Browsing by Subject "Electromagnetic fields--Mathematics."

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Open Access
Fast algorithms for large 3-D electromagnetic scattering and radiation problems
(1997) Şendur, İbrahim Kürşat
Some interesting real-life radiation and scattering problems are electrically very large and cannot be solved using traditional solution algorithms. Despite the difficulties involved, the solution of these problems usually offer valuable results that are immediately useful in real-life applications. The fast multipole method (FMM) enables the solution of larger problems with existing computational resources by reducing the computational complexity and the memory requirement of the solution without sacrificing the accuracy. This is achieved by replacing the matrix-vector multiplications of O(N^) complexity by a faster equivalent of complexity in each iteration of an iterative scheme. Fast Far-Field Algorithm(FAFFA) further reduces 0{N^) complexity to 0{N^·^). A direct solution would require 0{N^) operations.
Open Access
Finite element method based simulations of low frequency magnetic field in seawater
(2013) Şimşek, Fatih Emre
Propagation properties of the electromagnetic waves in seawater are different than in air (vacuum) due to electrical conductivity (σ) and high relative permittivity (εr) of the seawater. Numerically it is hard to solve the electromagnetic waves in seawater for the complex geometries. With the help of the advances in the Finite Element Method (FEM) tools as well as the personal computers, we have chance to analyze magnetic field of the complicated and complex geometries of physical systems in seawater. In this thesis; an air-cored multilayer transmitting coil is designed. Then the low frequency magnetic flux density of this coil in different studies in seawater in COMSOL Multiphysics is solved. In the first study; the magnetic flux density of the coil in air and in seawater for different frequencies on different observation points is solved. In the second study; the shielding effect of the material of the case of the coil as well as the thickness of the case is analyzed. Specific materials as well as thickness for the case are proposed. In the third study; the perturbation of the magnetic flux density of the coil due to a metal plate is analyzed. The material of the metal plate is taken iron and copper. Iron has high relative permeability (  r) and high electrical conductivity (σ). Copper has unity permeability (  0) and high electrical conductivity (σ). Effect of the high electrical conductivity on the perturbation of the magnetic flux density on the observation point is analyzed. Effect of high relative permeability on the phase shift of the field on the observation point is observed. A detection region for the plate and coil geometries according to the attenuation of the secondary fields caused by the eddy currents on the metal plate is proposed. In the last study; perturbation of ambient Earth magnetic field due to a submarine is solved and how this perturbation can be imitated by an underwater system, which tows a DC current carrying wire is analyzed. These underwater systems are used to test detection performance of magnetic anomaly detector (MAD) equipped aircrafts.
Open Access
Finite-difference time-domain solution of electromagnetic scattering problems
(1997) Oğuz, Uğur
The "finite-difference time-domain" (FDTD) method is an efficient and powerful way to solve three-dimensional scattering problems. Unbounded medium problems are easily solved in this method using the absorbing boundaries, but the FDTD method is especially efficient for problems involving inhomogeneous media, since the number of unknowns remains the same when the scatterer is changed in the same geometry of the computational domain. Perfectly matched layers (PML) can be incorporated to match nonhomogeneous media, which helps the FDTD to solve the scattering from special geometries such as buried scatterers. The total-field formulation can be used to simulate the propagation of the incident waves into the computational region. The far-zone transformation technique enables us to compute field parameters far from the scatterer using near-field scattering information. However, there are errors in the plane-wave generations in the FDTD method. These errors are observed in both the near-field and the far-field variables. The major sources of these errors are the high-frequency components in the input signal and the numerical dispersion. These errors can be significantly reduced by using special techniques.