The structure of fault zones (FZs) plays an important role in understanding fault mechanics, earthquake rupture and seismic hazards. Fault zone seismic guided waves (GW) carry important information about internal structure of the low-velocity fault damage zone. Numerical modeling of observed FZGWs has been used to construct models of FZ structure. However, the depth extent of the waveguide and the uniqueness of deep structure in the models have been debated. Elastic finite-difference synthetic seismograms were generated for FZ models that include an increase in seismic velocity with depth both inside and outside the FZ. Strong GWs were created from sources both in and out of the waveguide, in contrast with previous homogenous-FZ studies that required an in-fault source to create GW. This is because the frequency-dependent trapping efficiency of the waveguide changes with depth. The near-surface fault structure efficiently guides waves at lower frequencies than the deeper fault. Fault structure at seismogenic depth requires the analysis of data at higher frequencies than the GWs that dominate at the surface. Adapting a two-station technique from surface wave studies, dispersive differential group arrival times between two earthquakes can be used to solve for FZ structures between the earthquakes. This method was tested with synthetic data and shallow events recorded in the SAFOD borehole in the San Andreas Fault. A pair of deep earthquakes recorded in the SAFOD borehole indicate a ~150 m wide San Andreas Fault waveguide with >20% velocity contrast at 10-12 km depth. With additional earthquakes, the full FZ structure at seismogenic depth could be imaged. Subsurface FZ structure can also be derived from a surface source and receiver array analogous to a body-wave refraction survey. Synthetic seismograms for such source-receiver geometry were generated and verified that FZGWs are refracted by the increase in velocity with depth. Synthetic data from a surface array were successfully inverted to derive FZ structure in the subsurface. The new methods presented in this dissertation extend the potential of FZGWs to image deeper FZ structure than has been uniquely constrained in the past. / Ph. D.

Yes / This work presents the development of a new approach of modelling the source excitation and the penetration of structures by continuous propagating electromagnetic (EM) plane waves. The technique incorporates the solution of time-dependent Maxwell's equations and the initial value problem as the structures are illuminated by the plane waves. The propagation of waves from source excitation is simulated by solving a finite-difference Maxwell's equation in the time domain. Subgridding method is used to condense the lattice at the point of interest locally for observing field distribution in high resolution. The computational burden due to huge number of time steps has been eased by employing quasi-static approach. An example of induced EM fields near an underground pipeline runs parallel to a 132 kV overhead power transmission line (OHTL) has been presented which paves the way in the development of new approach of EM fields interaction modelling. / MSCRC

This report presents a comprehensive investigation into the accuracy and stability of Finite Difference Methods (FDM) when applied to the acoustic wave equation. The analysis focuses on comparing the classical 2nd order FDM with highly-accurate computational stencil of order 2p = 2,4 and 6 with Summation-by-Parts (SBP) and Simultaneous Approximation Term (SAT) technique of the Finite Difference Method. The objective of the study is to investigate complex numerical techniques that contributes to highly-accurate and stable solutions to many hyperbolic PDEs.  The report starts by introducing the governing problem and studies its well-posedness to ensure stable and unique solutions of the governing equations. It continues with basic introduction to the classic spatial discretization of the FDM and introduces the SBP-SAT implementation of the method. The governing equations are rewritten as a semi-discrete problem, such that it can be written as a system of ordinary differential equations (ODEs) only dependent on the temporal evolution. This system can be solved with classic Runge-Kutta methods to ensure robust and accurate time-stepping schemes.  The results show that the implementation of the higher-order SBP-SAT Finite Difference Method provides highly accurate solutions of the acoustic wave equation compared to the classic FDM. The results also show that the method provides stable solutions with no visible oscillations (dispersion), which can be a challenge for higher order methods. Overall, this paper contributes with valuable insights into the analysis of accuracy and stability in finite difference methods for acoustic wave equation.

Cette thèse participe à l'étude générale et à la compréhension des relations structure- propriétés optiques de couches minces d'oxyde de tungstène, nanostructurées lors de leur dépôt par la technique Glancing Angle Déposition. Cette technique repose sur le contrôle de l'orientation relative du substrat vis à vis de la source de vapeur.[...] / This thesis contributes to the general study and understanding of the relationship between structure and optical properties of nanostructured tungsten oxide by Glancing Angle Déposition technique. this technique relies on the control of the relative orientation of the substrate to the vapor source.[...]

Optical interconnects based on CMOS compatible photonic integrated circuits are regarded as a promising technique to tackle the issues traditional electronics faces, such as limited bandwidth, latency, vast energy consumption and so on. In recent years, plasmonic integrated components have gained great attentions due to the properties of nano-scale confinement, which may potentially bridge the size mismatch between photonic and electronic circuits. Based on silicon nanowire platform, this thesis work studies the design, fabrication and characterization of several integrated plasmonic components, aiming to combine the benefits of Si and plasmonics. The basic theories of surface plasmon polaritons are introduced in the beginning, where we explain the physics behind the diffraction-free confinement. Numerical methods frequently used in the thesis including finite-difference time-domain method and finite-element method are then reviewed. We summarize the device fabrication techniques such as film depositions, e-beam lithography and inductively coupled plasma etching as well as characterization methods, such as direct measurement method, butt coupling, grating coupling etc. Fabrication results of an optically tunable silicon-on-insulator microdisk and III-V cavities in applications as light sources for future nanophotonics interconnects are briefly discussed. Afterwards we present in details the experimental demonstrations and novel design of plasmonic components. Hybrid plasmonic waveguides and directional couplers with various splitting ratios are firstly experimentally demonstrated. The coupling length of two 170 nm wide waveguides with a separation of 140 nm is only 1.55 µm. Secondly, an ultracompact polarization beam splitter with a footprint of 2×5.1 μm2 is proposed. The device features an extinction ratio of 12 dB and an insertion loss below 1.5 dB in the entire C-band. Thirdly, we show that plasmonics offer decreased bending losses and enhanced Purcell factor for submicron bends. Novel hybrid plasmonic disk, ring and donut resonators with radii of ~ 0.5 μm and 1 μm are experimentally demonstrated for the first time. The Q-factor of disks with 0.5 μm radii are                         , corresponding to Purcell factors of . Thermal tuning is also presented. Fourthly, we propose a design of electro-optic polymer modulator based on plasmonic microring. The figure of merit characterizing modulation efficiency is 6 times better comparing with corresponding silicon slot polymer modulator. The device exhibits an insertion loss below 1 dB and a power consumption of 5 fJ/bit at 100 GHz. At last, we propose a tightly-confined waveguide and show that the radius of disk resonators based on the proposed waveguide can be shrunk below 60 nm, which may be used to pursue a strong light-matter interaction. The presented here novel components confirm that hybrid plasmonic structures can play an important role in future inter- and intra-core computer communication systems. / <p>QC 20140404</p>

The main objective of this research is to model and analyse complex electromagnetic problems by means of a new hybridised computational technique combining the frequency domain Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric materials irradiated by geometrically intricate sources. The Method of Moments modelling employed a two-dimensional electric surface patch integral formulation solved by independent linear basis function methods in the circumferential and axial directions of the antenna wires. A similar orthogonal basis function is used on the end surface and appropriate attachments with the wire surface are employed to satisfy the requirements of current continuity. The surface current distributions on structures which may include closely spaced parallel wires, such as dipoles, loops and helical antennas are computed. The results are found to be stable and showed good agreement with less comprehensive earlier work by others. The work also investigated the interaction between overhead high voltage transmission lines and underground utility pipelines using the FDTD technique for the whole structure, combined with a subgridding method at points of interest, particularly the pipeline. The induced fields above the pipeline are investigated and analysed. FDTD is based on the solution of Maxwell's equations in differential form. It is very useful for modelling complex, inhomogeneous structures. Problems arise when open-region geometries are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to circumvent this difficulty. The establishment of edge elements has greatly improved the performance of this method and the computational burden due to huge numbers of time steps, in the order of tens of millions, has been eased to tens of thousands by employing quasi-static methods. This thesis also illustrates the principle of the equivalent surface boundary employed close to the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid techniques due to their ability to analyse a system of multiple discrete regions by employing the principle of equivalent sources to excite the coupling surfaces. The method has been applied for modelling human body interaction with a short range RFID antenna to investigate and analyse the near field and far field radiation pattern for which the cumulative distribution function of antenna radiation efficiency is presented. The field distributions of the simulated structures show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of the phenomena in the interaction between electromagnetic fields and human tissues.

There is an increasing need for accurate models describing the electrical behaviour of individual biological cells exposed to electromagnetic fields. In this area of solving linear problem, the most frequently used technique for computing the EM field is the Finite-Difference Time-Domain (FDTD) method. When modelling objects that are small compared with the wavelength, for example biological cells at radio frequencies, the standard Finite-Difference Time-Domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD, based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating the Hodgkin and Huxley membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900MHz, 1800MHz and 2450MHz. This method will facilitate deeper investigation of the phenomena in the interaction between EM fields and biological systems. Moreover, the nonlinear response of biological cell exposed to a 0.9GHz signal was discussed on observing the second harmonic at 1.8GHz. In this, an electrical circuit model has been proposed to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with known nonlinear device. Meanwhile, the first and second harmonic responses of the cavity due to the loading of the cavity with the lossy material will also be demonstrated. The results from proposed mathematical model, give good indication of the input power required to detect the weakly effects of the second harmonic signal prior to perform the measurement. Hence, this proposed mathematical model will assist to determine how sensitivity of the second harmonic signal can be detected by placing the required specific input power.

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.

Magistro darbe pateikiami nauji rezultatai, gauti tiriant diskretųjį Šturmo ir Liuvilio uždavinį su viena klasikine (arba Noimano) ir antra nelokalia dvitaške kraštine sąlyga. Analitinėje dalyje pateikiama teorija, reikalinga nagrinėjamo uždavinio tyrimui ir trumpai pristatomi rezultatai, gauti tiriant panašų uždavinį. Projektinėje dalyje ištirta diferencialinio uždavinio ir baigtinių skirtumų schemų kompleksinės spektro dalies priklausomybė nuo nelokaliųjų kraštinių sąlygų parametrų $\gamma$ ir $\xi$. Dauguma tyrimo rezultatų pateikiama kompleksinės ir realiosios charakteristinių funkcijų grafikais. / In this Master thesis presented new results which are got investigated the Sturm--Liouville problem with one classical (or Neumann) and another two-point nonlocal boundary condition. In the analytical part are presented the theory, which is necessary to study the problem and presented the results of investigation a similar task. In the design part are investigated the spectrum in complex plane depends on the nonlocal boundary conditions parameters $\gamma$ and $\xi$ in differential problem and in the finite difference schemes. Simulation results are presented as graphs of complex-real characteristic functions.

Darbo tikslas — ištirti baigtiniu skirtumu metodo antrosios eiles hiperbolinio tipo diferencialinei lygciai su nelokaliosiomis integralinemis kraštinemis salygomis stabiluma. Siekiant numatyto tikslo buvo sprendžiami šie uždaviniai: • išnagrinetas antrosios eiles hiperbolines lygties trisluoksnes skirtumines schemos suvedimas i dvisluoksne skirtumine schema; • išanalizuotas skirtuminio operatoriaus perejimo matricos spektras; • gauta pakankamoji skirtumines schemos stabilumo salyga, nusakoma nelokaliuju salygu parametrais; • atlikti skaitiniai eksperimentai, patvirtinantys teorines išvadas. Nurodyta stabilumo salyga yra esmine, sprendžiant hiperbolinio tipo uždavinius su pakankamai didelemis T reikšmemis. Skirtuminio operatoriaus perejimo matricos spektro tyrimo metodika gali buti pritaikyta placios klases diferencialiniu lygciu su nelokaliosiomis salygomis stabilumui tirti. / On the stability of an explicit difference scheme for hyperbolic equation with integral conditions. The aim of the work is stability analysis of solution of finite difference method for hyperbolic equations. Trying to achieve formulated aim these tasks were solved: • a method of transformation of three-layered finite difference scheme into two-layered one was investigated; • a spectrum of transition matrix subject to the properties of second order differential operator Lambda was studied; • stability conditions of hyperbolic type equations with nonlocal conditions subject to boundary parameters were obtained; • numerical experiments, confirming theoretical derivations were made. Derived results could be used to solve one-dimensional tasks with hyperbolic equations in different sciences, to analyse spectrum structure of mathematical models and construct new numerical methods for solving hyperbolic PDEs.