Browsing by Subject "Electromagnetism--Mathematics."

Now showing 1 - 2 of 2

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.