initial approximation is known and that the scattering cross section is known forn distinct incoming plane waves in the resonant region.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 181 - 188
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Ahlfors, L.. Conformal Invariants: Topics in Geometric Function Theory (New York: McGrawHill, 1973).Google Scholar
2Backus, G. and Gilbert, F., Uniqueness in the inversion of inaccurate gross earth data. Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 123—197.Google Scholar
3Colton, D.. Analytic Theory of Partial Differential Equations (London: Pitman, 1980).Google Scholar
4Colton, D.. The inverse scattering problem for a cylinder. Proc. Roy. Soc. EdinburghSect. A 84 (1979), 135—143.Google Scholar
5Colton, D. amd Kirsch, A.. The determination of the surface impedance of an obstacle from measurements of the far field pattern. SIAM J. AppL Math., to appear.Google Scholar
6Colton, D. and Kleinman, R. E.. The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 86(1980), 29—42.CrossRefGoogle Scholar
7Garabedian, P. R.. An integral equation governing electromagnetic waves Quart. Appl.Math. 12 (1953), 428—433.Google Scholar
8Kolmogorov, A. N. and Fomin, S. V.. Elements of the Theory of Functions and Functional Analysis, Vol. I (Rochester: Graylock Press, 1957).Google Scholar
9Lax, P. D. and Phillips, R. S.. Scattering Theory (New York: Academic, 1957).Google Scholar
10Pommerenke, C.. Univalent Functions (Göttingen: Vandenhoeck and Ruprecht, 1975).Google Scholar
11Roger, A.. Newton Kantorovich algorithm applied to an electomagnetic inverse problem. IEEE Trans. Antennas and Propagation, to appea.Google Scholar