• Decentralized control of multi-agent aerial transportation system

      Toumi, Noureddine (2017-04)
      Autonomous aerial transportation has multiple potential applications including emergency cases and rescue missions where ground intervention may be difficult. In this context, the following work will address the control of multi-agent Vertical Take-off and Landing aircraft (VTOL) transportation system. We develop a decentralized method. The advantage of such a solution is that it can provide better maneuverability and lifting capabilities compared to existing systems. First, we consider a cooperative group of VTOLs transporting one payload. The main idea is that each agent perceive the interaction with other agents as a disturbance while assuming a negotiated motion model and imposing certain magnitude bounds on each agent. The theoretical model will be then validated using a numerical simulation illustrating the interesting features of the presented control method. Results show that under specified disturbances, the algorithm is able to guarantee the tracking with a minimal error. We describe a toolbox that has been developed for this purpose. Then, a system of multiple VTOLs lifting payloads will be studied. The algorithm assures that the VTOLs are coordinated with minimal communication. Additionally, a novel gripper design for ferrous objects is presented that enables the transportation of ferrous objects without a cable. Finally, we discuss potential connections to human in the loop transportation systems.
    • Decoupling Linear and Nonlinear Associations of Gene Expression

      Itakura, Alan (2013-05)
      The FANTOM consortium has generated a large gene expression dataset of different cell lines and tissue cultures using the single-molecule sequencing technology of HeliscopeCAGE. This provides a unique opportunity to investigate novel associations between gene expression over time and different cell types. Here, we create a MatLab wrapper for a powerful and computationally intensive set of statistics known as Maximal Information Coefficient, and then calculate this statistic for a large, comprehensive dataset containing gene expression of a variety of differentiating tissues. We then distinguish between linear and nonlinear associations, and then create gene association networks. Following this analysis, we are then able to identify clusters of linear gene associations that then associate nonlinearly with other clusters of linearity, providing insight to much more complex connections between gene expression patterns than previously anticipated.
    • Deformation of Man Made Objects

      Ibrahim, Mohamed (2012-07)
      We introduce a framework for 3D object deformation with primary focus on man-made objects. Our framework enables a user to deform a model while preserving its defining characteristics. Moreover, our framework enables a user to set constraints on a model to keep its most significant features intact after the deformation process. Our framework supports a semi-automatic constraint setting environment, where some constraints could be automatically set by the framework while others are left for the user to specify. Our framework has several advantages over some state of the art deformation techniques in that it enables a user to add new features to the deformed model while keeping its general look similar to the input model. In addition, our framework enables the rotation and extrusion of different parts of a model.
    • A Density Functional Theory Study of Doped Tin Monoxide as a Transparent p-type Semiconductor

      Bianchi Granato, Danilo (2012-05)
      In the pursuit of enhancing the electronic properties of transparent p-type semiconductors, this work uses density functional theory to study the effects of doping tin monoxide with nitrogen, antimony, yttrium and lanthanum. An overview of the theoretical concepts and a detailed description of the methods employed are given, including a discussion about the correction scheme for charged defects proposed by Freysoldt and others [Freysoldt 2009]. Analysis of the formation energies of the defects points out that nitrogen substitutes an oxygen atom and does not provide charge carriers. On the other hand, antimony, yttrium, and lanthanum substitute a tin atom and donate n-type carriers. Study of the band structure and density of states indicates that yttrium and lanthanum improves the hole mobility. Present results are in good agreement with available experimental works and help to improve the understanding on how to engineer transparent p-type materials with higher hole mobilities.
    • Design and Fabrication of a Reconfigurable MEMS-Based Antenna

      Martinez, Miguel Angel Galicia (2011-06-22)
      This thesis presents the design and fabrication of a customized in house Micro-Electro-Mechanical-Systems (MEMS) process based on-chip antenna that is both frequency and polarization reconfigurable. It is designed to work at both 60 GHz and 77 GHz through MEMS switches. This antenna can also work in both horizontal and vertical linear polarizations by utilizing a moveable plate. The design is intended for Wireless Personal Area Networks (WPAN) and automotive radar applications. Typical on-chip antennas are inefficient and difficult to reconfigure. Therefore, the focus of this work is to develop an efficient on-chip antenna solution, which is reconfigurable in frequency and in polarization. A fractal bowtie antenna is employed for this thesis, which achieves frequency reconfigurability through MEMS switches. The design is simulated in industry standard Electromagnetic (EM) simulator Ansoft HFSS. A novel concept for horizontal to vertical linear polarization agility is introduced which incorporates a moveable polymer plate. For this work, a microprobe is used to move the plate from the horizontal to vertical position. For testing purposes, a novel mechanism has been designed in order to feed the antenna with RF-probes in both horizontal and vertical positions. A simulated gain of approximately 0 dB is achieved at both target frequencies (60 and 77 GHz), in both horizontal and vertical positions. In all the cases mentioned above (both frequencies and positions), the antenna is well matched (< -10 dB) to the 50 Ω system impedance. Similarly, the radiation nulls are successfully shifted by changing the position of the antenna from horizontal to vertical. The complete design and fabrication of the reconfigurable MEMS antenna has been done at KAUST facilities. Some challenges have been encountered during its realization due to the immaturity of the customized MEMS fabrication process. Nonetheless, a first fabrication attempt has highlighted such shortcomings. According to the high gain obtained in a lossy silicon substrate and the compatibility of the custom MEMS process with the state of the art standard CMOS process, it is believed that the design of this antenna can lead to efficient and low cost reconfigurable millimeter-wave System-on-Chip (SoC) solution.
    • Design and Implementation of a Laser-Based Ammonia Breath Sensor for Medical Applications

      Owen, Kyle (2012-06)
      Laser-based sensors can be used as non-invasive monitoring tools to measure parts per billion (ppb) levels of trace gases. Ammonia sensors are useful for applications in environmental pollutant monitoring, atmospheric and combustion kinetic studies, and medical diagnostics. This sensor was specifically designed to measure ammonia in exhaled breath to be used as a medical diagnostic and monitoring tool, however, it can also be extended for use in other applications. Although ammonia is a naturally occurring species in exhaled breath, abnormally elevated levels can be an indication of adverse medical conditions. Laser-based breath diagnostics have many benefits since they are cost effective, non-invasive, painless, real time monitors. They have the potential to improve the quality of medical care by replacing currently used blood tests and providing immediate feedback to physicians. This sensor utilizes a Quantum Cascade Laser and Wavelength Modulation Spectroscopy with second harmonic normalized by first harmonic detection in a 76 m multi-pass absorption cell to measure ppb levels of ammonia with improved sensitivity over previous sensors. Initial measurements to determine the ammonia absorption line parameters were performed using direct absorption spectroscopy. This is the first experimental study of the ammonia absorption line transitions near 1103.46 cm-1 with absorption spectroscopy. The linestrengths were measured with uncertainties less than 10%. The collisional broadening coefficients for each of the ammonia lines with nitrogen, oxygen, water vapor, and carbon dioxide were also measured, many of which had uncertainties less than 5%. The sensor was characterized to show a detectability limit of 10 ppb with an uncertainty of less than 5% at typical breath ammonia levels. Initial breath test results showed that some of the patients with chronic kidney disease had elevated ammonia levels while others had ammonia levels in the same range as expected for healthy patients. For all of the patients the breath ammonia level decreased during dialysis but the percent decrease varied considerably for each patient. The sensor has demonstrated improved sensitivity and has been applied to measure ppb levels of ammonia in exhaled breath. Further tests have been designed to improve the sensor and continue to investigate the medical applications.
    • Design and Optimization of OpenFOAM-based CFD Applications for Modern Hybrid and Heterogeneous HPC Platforms

      AlOnazi, Amani A. (2014-02)
      The progress of high performance computing platforms is dramatic, and most of the simulations carried out on these platforms result in improvements on one level, yet expose shortcomings of current CFD packages. Therefore, hardware-aware design and optimizations are crucial towards exploiting modern computing resources. This thesis proposes optimizations aimed at accelerating numerical simulations, which are illus- trated in OpenFOAM solvers. A hybrid MPI and GPGPU parallel conjugate gradient linear solver has been designed and implemented to solve the sparse linear algebraic kernel that derives from two CFD solver: icoFoam, which is an incompressible flow solver, and laplacianFoam, which solves the Poisson equation, for e.g., thermal dif- fusion. A load-balancing step is applied using heterogeneous decomposition, which decomposes the computations taking into account the performance of each comput- ing device and seeking to minimize communication. In addition, we implemented the recently developed pipeline conjugate gradient as an algorithmic improvement, and parallelized it using MPI, GPGPU, and a hybrid technique. While many questions of ultimately attainable per node performance and multi-node scaling remain, the ex- perimental results show that the hybrid implementation of both solvers significantly outperforms state-of-the-art implementations of a widely used open source package.
    • Design of a Hydraulic Variable Compression Ratio Piston for a Heavy Duty Internal Combustion Engine

      Al Mudraa, Sultan (2018-07)
      A High percentage of fuel consumption worldwide is in internal combustion engines which has led environmental organizations and authorities to put further pressure on the engine industries to reduce CO2 emissions and enhance engine efficiency. However, historically, the effect of the compression ratio on increasing thermal efficiency of the engine is well known, hence; numerous technical solutions have been proposed to implement a variable compression ratio concept. A new first-class engineering solution to use a hydraulic piston was initially patented by BICERA (British Internal Combustion Engine Research Association) , then improved by Continental and Daimler Benz. A Hydraulic variable compression ratio piston is a hydraulically actuated piston that provides a practical method of obtaining a variable compression ratio piston. In this literature, a hydraulic variable compression ratio piston for a Volvo D13 diesel engine was designed, analyzed, modeled and discussed. This analysis was accomplished by first performing kinematic and dynamic analyses for the piston motion and acceleration based on the crank-slider mechanism. Following this the oil flow characteristics were defined in every mechanical element transferring the oil in its journey from the engine pump to the piston. Moreover, two different designs were proposed in an attempt to predict the compression ratio by modeling the hydraulic, dynamic and engine execution simultaneously. Additionally, stress on the piston was analyzed using Finite Element Analysis (FEA) to assure piston sustainment and rigidity against the harsh combustion chamber environment. In conclusion, the best design was successfully selected and finalized to reach a wide compression ratio range under a boosted inlet pressure based on the selected design, dimensions, check valves and relief valves.
    • Design of LTCC Based Fractal Antenna

      AdbulGhaffar, Farhan (2010-09)
      The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
    • Design, Synthesis and Characterization of Functional Metal-Organic Framework Materials

      Alamer, Badriah (2015-06)
      Over the past few decades, vast majority of industrial and academic research throughout the world has witnessed the emergence of materials that can serve as ideal candidates for potential utility in desired applications, and these materials are known as Metal Organic Framework (MOFs). This exceptional new family of porous materials is fabricated by linkage of metal ions or clusters and organic linkers via strong bonds. MOFs have been awarded with remarkable interest and widely studied due to their inherent structural methodology (e.g. use of various metals, expanded library of organic building blocks with different geometry and functionality particularly frameworks designed from carboxylate organic linkers) and unquestionably unique structural and chemical features for many practical applications. (i.e. gas storage/separation, catalysis, drug delivery etc). Simply, metal organic frameworks epitomize the beauty of porous chemical structures. From a design perspective, the introduction of the Molecular Building Block (MBB) approach is actively being pursued pathway by researchers toward the construction of MOFs by employing inorganic building blocks and organic linkers and taking advantage of not only their multiple coordination modes and geometries but also the way in which they are reticulated to generate final framework. In this thesis, research studies will be directed toward (i) the investigation of the relationship between experimental parameters and synthesis of well-known fcu –MOF, (ii) rational design and synthesis of new rare earth (RE) based MOFs, (ii) isoreticular materials based on particular MBB ([M3O(RCO2)6]), M= p-and d-block metals, and (iv) zeolite- like metal organic framework assembled from single-metal ion based MBB ([MN2(CO2)4]) via 2-, 3-,and 4-connected organic linkers. Consequently, the porosity, chemical and thermal stability, and gas sorption properties will be evaluated and detailed.
    • Detection of Cardiovascular Anomalies: An Observer-Based Approach

      Ledezma, Fernando (2012-07)
      In this thesis, a methodology for the detection of anomalies in the cardiovascular system is presented. The cardiovascular system is one of the most fascinating and complex physiological systems. Nowadays, cardiovascular diseases constitute one of the most important causes of mortality in the world. For instance, an estimate of 17.3 million people died in 2008 from cardiovascular diseases. Therefore, many studies have been devoted to modeling the cardiovascular system in order to better understand its behavior and find new reliable diagnosis techniques. The lumped parameter model of the cardiovascular system proposed in [1] is restructured using a hybrid systems approach in order to include a discrete input vector that represents the influence of the mitral and aortic valves in the different phases of the cardiac cycle. Parting from this model, a Taylor expansion around the nominal values of a vector of parameters is conducted. This expansion serves as the foundation for a component fault detection process to detect changes in the physiological parameters of the cardiovascular system which could be associated with cardiovascular anomalies such as atherosclerosis, aneurysm, high blood pressure, etc. An Extended Kalman Filter is used in order to achieve a joint estimation of the state vector and the changes in the considered parameters. Finally, a bank of filters is, as in [2], used in order to detect the appearance of heart valve diseases, particularly stenosis and regurgitation. The first numerical results obtained are presented.
    • Development of a Computational Steering Framework for High Performance Computing Environments on Blue Gene/P Systems

      Danani, Bob K. (2012-07)
      Computational steering has revolutionized the traditional workflow in high performance computing (HPC) applications. The standard workflow that consists of preparation of an application’s input, running of a simulation, and visualization of simulation results in a post-processing step is now transformed into a real-time interactive workflow that significantly reduces development and testing time. Computational steering provides the capability to direct or re-direct the progress of a simulation application at run-time. It allows modification of application-defined control parameters at run-time using various user-steering applications. In this project, we propose a computational steering framework for HPC environments that provides an innovative solution and easy-to-use platform, which allows users to connect and interact with running application(s) in real-time. This framework uses RealityGrid as the underlying steering library and adds several enhancements to the library to enable steering support for Blue Gene systems. Included in the scope of this project is the development of a scalable and efficient steering relay server that supports many-to-many connectivity between multiple steered applications and multiple steering clients. Steered applications can range from intermediate simulation and physical modeling applications to complex computational fluid dynamics (CFD) applications or advanced visualization applications. The Blue Gene supercomputer presents special challenges for remote access because the compute nodes reside on private networks. This thesis presents an implemented solution and demonstrates it on representative applications. Thorough implementation details and application enablement steps are also presented in this thesis to encourage direct usage of this framework.
    • Development of a Multi-User Polyimide-MEMS Fabrication Process and its Application to MicroHotplates

      Lizardo, Ernesto B. (2013-05-08)
      Micro-electro-mechanical systems (MEMS) became possible thanks to the silicon based technology used to fabricate integrated circuits. Originally, MEMS fabrication was limited to silicon based techniques and materials, but the expansion of MEMS applications brought the need of a wider catalog of materials, including polymers, now being used to fabricate MEMS. Polyimide is a very attractive polymer for MEMS fabrication due to its high temperature stability compared to other polymers, low coefficient of thermal expansion, low film stress and low cost. The goal of this thesis is to expand the Polyimide usage as structural material for MEMS by the development of a multi-user fabrication process for the integration of this polymer along with multiple metal layers on a silicon substrate. The process also integrates amorphous silicon as sacrificial layer to create free-standing structures. Dry etching is used to release the devices and avoid stiction phenomena. The developed process is used to fabricate platforms for micro-hotplate gas sensors. The fabrication steps for the platforms are described in detail, explaining the process specifics and capabilities. An initial testing of the micro-hotplate is presented. As the process was also used as educational tool, some designs made by students and fabricated with the Polyimide-MEMS process are also presented.
    • Development of highly porous flat sheet polyvinylidene fluoride (PVDF) membranes for membrane distillation

      Alsaery, Salim A. (2017-05)
      With the increase of population every year, fresh water scarcity has rapidly increased and it is reaching a risky level, particularly in Africa and the Middle East. Desalination of seawater is an essential process for fresh water generation. One of the methods for desalination is membrane distillation (MD). MD process separates an aqueous liquid feed across a porous hydrophobic membrane to produce pure water via evaporation. Polyvinlidene fluoride (PVDF) membranes reinforced with a polyester fabric were fabricated as potential candidates for MD. Non-solvent induced phase separation coupled with steam treatment was used to prepare the PVDF membranes. A portion of the prepared membrane was coated with Teflon (AF2400) to increase its hydrophobicity. In the first study, the fabricated membranes were characterized using scanning electron microscopy and other techniques, and they were evaluated using direct contact MD (DCMD). The fabricated membranes showed a porous sponge-like structure with some macrovoids. The macrovoid formation and the spongy structure in the membrane cross-sections contributed significantly to a high permeate flux as they provide a large space for vapor water transport. The modified PVDF membranes with steaming and coating exhibited a permeate flux of around 40 L/h m2 (i.e. 27-30% increase to the control PVDF membrane) at temperatures of 60 °C (feed) and 20 °C (permeate). This increase in the permeate flux for the modified membranes was mainly attributed to its larger pore size on the bottom surface. In the second study, the control PVDF membrane was tested in two different module designs (i.e. semi-circular pipe and rectangular duct module designs). The semi-circular module design (turbulent regime) exhibited a higher permeate flux, 3-fold higher than that of the rectangular duct module design (laminar regime) at feed temperature of 60 °C. Furthermore, a heat energy balance was performed for each module design to determine the temperature polarization coefficients (TPC). The turbulent module design showed higher TPC (0.5-0.58) than the laminar module (0.1-0.14) (i.e. a poor module design). This indicates that the effect of temperature polarization on the laminar flow was significant, which is below the reported TPC range of 0.4-0.70.
    • Device Characterization of High Performance Quantum Dot Comb Laser

      Rafi, Kazi (2012-02)
      The cost effective comb based laser sources are considered to be one of the prominent emitters used in optical communication (OC) and photonic integrated circuits (PIC). With the rising demand for delivering triple-play services (voice, data and video) in FTTH and FTTP-based WDM-PON networks, metropolitan area network (MAN), and short-reach rack-to-rack optical computer communications, a versatile and cost effective WDM transmitter design is required, where several DFB lasers can be replaced by a cost effective broadband comb laser to support on-chip optical signaling. Therefore, high performance quantum dot (Q.Dot) comb lasers need to satisfy several challenges before real system implementations. These challenges include a high uniform broadband gain spectrum from the active layer, small relative intensity noise with lower bit error rate (BER) and better temperature stability. Thus, such short wavelength comb lasers offering higher bandwidth can be a feasible solution to address these challenges. However, they still require thorough characterization before implementation. In this project, we briefly characterized the novel quantum dot comb laser using duty cycle based electrical injection and temperature variations where we have observed the presence of reduced thermal conductivity in the active layer. This phenomenon is responsible for the degradation of device performance. Hence, different performance trends, such as broadband emission and spectrum stability were studied with pulse and continuous electrical pumping. The tested comb laser is found to be an attractive solution for several applications but requires further experiments in order to be considered for photonic intergraded circuits and to support next generation computer-communications.
    • Device Fabrication and Probing of Discrete Carbon Nanostructures

      Batra, Nitin M (2015-05-06)
      Device fabrication on multi walled carbon nanotubes (MWCNTs) using electrical beam lithography (EBL), electron beam induced deposition (EBID), ion beam induced deposition (IBID) methods was carried out, followed by device electrical characterization using a conventional probe station. A four-probe configuration was utilized to measure accurately the electrical resistivity of MWCNTs with similar results obtained from devices fabricated by different methods. In order to reduce the contact resistance of the beam deposited platinum electrodes, single step vacuum thermal annealing was performed. Microscopy and spectroscopy were carried out on the beam deposited electrodes to follow the structural and chemical changes occurring during the vacuum thermal annealing. For the first time, a core-shell type structure was identified on EBID Pt and IBID Pt annealed electrodes and analogous free standing nanorods previously exposed to high temperature. We believe this observation has important implications for transport properties studies of carbon materials. Apart from that, contamination of carbon nanostructure, originating from the device fabrication methods, was also studied. Finally, based on the observations of faster processing time together with higher yield and flexibility for device preparation, we investigated EBID to fabricate devices for other discrete carbon nanostructures.
    • Diagnosis of Constant Faults in Read-Once Contact Networks over Finite Bases using Decision Trees

      Busbait, Monther I. (2014-05)
      We study the depth of decision trees for diagnosis of constant faults in read-once contact networks over finite bases. This includes diagnosis of 0-1 faults, 0 faults and 1 faults. For any finite basis, we prove a linear upper bound on the minimum depth of decision tree for diagnosis of constant faults depending on the number of edges in a contact network over that basis. Also, we obtain asymptotic bounds on the depth of decision trees for diagnosis of each type of constant faults depending on the number of edges in contact networks in the worst case per basis. We study the set of indecomposable contact networks with up to 10 edges and obtain sharp coefficients for the linear upper bound for diagnosis of constant faults in contact networks over bases of these indecomposable contact networks. We use a set of algorithms, including one that we create, to obtain the sharp coefficients.
    • Dilution-to-extinction culturing of SAR11 members and other marine bacteria from the Red Sea

      Mohamed, Roslinda B. (2013-12)
      Life in oceans originated about 3.5 billion years ago where microbes were the only life form for two thirds of the planet’s existence. Apart from being abundant and diverse, marine microbes are involved in nearly all biogeochemical processes and are vital to sustain all life forms. With the overgrowing number of data arising from culture-independent studies, it became necessary to improve culturing techniques in order to obtain pure cultures of the environmentally significant bacteria to back up the findings and test hypotheses. Particularly in the ultra-oligotrophic Red Sea, the ubiquitous SAR11 bacteria has been reported to account for more than half of the surface bacterioplankton community. It is therefore highly likely that SAR11, and other microbial life that exists have developed special adaptations that enabled them to thrive successfully. Advances in conventional culturing have made it possible for abundant, unculturable marine bacteria to be grown in the lab. In this study, we analyzed the effectiveness of the media LNHM and AMS1 in isolating marine bacteria from the Red Sea, particularly members of the SAR11 clade. SAR11 strains obtained from this study AMS1, and belonged to subgroup 1a and phylotype 1a.3. We also obtained other interesting strains which should be followed up with in the future. In the long run, results from this study will enhance our knowledge of the pelagic ecosystem and allow the impacts of rising temperatures on marine life to be understood.
    • Direct Closed-Form Design of Finite Alphabet Constant Envelope Waveforms for Planar Array Beampatterns

      Bouchoucha, Taha (2015-05)
      Multiple Input Multiple Output (MIMO) radar systems has attracted lately a lot of attention thanks to its advantage over the classical phased array radar systems. We site among these advantages the improvement of parametric identifiability, achievement of higher spatial resolution and design of complex beampatterns. In colocated multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest in order to increase the Signal to Noise Ratio (SNR) and reduce any undesired signal and thus improve the detection process. This problem is also known as transmit beampattern design. To achieve this goal, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate the actual transmitted waveforms. Both steps require constrained optimization. Most of the existing methods use iterative algorithms to solve these problems, therefore their computational complexity is very high which makes them hard to use in practice especially for real time radar applications. In this paper, we provide a closed-form solution to design the covariance matrix for a given beampattern in the three dimensional space using planar arrays, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope waveforms. The proposed algorithm exploits the two-dimensional discrete Fourier transform which is implemented using fast Fourier transform algorithm. Consequently, the computational complexity of the proposed beampattern solution is very low allowing it to be used for large arrays to change the beampattern in real time. We also show that the number of required snapshots in each waveform depends on the beampattern and that it is less than the total number of transmit antennas. In addition, we show that the proposed waveform design method can be used with non symmetric beampatterns. The performance of our proposed algorithm compares favorably with the existing iterative methods in terms of mean square error.
    • Discontinuous Galerkin Method for Hyperbolic Conservation Laws

      Mousikou, Ioanna (2016-11-11)
      Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.