Browsing by Subject "iterative solution"

Now showing 1 - 2 of 2

Open Access
Electromagnetic imaging of three-dimensional conducting objects using the Newton minimization approach
(2013) Etminan, Aslan
The main goal of shape reconstruction is to retrieve the location and shape of an unknown target. This approach is used in a wide range of areas, from detecting cancer tumors to finding buried objects. Various methods can be applied to detect objects in different applications. One of the important challenges in many of these methods is to solve the non-linearity and non-uniqueness of the solutions. Inverse scattering is one of the most efficient ways to retrieve shapes and locations of targets. By illuminating the objects with electromagnetic waves and collecting the scattering fields using appropriate methods, we try to obtain the shape of unknown object. To achieve this goal, we start with an initial guess of the unknown object, then by comparing the scattered far-field patterns of the guess and the real object, we evolve that object and update it iteratively such that we decrease the difference between the patterns and finally achieve the shape of the unknown object. In this thesis, we model the object by one of its parameters, such as the location of the nodes on the surface of the object, or by the conductivity, permittivity, and permeability of the discretized space in which the object is placed. Then, the model parameters are updated iteratively by minimizing the mismatch between the measured data of the target and the collected data from the modeled object. Using surface nodes to model a three-dimensional object is a good choice because we decrease the number of unknowns.
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.