zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Inverse scattering from an orthotropic medium. (English) Zbl 0885.35143
The authors consider the scattering of time harmonic electromagnetic waves by a two-dimensional orthotropic medium with constant dielectric. In the first part, they study the direct problem by boundary integral equation methods. The fundamental solution and the single- and double-layer potentials are constructed via transformation to the classical Helmholtz equation. The second part is devoted to the inverse scattering problem. This is the problem to determine the refractive index from measurements of the far field pattern. A uniqueness result is proven and a numerical method for the reconstruction of the index of refraction is proposed. Some numerical results demonstrate advantages and disadvantages of the method.

MSC:
35R30Inverse problems for PDE
35Q60PDEs in connection with optics and electromagnetic theory
35P25Scattering theory (PDE)
WorldCat.org
Full Text: DOI
References:
[1] Colton, D.; Erbe, C.: Spectral theory for the magnetic far field operator in an orthotropic medium. Nonlinear problems in applied mathematics, 96-103 (1996) · Zbl 0886.35167
[2] Colton, D.; Kirsch, A.: A simple method for solving inverse scattering problems in the resonance region. Inverse problems 12, 383-393 (1996) · Zbl 0859.35133
[3] Colton, D.; Kress, R.: Integral equation methods in scattering theory. (1983) · Zbl 0522.35001
[4] Colton, D.; Kress, R.: Inverse acoustic and electromagnetic scattering theory. (1992) · Zbl 0760.35053
[5] D. Colton, P. Monk, A linear sampling method for the detection of leukemia using microwaves. SIAM J. Applied Math., to appear. · Zbl 0907.92014
[6] Dautry, R.; Lions, J. L.: 4th ed. Mathematical analysis and numerical methods for science and technology. Mathematical analysis and numerical methods for science and technology 1 (1990)
[7] Isakov, V.: On uniqueness in the inverse transmission scattering problem. Comm. partial differential equations 15, 1565-1587 (1990) · Zbl 0728.35148
[8] Kirsch, A.; Kress, R.: Uniqueness in inverse obstacle scattering. Inverse problems 9, 285-299 (1993) · Zbl 0787.35119
[9] Kress, R.: Linear integral equations. (1989) · Zbl 0671.45001
[10] Kress, R.; Roach, G. F.: Transmission problems for the Helmholtz equation. J. math. Phys. 19, 1433-1437 (1978) · Zbl 0433.35017
[11] Maue, A. W.: Über die formulierung eines allgemeinen beugungsproblems durch eine integralgleichung. Z. physik 126, 601-618 (1949) · Zbl 0033.14101
[12] Miranda, C.: Partial differential equations of elliptic type. (1970) · Zbl 0198.14101
[13] R. Potthast, Electromagnetic scattering from an orthotropic medium, submitted for publication. · Zbl 0980.78004
[14] R. Potthast, Integral equation methods in electromagnetic scattering from an anisotropic medium, submitted for publication. · Zbl 1054.78014
[15] Vekua, I. N.: New methods for solving elliptic equations. (1967) · Zbl 0146.34301