Driving aim of this study was to develop a solver which is accurate enough to be used in analysis and fast enough to be used in optimization purposes. As a first step, a three-dimensional potential flow solver is developed using Fast Multipole Boundary Element (FMBEM) for calculating the pressure distributions in non-lifting flows. It is a steady state solver which uses planar triangular unstructured mesh. After the geometry is introduced, the program creates a prescribed wake surface attached to the trailing edge(s), obtains a solution using panel elements on which the doublet and source strengths vary linearly. The reason for using FMBEM instead of classical BEM is the availability of solutions of systems having DOFs up to several millions within a few hours using a standard computer which is impossible to accomplish with classical BEM. Solutions obtained for different test cases are compared with the analytical solution (if applicable), the experimental data or the results obtained by JavaFoil.

The dissertation focuses on the analysis and design for the new fiber-optic passive components based on the photonic-crystal-fiber (PCF). The vector boundary element method (VBEM) and the finite-difference time-domain (FDTD) method are employed to the propagation characteristics of PCF components. A novel octagonal microstructured fiber (OMF) with eight air-holes in the first ring has been proposed. The OMF has significantly wider wavelength range for single-mode operation, more circular-like field distribution, and less confinement loss. In addition, a novel compact polarization beam splitter (PBS) based on the twin-elliptical-core PCF (TEC-PCF) has also been proposed. It behaves with high extinction ration and broad bandwidth with significantly short splitter length. The design concept and the coupling mechanism are presented in this dissertation based on the normal-mode coupling theory and VBEM.

A formulation is proposed for the boundary element analysis of poro-elastic media with axi-symmetric geometry. The boundary integral equation is reduced to a set of line integral equations in the generating plane for each of the Fourier coefficients, through complex Fourier series expansion of boundary quantities in circumferential direction. The method is implemented into a computer program, where the fundamental solutions are integrated by Gaussian Quadrature along the generator, while Fast Fourier Transform algorithm is employed for integrations in circumferential direction. The strongly singular integrands in boundary element equations are regularized by a special technique. The Fourier transform solution is then inverted in to R&amp / #952 / z space via inverse FFT. The success of the method is assessed by problems with analytical solutions. A good fit is observed in each case, which indicates effectiveness and reliability of the present method.

In this study, the effects of design parameters on the fan noise level are investigated both theoretically and experimentally. For the theoretical study, a computational aero- acoustic method is used to predict the flow induced noise of a fan. This method involves the coupling of a flow solver and a wave equation solver. Unsteady flow analysis is performed with URANS using FLUENT. Then the time dependent data are processed with LMS Sysnoise to compute the acoustic radiation. Experimental studies are performed to verify the theoretical results and additionally to investigate the effects of different design alternatives on noise level of the fan. The sound pressure and intensity level measurements are performed in the full anechoic room of Ar&ccedil / elik A.S. Research and Development Laboratories. The validation experiments indicate that there is a good agreement between numerical and experimental results. The experimental study with different fan designs gives information about the noise reduction possibilities.

A computational approach to analyze the hydrodynamic performance of a hydrofoil or a marine propeller undergoing unsteady motion has been developed. In order to simulate heave and pitch motion of a hydrofoil, an unsteady boundary element method based modeling is performed. The wake of the hydrofoil is modeled by a continuous dipole sheet and determined in time by applying a force-free condition on its surface. An explicit vortex core model is adapted in this model to capture the rolling up shape and to avoid instability due to roll-up deformation of the wake. The numerical results of the developed model are compared with analytical results and those from the commercial Reynolds-Averaged Navier-Stokes solver (ANSYS/FLUENT). The results show close level of agreement with each other. The problem of flow around a marine propeller performing surge, roll and heave motion in an unbounded fluid is formulated and solved using both a vortex-lattice method and a boundary element method. A fully unsteady wake alignment algorithm is implemented into the vortex-lattice method in order to satisfy the force-free condition on the propeller wake surface. Finally, a comparative study of transient propeller forces on a propeller blade obtained from BEM and VLM (with or without fully aligned wake) is carried out and results are presented. In some cases, results from the presented methods are compared with those from RANS or other numerical methods available in the literature. / text

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.

This thesis studies interactions between coupled acoustic domain(s) and enclosing rigid or elastic boundary. Boundary element-finite element (BE-FE) sound-structure interaction models are developed by coupling frequency domain BE acoustic and FE structural models using linear inviscid acoustic and elasticity theories. Flexibility in analyses is provided by discontinuous triangular and quadrilateral elements in the BE method (BEM), and a rectangular plate and a triangular shell element in the FE method (FEM). An analytical formulation is developed for an extended fundamental sound-structure interaction problem that involves locally reacting sound absorptive treatment on interior elastic boundary. This new formulation is built upon existing analytical solutions for a configuration known as the cavity-backed-plate problem. Results from developed analytical formulation are compared against those from independent BE-FE analyses. Analytical and BE-FE analysis results for a selection of cavity-plate(s) interaction cases are given. Single- and multi-domain BE analyses of cavity-Helmholtz resonator interaction are provided as an alternative to modal method of acoustoelasticity. A discrete-form of the existing BE acoustic particle velocity formulation is presented and demonstrated on a basic case study. Both the existing and the discretized BE acoustic particle velocity formulations could be utilized in acoustic studies. A selection of case studies involving fundamental configurations are studied both analytically and computationally (by BE or BE-FE methods). These studies could provide a basis for benchmark case development in the field of acoustics.

Electro-Magnetic Source Imaging (EMSI) is the estimation of the position, orientation and strength of active electrical sources within the brain from electrical and magnetic measurements. For an accurate source localization, the head model must correctly represent the electrical and geometrical properties of the head. To solve the forward problem using realistic head models numerical techniques must be used. This work uses the Boundary Element Method (BEM) for solving the forward problem. The accuracy of the existing BEM formulation is improved by using second order elements, recursive integration and the isolated problem approach (IPA). Two new formulations are developed to improve the solution speed by computing transfer matrices for EEG and MEG solutions. The IPA formulation is generalized and integrated into the accelerated BEM algorithm. Once the transfer matrices are computed, the forward solutions take about 300 ms for a 256 sensor EEG and MEG system. The head model used in the BEM solutions is constructed by segmenting three dimensional multimodal magnetic resonance images. For segmentation, a semi-automatic hybrid algorithm is developed that makes use of snakes, morphological operations, thresholding and region growing. The mesh generation algorithm allows intersecting tissue compartments. For the inverse problem solution genetic algorithm (GA) is used to search for a given number of dipoles. Source localization with simulated data show that the localization error is within 1.1 mm for EEG and 1.2 mm for MEG when SNR is 10 on a realistic model with 7 compartments. When a single-dipole source in a realistic model is explored using a best-fit spherical model, the localization errors increase up to 8.5 mm for EEG and 7 mm for MEG. Similar tests are also performed with multiple dipoles. It was observed that realistic models provide definitely more accurate results compared to spherical models. The EMSI approach is also tested using experimental EEG data to localize the sources of auditory evoked potentials. The reconstructed source locations are correctly found in the Heschl&#039 / s gyrus. In conclusion, this thesis presents a complete source localization framework for future brain research using the EMSI.

Human brain functions are based on the electrochemical activity and interaction of the neurons constituting the brain. Some brain diseases are characterized by abnormalities of this activity. Detection of the location and orientation of this electrical activity is called electro-magnetic source imaging (EMSI) and is of signicant importance since it promises to serve as a powerful tool for neuroscience. Boundary Element Method (BEM) is a method applicable for EMSI on realistic head geometries that generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming due to the size of the matrices and high computational complexity of direct methods. This study presents a relatively cheap and eective solution the this problem and reduces the processing times to clinically acceptable values using parallel cluster of personal computers on a local area network. For this purpose, a cluster of 8 workstations is used. A parallel BEM solver is implemented that distributes the model eciently to the processors. The parallel solver for BEM is developed using the PETSc library. The performance of the iv solver is evaluated in terms of CPU and memory usage for dierent number of processors. For a 15011 node mesh, a speed-up eciency of 97.5% is observed when computing transfer matrices. Individual solutions can be obtained in 520 ms on 8 processors with 94.2% parallellization eciency. It was observed that workstation clusters is a cost eective tool for solving complex BEM models in clinically acceptable time. Eect of parallelization on inverse problem is also demonstrated by a genetic algorithm and very similar speed-up is obtained.