Browsing by Subject "Galerkin"
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Item Open Access Integral equation based method for the fast analysis of irregularly contoured large finite phased arrays(Institution of Engineering and Technology, 2007) Ertürk, Vakur B.; Çivi, Ö. A.A fast and accurate integral equation based hybrid method that can investigate electrically large, arbitrarily contoured finite planar arrays of printed elements is developed. The method is a hybridization of the Galerkin type method of moments (MoM) and generalized forward backward method (GFBM) with the grounded dielectric slab's Green's function; and the acceleration of the resultant hybrid method by a discrete Fourier transform (DFT) based acceleration algorithm. Numerical results in the form of array current distribution are given for arbitrarily contoured as well as thinned arrays of probe fed microstrip patches where current on each element expanded by more than one subsectional basis function.Item Open Access Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization(Institute of Physics Publishing, 2012-07-27) Oran, O. F.; Ider, Y. Z.Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇ 2B z) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇ 2B z-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convectiondiffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.