3 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 3 / 3
Yayın On a class of functional equations of the Wiener-Hopf type and their applications in n-part scattering problems(Oxford Univ Press, 2003-12) İdemen, Mehmet Mithat; Alkumru, AliAn asymptotic theory for the functional equation K-phi=f, where K : X-->Y stands for a matrix-valued linear operator of the form K=K1P1+K2P2+...+KnPn, is developed. Here X and Y refer to certain Hilbert spaces, {P-alpha} denotes a partition of the unit operator in X while K-alpha are certain operators from X to Y. One assumes that the partition {P-alpha} as well as the operators K-alpha depend on a complex parameter nu such that all K-alpha are multi-valued around certain branch points at nu=k(+) and nu=k(-) while the inverse operators K-alpha(-1) exist and are bounded in the appropriately cut nu-plane except for certain poles. Then, for a class of {P-alpha} having certain analytical properties, an asymptotic solution valid for \k(+/-)\-->infinity is given. The basic idea is the decomposition of phi into a sum of projections on n mutually orthogonal subspaces of X. The results can be extended in a straightforward manner to the cases of no or more branch points. If there is no branch point or n=2, then the results are all exact. The theory may have effective applications in solving some direct and inverse multi-part boundary-value problems connected with high-frequency waves. An illustrative example shows the applicability as well as the effectiveness of the method.Yayın Diffraction of two-dimensional high-frequency electromagnetic waves by a locally perturbed two-part impedance plane(Elsevier Science BV, 2005-06) İdemen, Mehmet Mithat; Alkumru, AliDuring the second half of the last century mixed boundary-value problems had been an appealing research subject for both mathematicians and engineers. Among this kind of problems those connected with wave propagation in half-spaces or slabs bounded by sectionally homogeneous boundaries took an important place because they were motivated by microwave applications. The simplest problem of this kind is the classical two-part problem which can be reduced to a functional equation involving two unknown functions, say psi(+)(v) and psi(-)(v), which are regular in the upper and lower halves of the complex v-plane, respectively. This functional equation can be rigorously treated by the Wiener-Hopf technique. When the boundary consists of three (or more) parts, the resulting functional equation involves also an entire function, say P(v), in addition to psi(+)(v) and psi(-)(v), which makes the problem not solvable exactly. A local (non-homogeneous) perturbation on a two-part boundary, which is of extreme importance from engineering point of view, gives also rise to a problem of this type. The known methods established to overcome the difficulties inherent to the three-part problems are based on the elimination of the entire function P(v) first to obtain a linear system of two singular integral equations for psi(+) and psi(-). After having determined the functions psi(+)(v) and psi(-)(v) by solving this system of integral equations numerically, the function P(v) is found from the functional equation in question. Numerical solutions to the aforementioned system, which need rather hard computations, cannot provide results which are suitable to physical interpretations. The aim of the present paper is to establish a new method which is based, conversely, on the elimination of the unknown functions psi(+)(v) and psi(-)(v) first to obtain a linear integral equation of the first kind for the entire function P(v), which can be solved rather easily by regularized numerical methods. Then the functions psi(+)(v) and psi(-)(v) are determined through the classical Wiener-Hopf technique. The result to be obtained by this approach seems to be more suitable to physical interpretations and permits one to reveal the effect of the perturbation on the scattered wave. Some illustrative examples show the applicability and effectiveness of the method.Yayın A generalization of the Wiener-Hopf approach to direct and inverse scattering problems connected with non-homogeneous half-spaces bounded by n-part boundaries(Oxford Univ Press, 2000-08) İdemen, Mehmet Mithat; Alkumru, AliThe classical Wiener-Hopf method connected with mixed two-part boundary-value problems is generalized to cover n-part boundaries. To this end one starts from an ad-hoc representation for the Green function, which involves n unknown functions having certain analytical properties. Thus the problem is reduced to a functional equation involving n unknowns, which constitutes a generalization of the classical Wiener-Hopf equation in two unknowns. To solve this latter which cannot be solved exactly when n greater than or equal to 3, one establishes a new method permitting one to obtain the asymptotic expressions valid when the wavelength is sufficiently small as compared with the widths of the inner strips of the boundary. The essentials of the method are elucidated through a concrete inverse scattering problem whose aim is to determine the constitutive electromagnetic parameters of a slab and a half-space bounded by an n-part impedance plane. Some illustrative numerical examples show the applicability as well as the accuracy of the method.
