The vector finite-element method in the interior and the boundary integral equation of the exterior domain are investigated in order to analyze open dielectric waveguides. Boundary conditions are obtained by applying the continuity of the magnetic and electric fields at the surface of the waveguide. Since both the finite-element method and boundary integral equations have the final matrices of the form Ax = λBx, the singular value decomposition method with iterations is used. This method provides excellent accurate solutions for a rectangular dielectric waveguides. The zero cutoff of the lowest order mode is also obtained. To avoid iterations, the finite-element formulation together with the boundary operator are solved using a penalty function method. Comparison with previously published results shows good agreement for the analysis of the rectangular dielectric waveguide. Finally, the pseudoinverse method with a penalty factor is used. This new method provides the simultaneous solutions of propagating modes at the operating frequency and it shows good agreement with previously published results for the analysis of the rectangular waveguide.

The electromagnetic scattering problem by surfaces of arbitrary objects is discussed based on the method of moments technique and surface integral equations. Similar to the case of the conducting scatterers, the arbitrary geometrical shapes have been modeled using triangulated patches when combined field integral formulations are developed for the scattering by dielectric objects. The treatment of singular integral equations is also mentioned and the results for the metal plate are compared for it. The approach is applied to the scattering problems of plane wave illumination of a dielectric finite circular cylinder and a cubic high dielectric resonator. Scattered fields are evaluated after determining the surface electric and magnetic currents as unknowns for the high dielectric cube to find the magnetic and electric dipole inside the cube.

The higher magnetic B₀ fields in MRI systems result in higher signal to noise ratios. However, as the wavelength decreases linearly with higher static magnetic field, image inhomogeneity occurs. This thesis demonstrates the use of the convex optimization with an iterative method to improve [special characters omitted] uniformity in an anatomic region of interest by varying the magnitude and phase of each RF channel element independently. The simulation results for 16 and 32 channels for 9.4T and 7T systems and experimental results for 8 channels in a 9.4T system confirming the prediction are presented.