“…To this aim, a circular domain is considered which covers the perfectly conducting object to be reconstructed and set an equivalent problem by imposing an inhomogeneous surface impedance Z(φ) on the new circular boundary (See figure 3). If the object has a slightly varying and smooth boundary, it can be represented in terms of a standard impedance boundary condition [5] and the following relation is valid between the surface function ( )…”
Section: Application To Shape Reconstruction Of Conducting Objectsmentioning
confidence: 99%
“…Then the surface impedance is reconstructed via the method described above from the measured values of the scattered field due to the object to be reconstructed. The determination of the surface impedance is achieved using the explicit expression between the surface impedance and the shape of the actual object given in [5] the determination of the shape is achieved. The method is very effective for the reconstruction of smooth and slightly varying impedances.…”
“…To this aim, a circular domain is considered which covers the perfectly conducting object to be reconstructed and set an equivalent problem by imposing an inhomogeneous surface impedance Z(φ) on the new circular boundary (See figure 3). If the object has a slightly varying and smooth boundary, it can be represented in terms of a standard impedance boundary condition [5] and the following relation is valid between the surface function ( )…”
Section: Application To Shape Reconstruction Of Conducting Objectsmentioning
confidence: 99%
“…Then the surface impedance is reconstructed via the method described above from the measured values of the scattered field due to the object to be reconstructed. The determination of the surface impedance is achieved using the explicit expression between the surface impedance and the shape of the actual object given in [5] the determination of the shape is achieved. The method is very effective for the reconstruction of smooth and slightly varying impedances.…”
“…On the other hand, (5) cannot be considered as a HIBC on a circular boundary with radius a as it contains derivatives with respect to f, which means that an arbitrary shaped object with SIBC cannot be transformed into HIBC on a circle as claimed in [1]. As was shown in [2], this can be done only for the perfectly conducting objects with boundary condition E(q,f) ¼ 0, q ¼ f(f).
…”
(5) is not the same with the expression given by (4) in [1] and contains also derivatives of @ m Eðq;/Þ @q m with respect to f. Thus, the HIBC given by (4)-(6) in [1] is not correct and does not create an equivalent problem for the original scatterer. As a result, all the remaining formulation after Eq. (6) in [1] is not valid. On the other hand, (5) cannot be considered as a HIBC on a circular boundary with radius a as it contains derivatives with respect to f, which means that an arbitrary shaped object with SIBC cannot be transformed into HIBC on a circle as claimed in [1]. As was shown in [2], this can be done only for the perfectly conducting objects with boundary condition E(q,f) ¼ 0, q ¼ f(f).
CONCLUSIONThe derivation of the equivalent HIBC in [1] from the Taylor expansion of the total field is not true. Consequently, the presented numerical results that are claimed to be produced from this incorrect formulation are completely falsified. For that reason, the article and the results have no scientific value. is tried to be represented by a planar one with higher order impedance boundary condition (HIBC), where n is the normal direction of the periodic surface given by y ¼ f(x). With this in aim, the author first represents the total field u(x,y) in terms of Taylor expansion around the planar surface y ¼ and then, substitutes (2) in (1). The boundary condition (1) requires to calculate the normal derivative qu/qn, which can be evaluated by @uðx; yÞ @n ¼ñ:gradðuðx; yÞÞ;withñ being the unit vector in the normal direction. Thus, the explicit expression of the normal derivative of u(x,y) is Then, the substitution of (2) and (4) in (1)
“…Recently, Ö zdemir et al [1] presented new method for electromagnetic scattering from arbitrary shaped perfectly electrical conducting (PEC) objects. In the study [1], high-order impedance functions of circle covering the object is obtained by Taylor expansion of total field ϭ a straightforwardly as,…”
mentioning
confidence: 99%
“…In the study [1], high-order impedance functions of circle covering the object is obtained by Taylor expansion of total field ϭ a straightforwardly as,…”
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