Browsing by Subject "Galerkin methods"

Now showing 1 - 6 of 6

Open Access
An efficient method for electromagnetic characterization of 2-D geometries in stratified media
(IEEE, 2002) Aksun, M. I.; Çalışkan, F.; Gürel, Levent
A numerically efficient technique, based on the spectral-domain method of moments (MoM) in conjunction with the generalized pencil-of-functions (GPOF) method, is developed for the characterization of two-dimensional geometries in multilayer planar media. This approach provides an analytic expression for all the entries of the MoM matrix, explicitly including the indexes of the basis and testing functions provided that the Galerkin's MoM is employed. This feature facilitates an efficient modification of the geometry without the necessity of recalculating the additional elements in the MoM matrix. To assess the efficiency of the approach, the results and the matrix fill times are compared to those obtained with two other efficient methods, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, and a fast Fourier transform algorithm to evaluate the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries.
Open Access
Experimental results and bifurcation analysis on scaled feedback control for subsonic cavity flows
(IEEE, 2006) Yuan, X.; Caraballo, E.; Debiasi, M.; Little, J.; Serrani, A.; Özbay, Hitay; Samimy, M.
In this paper, we present the latest results of our ongoing research activities in the development of reduced-order models based feedback control of subsonic cavity flows. The model was developed using the Proper Orthogonal Decomposition of Particle Image Velocimetry images in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. Stochastic Estimation method was used to obtain the state estimation of the Galerkin system from real time surface pressure measurements. A linear-quadratic optimal controller was designed to reduce cavity flow resonance and tested in the experiments. Real-time implementation shows a significant reduction of the sound pressure level within the cavity, with a remarkable attenuation of the resonant tone and a redistribution of the energy into various modes with lower energy levels. A mathematical analysis of the performance of the LQ control, in agreement with the experimental results, is presented and discussed.
Open Access
Integral action based Dirichlet boundary control of Burgers equation
(IEEE, 2003) Efe, M. Ö.; Özbay, Hitay
Modeling and boundary control for Burgers Equation is studied in this paper. Modeling has been done via processing of numerical observations through singular value decomposition with Galerkin projection. This results in a set of spatial basis functions together with a set of Ordinary Differential Equations (ODEs) describing the temporal evolution. Since the dynamics described by Burgers equation is nonlinear, the corresponding reduced order dynamics turn out to be nonlinear. The presented analysis explains how boundary condition appears as a control input in the ODEs. The controller design is based on the linearization of the dynamic model. It has been demonstrated that an integral controller, whose gain is a function of the spatial variable, is sufficient to observe reasonably high tracking performance with a high degree of robustness.
Open Access
Low dimensional modelling and Dirichlét boundary controller design for Burgers equation
(Taylor & Francis, 2004) Efe, M. Ö.; Özbay, Hitay
Modelling and boundary control for the Burgers equation is studied in this paper. Modelling has been done via processing of numerical observations through proper orthogonal decomposition (POD) with Galerkin projection. This results in a set of spatial basis functions together with a set of ordinary differential equations (ODEs) describing the temporal evolution. Since the dynamics described by the Burgers equation are non-linear, the corresponding reduced-order dynamics turn out to be non-linear. The presented analysis explains how the free boundary condition appears as a control input in the ODEs and how controller design can be accomplished. The issues of control system synthesis are discussed from the point of practicality, performance and robustness. The numerical results obtained are in good compliance with the theoretical claims. A comparison of various different approaches is presented. © 2004 Taylor and Francis Ltd.
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.
Open Access
Reduced-order model-based feedback controller design for subsonic cavity flows
(American Institute of Aeronautics and Astronautics, 2005-01) Yuan, X.; Caraballo, E.; Yan, P.; Özbay, Hitay; Serrani, A.; DeBonis, J.; Myatt, J. H.; Samimy, M.
This paper explores feedback controller design for cavity flows based on reduced-order models derived using Proper Orthogonal Decomposition (POD) along with Galerkin projection method. Our preliminary analysis shows that the equilibrium of the POD model is unstable and a static output feedback controller cannot stabilize it. We develop Linear Quadratic (LQ) optimal state feedback controllers and LQ optimal observers for the linearized models. The linear controllers and observers are applied to the nonlinear system using simulations. The controller robustness is numerically tested with respect to different POD models generated at different forcing frequencies. An estimation for the region of attraction of the linear controllers is also provided.