The North Caspian Basin (NCB) contains a significant number of major oil fields, some of which are yet to be put into production. The reason why some of these fields are not yet put into production is the exploration challenge that the NCB poses. In particular, the complex geological structure of this region makes it quite difficult to image its oil fields with conventional seismic techniques. This thesis sheds more light on difficulties associated with acquiring and processing seismic data in the NCB. The two central tools for investigation of these imaging challenges were the construction of a geological model of the NCB and the use of an accurate elastic wave-propagation technique to analyze the capability of seismic to illuminate the geological structures of the NCB. Using all available regional and local studies and my knowledge gained with oil companies, where I worked on subsalt and suprasalt 2D and 3D seismic data from the North Caspian Basin, I constructed a 2D elastic isotropic 10-by-6 km geological model of a typical oil field located on the shelf of the Caspian Sea in the southeastern part of the North Caspian Basin, which has the largest oil fields. We have propagated seismic waves through this model. The technique we used to compute wave propagation is known as the Finite-Difference Modeling (FDM) technique. Generating 314 shot gathers with stationary multicomponent OBS receivers that were spread over 10 km took two weeks of CPU time using two parallel computers (8 CPU V880 Sun Microsystems and 24 CPU Sun Enterprise). We have made the data available to the public. The dataset can be uploaded at http://casp.tamu.edu in the SEGY format. The key conclusions of the analysis of these data are as follows: - Combined usage of P- and S-waves allows us to illuminate subsalt reef, clastics and complex salt structures despite the 4-km overburden. - Free-surface multiples and guided waves are one of the key processing challenges in NCB, despite relatively shallow (less than 15 m) shelf water.

The finite-Difference Time Domain method (FDTD) derives the discrete form of the Maxwell¡¦s equations with second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space using leapfrog for time derivatives. This method is different from the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s difficult to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always causes error. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. In this dissertation, an efficient scheme for processing arbitrary one-port devices in the finite-difference time-domain (FDTD) method is proposed. Generally speaking, methods invoking analytic pre-processing of the device¡¦s V-I relations (admittance or impedance) are computationally more efficient than methods employing numerical procedure to iteratively process the device at each time step. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable.

This research focuses on the creation of a thermal estimator to be used in an integrated electromagnetic, thermo-mechanical design tool for the rapid optimal initial sizing of switched reluctance and induction machines. The switched reluctance model includes heat generation in the rotor due to core losses, heat transfer across the air gap through convection, and a heat transfer path through the shaft to ambient. Empirical Nusselt correlations for laminar shear flow, laminar flow with vortices and turbulent flow are used to estimate the convective heat transfer coefficient in the air gap. The induction model adds ohmic heat generation within the rotor bars of the machine as an additional rotor heat source. A parametric, self-segmenting mesh generation tool was created to capture the complex rotor geometries found within switched reluctance or induction machines. Modeling the rotor slot geometries in the R-θ polar coordinate system proved to be a key challenge in the work. Segmentation algorithms were established to model standard slot geometries including radial, rectangular (parallel-sided), circular and kite-shaped features in the polar coordinate system used in the R-θ solution plane. The center-node mesh generation tool was able optimize the size and number of nodes to accurately capture the cross sectional area of the feature, in the solution plane. The algorithms pursue a tradeoff between computational accuracy and computational speed by adopting a hybrid approach to estimate three dimensional effects. A thermal circuits approach links the R-θ finite difference solution to the three dimensional boundary conditions. The thermal estimator was able to accurately capture the temperature distribution in switched reluctance and induction machines as verified with experimental results.

- / We extend the theory for a novel approach for solving Elliptic Partial Differential Equations.

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

The unique frequency range and robustness of surface acoustic wave (SAW) devices has been a catalyst for their adoption as integral components in a range of consumer and military electronics. Furthermore, the strain and piezoelectric fields associated with SAWs are finding novel applications in nanostructured devices. In this thesis, the interaction of SAWs with periodic elastic structures, such as photonic or phononic crystals (PnCs), is studied both computationally and experimentally. To predict the behaviour of elastic waves in PnCs, a finite-difference time-domain simulator (PnCSim) was developed using C++. PnCSim was designed to calculate band structures and transmission spectra of elastic waves through two-dimensional PnCs. By developing appropriate boundary conditions, bulk waves, surface acoustic waves, and plate waves can be simulated. Results obtained using PnCSim demonstrate good agreement with theoretical data reported in the literature. To experimentally investigate the behaviour of SAWs in PnCs, fabrication procedures were developed to create interdigitated transducers (IDTs) and PnCs. Using lift-off photolithography, IDTs with finger widths as low as 1.8 um were fabricated on gallium arsenide (GaAs), corresponding to a SAW frequency of 397 MHz. A citric acid and hydrogen peroxide wet-etching solution was used to create shallow air hole PnCs in square and triangular lattice configurations, with lattice constants of 8 um and 12 um, respectively. The relative transmission of SAWs through these PnCs as a function of frequency was determined by comparing the insertion losses before and after etching the PnCs. In addition, using a scanning Sagnac interferometer, displacement maps were measured for SAWs incident on square lattice PnCs by Mathew (Creating and Imaging Surface Acoustic Waves on GaAs, Master’s Thesis). Reasonable agreement was found between simulations and measurements. Additional simulations indicate that SAW waveguiding should be possible with a PnC consiting of air holes in GaAs. The phononic properties of a commonly used photonic plate were also determined. Band structure simulations of the plate displayed no complete elastic band gaps. However, transmission simulations indicated that a pseudo-gap may form for elastic waves polarized in the sagittal plane. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-12-23 16:24:33.164

In this paper, we examine a method on how to model and produce Chladni Figures. We walk through how a thin metal plate, when vibrating at certain frequencies, can create various interest patterns. First we discuss the equation for the vertical force exerted on the plate, then we derive a PDE to solve for the nodal lines (lines that remain fixed, while the rest of the plate is oscillating). And, discuss how to create and model these figures, through a finite difference method. There have been several experiments on Chladni Figures, using some sort of vibrating membrane or plate and then either through the use of a speaker or a violin bow, produce frequencies in order to resonate with the membrane. These eigenvalue solutions can been physically observed by putting sand on the plate and vibrating it. We will approximate theses figures, calculate the convergence of the approximation, and relate the generated figures to figures produced in experiments.

A stable boundary treatment of the dynamic beam equation (DBE) with two different sets of boundary conditions has been conducted using the summation-by-parts-simultaneous-approximation-term (SBP-SAT) method. As the DBE involves a fourth derivative in space the numerical boundary treatment is highly non-trivial. Using SBP-SAT operators together with suitable time integration schemes the DBE has been simulated and a convergence study has been made. The results show that the SBP-SAT method produces a stable discretistation that is accurate enough to capture the dispersive nature of the dynamic beam equation. In additions simulations were made presenting the importance of a stable boundary treatment showing that the numerical solutions diverge when the boundaries were not handled correctly.

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

In this thesis a high order finite difference scheme is derived and implemented solving the shallow water equations using the SBP-SAT method. This method was tested against various benchmark problems were convergence was verified. The shallow water equations were also solved on a multi-block setup representing a tsunami approaching a shoreline from the ocean. Experiments show that a bottom topography with many spikes provides a dispersing effect on the incoming tsunami wave. Higher order convergence is not guaranteed for the multi-block simulations and could be investigated further in a future study.