Browsing by Subject "Electromagnetic waves--Scattering--Mathematics."

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Open Access
Scattering from impedance objects at the edge of a perfectly conducting wedge
(2012) Ghassemiparvin, Behnam
In this study, scattering from impedance bodies positioned at the edge of a perfectly conducting (PEC) wedge is investigated. In the treatment of the problem, eigenfunction expansion in terms of spherical vector wave functions is employed. A complete dyadic Green’s function for the spherical impedance boss at the edge is developed and through decomposing the dyadic Green’s function, it can be observed that the contribution of the scatterer is separated from the wedge. It is shown that the scattering is highly enhanced by the edge guided waves. For the general case of irregularly shaped scatterer the solution is extended using T-matrix method. The method is implemented by replacing free space Green’s function with the dyadic Green’s function of the PEC wedge. The solution is verified by applying it to the case of spherical scatterer and results are compared with the dyadic Green’s function solution. The T-matrix solution is generalized for the multiple scatterer case. Numerical results are obtained for two impedance scatterers at the edge and compared with the PEC case.
Open Access
Solution of electromagnetic scattering problems with the locally corrected Nyström method
(2010) Kılınç, Seçil
The locally corrected Nystr¨om (LCN) method is used to solve integral equations with high accuracy and efficiency. Unlike commonly used methods, the LCN method employs high-order basis functions on high-order surfaces. Hence, the number of unknowns in the electromagnetic problem decreases substantially, this also reduces the total solution time of the problem. In this thesis, electromagnetic scattering problems for arbitrary, three-dimensional, and conducting geometries are solved with the LCN method. Both the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) are implemented. The solution time for Duffy integrals is reduced significantly by modifying the Duffy transform. Then, mixed-order basis functions are implemented to accurately represent the charge density for EFIE. Finally, both the accuracy and the efficiency (in terms of solutions times and the number of unknowns) of the LCN method are compared with the method of moments and the multilevel fast multipole algorithm.
Open Access
Solution of electromagnetics problems with the equivalence principle algorithm
(2010) Tiryaki, Burak
A domain decomposition scheme based on the equivalence principle for integral equations is studied. This thesis discusses the application of the equivalence principle algorithm (EPA) in solving electromagnetics scattering problems by multiple three-dimensional perfect electric conductor (PEC) objects of arbitrary shapes. The main advantage of EPA is to improve the condition number of the system matrix. This is very important when the matrix equation is solved iteratively, e.g., with Krylov subspace methods. EPA starts solving electromagnetics problems by separating a large complex structure into basic parts, which may consist of one or more objects with arbitrary shapes. Each one is enclosed by an equivalence surface (ES). Then, the surface equivalence principle operator is used to calculate scattering via equivalent surface, and radiation from one ES to an other can be captured using the translation operators. EPA loses its accuracy if ESs are very close to each other, or if an ES is very close to PEC object. As a remedy of this problem, tangential-EPA (T-EPA) is introduced. Properties of both algorithms are investigated and discussed in detail. Accuracy and the efficiency of the methods are compared to those of the multilevel fast multipole algorithm.