<p>In this thesis we study hybrid numerical methods to be used in computational electromagnetics. The purpose is to address a wide frequency range relative to a given geometry. We also focus on efficient and robust numerical algorithms for computing the so called Smooth Surface Diffraction predicted by Geometrical Theory of Diffraction (GTD). We restrict the presentation to frequency domain scattering problems.</p><p>The hybrid methods consist in combinations of Boundary Element Methods and asymptotic methods. Three hybrids will be presented. One of them has been developed from a theoretical idea to an industrial code. The two other hybrids will be presented mainly from a theoretical perspective.</p><p>To be able to compute the Smooth Surface Diffracted field we introduce a numerical method that is to be used with surface curvature sensitive meshing, complemented with auxiliary data taken from a geometry database. By using two geometry representations we can show first order convergence and we then achieve an efficient and robust numerical algorithm. This numerical algorithm may be an essential part of an GTD implementation which in its turn is a component in the hybrid methods.</p><p>As a background to our new techiniques we will also give short introductions to the Boundary Element Method and the Geometrical Theory of Diffraction from a theoretical and implementational point of view.</p>

We report a Hessian-implicit optimization method to quickly solve the charge optimization problem over protein molecules: given a ligand and its complex with a receptor, determine the ligand charge distribution that minimizes the electrostatic free energy of binding. The new optimization couples boundary element method (BEM) and primal-dual interior point method (PDIPM); initial results suggest that the method scales much better than the previous methods. The quadratic objective function is the electrostatic free energy of binding where the Hessian matrix serves as an operator that maps the charge to the potential. The unknowns are the charge values at the charge points, and they are limited by equality and inequality constraints that model physical considerations, i.e. conservation of charge. In the previous approaches, finite-difference method is used to model the Hessian matrix, which requires significant computational effort to remove grid-based inaccuracies. In the novel approach, BEM is used instead, with precorrected FFT (pFFT) acceleration to compute the potential induced by the charges. This part will be explained in detail by Shihhsien Kuo in another talk. Even though the Hessian matrix can be calculated an order faster than the previous approaches, still it is quite expensive to find it explicitly. Instead, the KKT condition is solved by a PDIPM, and a Krylov based iterative solver is used to find the Newton direction at each step. Hence, only Hessian times a vector is necessary, which can be evaluated quickly using pFFT. The new method with proper preconditioning solves a 500 variable problem nearly 10 times faster than the techniques that must find a Hessian matrix explicitly. Furthermore, the algorithm scales nicely due to the robustness in number of IPM iterations to the size of the problem. The significant reduction in cost allows the analysis of much larger molecular system than those could be solved in a reasonable time using the previous methods. / Singapore-MIT Alliance (SMA)

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles. / Singapore-MIT Alliance (SMA)

In this thesis we study hybrid numerical methods to be used in computational electromagnetics. The purpose is to address a wide frequency range relative to a given geometry. We also focus on efficient and robust numerical algorithms for computing the so called Smooth Surface Diffraction predicted by Geometrical Theory of Diffraction (GTD). We restrict the presentation to frequency domain scattering problems. The hybrid methods consist in combinations of Boundary Element Methods and asymptotic methods. Three hybrids will be presented. One of them has been developed from a theoretical idea to an industrial code. The two other hybrids will be presented mainly from a theoretical perspective. To be able to compute the Smooth Surface Diffracted field we introduce a numerical method that is to be used with surface curvature sensitive meshing, complemented with auxiliary data taken from a geometry database. By using two geometry representations we can show first order convergence and we then achieve an efficient and robust numerical algorithm. This numerical algorithm may be an essential part of an GTD implementation which in its turn is a component in the hybrid methods. As a background to our new techiniques we will also give short introductions to the Boundary Element Method and the Geometrical Theory of Diffraction from a theoretical and implementational point of view.

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

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.