This thesis applies a Partial Integral Differential Equation model, along with a Monte Carlo approach to quantitatively analyze the no arbitrage value of hedge fund performance fees. From a no-arbitrage point of view, the investor in a hedge fund is providing a free option to the manager of the hedge fund. The no-arbitrage value of this option can be locked in by the hedge fund manager using a simple hedging strategy. Interpolation methods, grid construction techniques and parallel computation techniques are discussed to improve the performance of the numerical methods for valuing this option.

The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological heterogeneity, unfavorable mobility ratio, and capillary forces, conventional oil recovery (including water flooding) leaves behind much oil in reservoir, often as much as 70% OOIP (original oil in place). Surfactant/polymer flooding targets these bypassed oil left after waterflood by reducing water mobility and oil/water interfacial tension. The complexity and uncertainty of reservoir characterization make the design and implementation of a robust and effective surfactant/polymer flooding to be quite challenging. Accurate numerical simulation prior to the field surfactant/polymer flooding is essential for a successful design and implementation of surfactant/polymer flooding. A recently developed unified polymer viscosity model was implemented into our existing polymer module within our in-house reservoir simulator, the Implicit Parallel Accurate Reservoir Simulator (IPARS). The new viscosity model is capable of simulating not only the Newtonian and shear-thinning rheology of polymer solution but also the shear-thickening behavior, which may occur near the wellbore with high injection rates when high molecular weight Partially Hydrolyzed Acrylamide (HPAM) polymers are injected. We have added a full capability of surfactant/polymer flooding to TRCHEM module of IPARS using a simplified but mechanistic and user-friendly approach for modeling surfactant/water/oil phase behavior. The features of surfactant module include: 1) surfactant component transport in porous media; 2) surfactant adsorption on the rock; 3) surfactant/oil/water phase behavior transitioned with salinity of Type II(-), Type III, and Type II(+) phase behaviors; 4) compositional microemulsion phase viscosity correlation and 5) relative permeabilities based on the trapping number. With the parallel capability of IPARS, commercial scale simulation of surfactant/polymer flooding becomes practical and affordable. Several numerical examples are presented in this dissertation. The results of surfactant/polymer flood are verified by comparing with the results obtained from UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability and scalability are also demonstrated. / text

This work discusses available approaches for programming graphic hardware as a platform for executing parallel calculations. Text of the work is focused on new OpenCL technology, which allows executing the same high level code for taking control of full potential of multicore CPUs and GPUs, without explicit bindings to hardware vendor or operating system. Author provides the reader with libraries and tools based on OpenCL, along with practical examples and own observations about the current state of mentioned technology.

Recent advancements in data acquisition, storage, and computing power have enabled scientists from various scientific and engineering domains to simulate more complex and longer phenomena. Scientists are usually interested in understanding the behavior of a phenomenon in different conditions. To do so, they run multiple simulations with different configurations (i.e., parameter settings, boundary/initial conditions, or computational models), resulting in an ensemble dataset. An ensemble empowers scientists to quantify the uncertainty in the simulated phenomenon in terms of the variability between ensemble members, the parameter sensitivity and optimization, and the characteristics and outliers within the ensemble members, which could lead to valuable insight(s) about the simulated model. The size, complexity, and high dimensionality (e.g., simulation input and output parameters) of simulation ensembles pose a great challenge in their analysis and exploration. Ensemble visualization provides a convenient way to convey the main characteristics of the ensemble for enhanced understanding of the simulated model. The majority of the current ensemble visualization techniques are mainly focused on analyzing either the ensemble space or the parameter space. Most of the parameter space visualizations are not designed for high-dimensional data sets or did not show the intrinsic structures in the ensemble. Conversely, ensemble space has been visualized either as a comparative visualization of a limited number of ensemble members or as an aggregation of multiple ensemble members omitting potential details of the original ensemble. Thus, to unfold the full potential of simulation ensembles, we designed and developed an approach to the visual analysis of high-dimensional simulation ensembles that merges sensemaking, human expertise, and intuition with machine learning and statistics. In this work, we explore how semantic interaction and sensemaking could be used for building interactive and intelligent visual analysis tools for simulation ensembles. Specifically, we focus on the complex processes that derive meaningful insights from exploring and iteratively refining the analysis of high dimensional simulation ensembles when prior knowledge about ensemble features and correlations is limited or/and unavailable. We first developed GLEE (Graphically-Linked Ensemble Explorer), an exploratory visualization tool that enables scientists to analyze and explore correlations and relationships between non-spatial ensembles and their parameters. Then, we developed Spatial GLEE, an extension to GLEE that explores spatial data while simultaneously considering spatial characteristics (i.e., autocorrelation and spatial variability) and dimensionality of the ensemble. Finally, we developed Image-based GLEE to explore exascale simulation ensembles produced from in-situ visualization. We collaborated with domain experts to evaluate the effectiveness of GLEE using real-world case studies and experiments from different domains. The core contribution of this work is a visual approach that enables the exploration of parameter and ensemble spaces for 2D/3D high dimensional ensembles simultaneously, three interactive visualization tools that explore search, filter, and make sense of non-spatial, spatial, and image-based ensembles, and usage of real-world cases from different domains to demonstrate the effectiveness of the proposed approach. The aim of the proposed approach is to help scientists gain insights by answering questions or testing hypotheses about the different aspects of the simulated phenomenon or/and facilitate knowledge discovery of complex datasets. / Doctor of Philosophy / Scientists run simulations to understand complex phenomena and processes that are expensive, difficult, or even impossible to reproduce in the real world. Current advancements in high-performance computing have enabled scientists from various domains, such as climate, computational fluid dynamics, and aerodynamics to run more complex simulations than before. However, a single simulation run would not be enough to capture all features in a simulated phenomenon. Therefore, scientists run multiple simulations using perturbed input parameters, initial and boundary conditions, or different models resulting in what is known as an ensemble. An ensemble empowers scientists to understand the model's behavior by studying relationships between and among ensemble members, the optimal parameter settings, and the influence of input parameters on the simulation output, which could lead to useful knowledge and insights about the simulated phenomenon. To effectively analyze and explore simulation ensembles, visualization techniques play a significant role in facilitating knowledge discoveries through graphical representations. Ensemble visualization offers scientists a better way to understand the simulated model. Most of the current ensemble visualization techniques are designed to analyze or/and explore either the ensemble space or the parameter space. Therefore, we designed and developed a visual analysis approach for exploring and analyzing high-dimensional parameter and ensemble spaces simultaneously by integrating machine learning and statistics with sensemaking and human expertise. The contribution of this work is to explore how to use semantic interaction and sensemaking to explore and analyze high-dimensional simulation ensembles. To do so, we designed and developed a visual analysis approach that manifested in an exploratory visualization tool, GLEE (Graphically-Linked Ensemble Explorer), that allowed scientists to explore, search, filter, and make sense of high dimensional 2D/3D simulations ensemble. GLEE's visualization pipeline and interaction techniques used deep learning, feature extraction, spatial regression, and Semantic Interaction (SI) techniques to support the exploration of non-spatial, spatial, and image-based simulation ensembles. GLEE different visualization tools were evaluated with domain experts from different fields using real-world case studies and experiments.

In this thesis we present a parallel implementation of an engineering code which simulates the deformations caused when forces are applied to a piezoelectric-controlled smart structure. The parallel simulation, whose domain decomposition relies on the finite element representation of the structure, is created with an emphasis on scalability of both memory requirements and run time. We take into consideration sequential performance enhancements, the structure of a banded symmetric positive definite linear system, and the overhead required to completely distribute the problem across the processors. The resulting code is scalable, with the exception of a banded Cholesky factorization, which does not fully utilize the parallel environment. / Master of Science

This thesis describes the development of a general Fortran 90 framework for the solution of composite laminate design problems using a genetic algorithm (GA). The initial Fortran 90 module and package of operators result in a standard genetic algorithm (sGA). The sGA is extended to operate on a parallel processor, and a migration algorithm is introduced. These extensions result in the distributed genetic algorithm with migration (dGA). The performance of the dGA in terms of cost and reliability is studied and compared to an sGA baseline, using two types of composite laminate design problems. The nondeterminism of GAs and the migration and dynamic load balancing algorithm used in this work result in a changed (diminished) workload, so conventional measures of parallelizability are not meaningful. Thus, a set of experiments is devised to characterize the run time performance of the dGA. The migration algorithm is found to diminish the normalized cost and improve the reliability of a GA optimization run. An effective linear speedup for constant work is achieved, and the dynamic load balancing algorithm with distributed control and token ring termination detection yield improved run time performance. / Master of Science

Cette thèse est composée de deux axes principaux, le premier portant sur le chiffrement homomorphe et le second sur l’algèbre linéaire creuse sur corps finis. Avec l’essor des technologies de communication et en particulier d’internet, de nouveaux protocoles de chiffrement sont développés. En particulier, le besoin de systèmes de chiffrement permettant de manipuler les données chiffrées tout en assurant leur sécurité. C’est dans ce contexte que des systèmes de chiffrement homomorphe sont développés, ces protocoles permettent d’effectuer des calculs avec des données chiffrées. La sécurité de ce type système repose sur l’ajout de bruit aux messages à chiffrer. Ce bruit augmente avec chaque opération effectuée, mais il ne doit pas dépasser un certain seuil. Pour contourner ce problème, une technique nommée bootstrapping est utilisée permettant de réduire le bruit d’un chiffré. Les bootstrappings sont le goulot d’étranglement lors des calculs sur des données chiffrées, il est important d’en faire le moins possible. Or la quantité de bootstrappings à faire est déterminée par la nature des calculs à effectuer ainsi que du protocole de chiffrement utilisé.C’est dans ce contexte que notre travail intervient, nous proposons une méthode effective pour réduire le nombre bootstrappings basé sur la programmation linéaire en nombre entier. Cette méthode s’adapte à un grand nombre de protocoles de chiffrement. De plus, nous effectuons une analyse de la complexité de ce problème en montrant qu’il est APX-complet et nous fournissons un algorithme d’approximation.La résolution de système linéaire sur corps finis est une brique de calcul essentielle dans de nombreux problèmes de calcul formel. En particulier, beaucoup de problèmes produisent des matrices comprenant un grand nombre de zéros, on dit qu’elles sont creuses. Les meilleurs algorithmes permettant de résoudre ce type de système linéaire creux sont des algorithmes dits itératifs. L’opération fondamentale de ces algorithmes itératifs est la multiplication de la matrice par un vecteur ou une matrice dense. Afin d’obtenir les meilleures performances, il est important de tenir compte des propriétés (SIMD, multicoeurs, hiérarchie des caches ....) des processus modernes .C’est dans ce contexte que notre travail intervient, nous étudions la meilleure façon d’implanter efficacement cette opération sur les processeurs récents.Nous proposons un nouveau format permettant de tenir compte du grand nombre de +- 1 présents dans une matrice.Nous proposons une implantation parallèle basée sur le paradigme du vol de tâche offrant un meilleur passage à l’échelle que le parallélisme par threads.Nous montrons comment exploiter au mieux les instructions SIMD des processeurs dans les différentes opérations.Finalement, nous proposons une méthode efficace permettant d’effectuer cette opération lorsque le corps finis est multiprécision (les éléments sont stockés sur plusieurs mots machine) en ayant recours au système de représentation RNS. / This thesis is composed of two independent parts.The first one is related to homomorphic encryption and the second part deal with sparse linear algebra on finite fields.Homomorphic encryption extends traditional encryption in the sense that it becomes feasible to perform operations on ciphertexts, without the knowledge of the secret decryption key. As such, it enables someone to delegate heavy computations on his sensitive data to an untrusted third party, in a secure way. More precisely, with such a system, one user can encrypt his sensitive data such that the third party can evaluate a function on the encrypted data, without learning any information on the underlying plain data. Getting back the encrypted result, the user can use his secret key to decrypt it and obtain, in clear, the result of the evaluation of the function on his sensitive plain data. For a cloud user, the applications are numerous, and reconcile both a rich user experience and a strong privacy protection.The first fully homomorphic encryption (FHE) scheme, able to handle an arbitrary number of additions and multiplications on ciphertexts, has been proposed by Gentry in 2009.In homomorphic encryption schemes, the executed function is typically represented as an arithmetic circuit. In practice, any circuit can be described as a set of successive operation gates, each one being either a sum or a product performed over some ring.In Gentry’s construction, based on lattices, each ciphertext is associated with some noise, which grows at each operation (addition or multiplication) done throughout the evaluation of the function. When this noise reaches a certain limit, decryption is not possible anymore.To overcome this limitation, closely related to the number of operations that the HE.Eval procedure can handle, Gentry proposed in a technique of noise refreshment called“bootstrapping”.The main idea behind this bootstrapping procedure is to homomorphically run the decryptionprocedure of the scheme on the ciphertext, using an encrypted version of the secret key. In this context, our contribution is twofold. We first prove that the lmax-minimizing bootstrapping problem is APX-complete and NP-complete for lmax ≥ 3. We then propose a new method to determine the minimal number of bootstrappings needed for a given FHE scheme and a given circuit.We use linear programming to find the best outcome for our problem. The main advantage of our method over the previous one is that it is highly flexible and can be adapted for numerous types of homomorphic encryption schemes and circuits.Computing a kernel element of a matrix is a fundamental kernel in many computer algebra and cryptography algorithms. Especially, many applications produces matrices with many matrix elements equals to 0.Those matrices are named sparse matrices. Sparse linear algebra is fundamentally relying on iterative approaches such as Wiedemann or Lanczos. The main idea is to replace the direct manipulation of a sparse matrix with its Krylov subspace. In such approach, the cost is therefore dominated by the computation of the Krylov subspace, which is done by successive product of a matrix by a vector or a dense matrix.Modern processor unit characteristics (SIMD, multicores, caches hierarchy, ...) greatly influence algorithm design.In this context our work deal with the best approach to design efficient implementation of sparse matrix vector product for modern processors.We propose a new sparse matrix format dealing with the many +-1 matrix elements to improve performance.We propose a parallel implementation based on the work stealing paradigm that provide a good scaling on multicores architectures.We study the impact of SIMD instructions on sparse matrix operations.Finally, we provide a modular arithmetic implementation based on residue number system to deal with sparse matrix vector product over multiprecision finite fields.

Most systems in HPC make use of hierarchical designs that allow multiple levels of parallelism to be exploited by programmers. The use of multiple multi-core/multi-processor computers to form a computer cluster supports both fine-grain and large-grain parallel computation. Aggregate function communications provide an easy to use and efficient set of mechanisms for communicating and coordinating between processing elements, but the model originally targeted only fine grain parallel hardware. This work shows that a hierarchical implementation of aggregate functions is a viable alternative to MPI (the standard Message Passing Interface library) for programming clusters that provide both fine grain and large grain execution. Performance of a prototype implementation is evaluated and compared to that of MPI.

The objective of this research is to develop an efficient and accurate methodology to resolve flow non-linearity of fluid-structural interaction. To achieve this purpose, a numerical strategy to apply the detached-eddy simulation (DES) with a fully coupled fluid-structural interaction model is established for the first time. The following novel numerical algorithms are also created: a general sub-domain boundary mapping procedure for parallel computation to reduce wall clock simulation time, an efficient and low diffusion E-CUSP (LDE) scheme used as a Riemann solver to resolve discontinuities with minimal numerical dissipation, and an implicit high order accuracy weighted essentially non-oscillatory (WENO) scheme to capture shock waves. The Detached-Eddy Simulation is based on the model proposed by Spalart in 1997. Near solid walls within wall boundary layers, the Reynolds averaged Navier-Stokes (RANS) equations are solved. Outside of the wall boundary layers, the 3D filtered compressible Navier-Stokes equations are solved based on large eddy simulation(LES). The Spalart-Allmaras one equation turbulence model is solved to provide the Reynolds stresses in the RANS region and the subgrid scale stresses in the LES region. An improved 5th order finite differencing weighted essentially non-oscillatory (WENO) scheme with an optimized epsilon value is employed for the inviscid fluxes. The new LDE scheme used with the WENO scheme is able to capture crisp shock profiles and exact contact surfaces. A set of fully conservative 4th order finite central differencing schemes are used for the viscous terms. The 3D Navier-Stokes equations are discretized based on a conservative finite differencing scheme, which is implemented by shifting the solution points half grid interval in each direction on the computational domain. The solution points are hence located in the center of the grid cells in the computational domain (not physical domain). This makes it possible to use the same code structure as a 2nd order finite volume method. A finite differencing high order WENO scheme is used since a finite differencing WENO scheme is much more efficient than a finite volume WENO scheme. The unfactored line Gauss-Seidel relaxation iteration is employed for time marching. For the time accurate unsteady simulation, the temporal terms are discretized using the 2nd order accuracy backward differencing. A pseudo temporal term is introduced for the unsteady calculation following Jameson's method. Within each physical time step, the solution is iterated until converged based on pseudo time step. A general sub-domain boundary mapping procedure is developed for arbitrary topology multi-block structured grids with grid points matched on sub-domain boundaries. The interface of two adjacent blocks is uniquely defined according to each local mesh index system (MIS) which is specified independently. A pack/unpack procedure based on the definition of the interface is developed to exchange the data in a 1D array to minimize data communication. A secure send/receive procedure is employed to remove the possibility of blocked communication and achieve optimum parallel computation efficiency. Two terms, "Order" and "Orientation", are introduced as the logics defining the relationship of adjacent blocks. The domain partitioning treatment of the implicit matrices is to simply discard the corner matrices so that the implicit Gauss-Seidel iteration can be implemented within each subdomain. This general sub-domain boundary mapping procedure is demonstrated to have high scalability. Extensive numerical experiments are conducted to test the performance of the numerical algorithms. The LDE scheme is compared with the Roe scheme for their behavior with RANS simulation. Both the LDE and the Roe scheme can use high CFL numbers and achieve high convergence rates for the algebraic Baldwin-Lomax turbulence model. For the Spalart-Allmaras one equation turbulence model, the extra equation changes the Jacobian of the Roe scheme and weakens the diagonal dominance. It reduces the maximum CFL number permitted by the Roe scheme and hence decreases the convergence rate. The LDE scheme is only slightly affected by the extra equation and maintains high CFL number and convergence rate. The high stability and convergence rate using the Spalart-Allmaras one equation turbulence model is important since the DES uses the same transport equation for the turbulence stresses closure. The RANS simulation with the Spalart-Allmaras one equation turbulence model is the foundation for DES and is hence validated with other transonic flows including a 2D subsonic flat plate turbulent boundary layer, 2D transonic inlet-diffuser, 2D RAE2822 airfoil, 3D ONERA M6 wing, and a 3D transonic duct with shock boundary layer interaction. The predicted results agree very well with the experiments. The RANS code is then further used to study the slot size effect of a co-flow jet (CFJ) airfoil. The DES solver with fully coupled fluid-structural interaction methodology is validated with vortex induced vibration of a cylinder and a transonic forced pitching airfoil. For the cylinder, the laminar Navier-Stokes equations are solved due to the low Reynolds number. The 3D effects are observed in both stationary and oscillating cylinder simulation because of the flow separations behind the cylinder. For the transonic forced pitching airfoil DES computation, there is no flow separation in the flow field. The DES results agree well with the RANS results. These two cases indicate that the DES is more effective on predicting flow separation. The DES code is used to simulate the limited cycle oscillation of NLR7301 airfoil. For the cases computed in this research, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment. The solutions appear to have bifurcation and are dependent on the initial perturbation. The developed methodology is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The DES code is also used to simulate the CFJ airfoil jet mixing at high angle of attack. In conclusion, the numerical strategy of the high order DES with fully coupled FSI model and parallel computing developed in this research is demonstrated to have high accuracy, robustness, and efficiency. Future work to further maturate the methodology is suggested.

The field of Information and Communication Technologies is witnessing a development speed unprecedented in history. Moore’s law proves that the processor speed and memory size are roughly doubling each 18 months, which is expected to continue in the next decade. If photonics is going to play a substantial role in the ICT market, it will have to follow the same dynamics. There are mainly two groups of components that need to be integrated. The active components, including light sources, electro-optic modulators, and detectors, are mostly fabricated in III-V semiconductors. The passive components, such as waveguides, resonators, couplers and splitters, need no power supply and can be realized in silicon-related semiconductors. The prospects of silicon photonics are particularly promising, the fabrication is mostly compatible with standard CMOS technology and the on-chip optical interconnects are expected to increase the speed of microprocessors to the next generation. This thesis starts with designs of various silicon-based devices using finite-difference time-domain simulations. Parallel computation is a powerful tool in the modeling of large-scale photonic circuits. High Q cavities and resonant channel drop filters are designed in photonic crystal platform. Different methods to couple light from a single mode fiber to silicon waveguides are studied by coupled-mode theory and verified using parallel simulations. The performance of waveguide grating coupler for vertical radiation is also studied. The fabrication of silicon-based photonic devices involves material deposition, E-beam or optical lithography for pattern defining, and plasma/wet-chemistry etching for pattern transfer. For nanometer-scaled structures, E-beam lithography is the most critical process. Depending on the structures of the devices, both positive resist (ZEP520A) and negative resist (maN2405) are used. The proximity and stitch issues are addressed by careful dose correction and patches exposure. Some examples are given including photonic crystal surface mode filter, micro-ring resonators and gold grating couplers. In particular, high Q (2.6×105), deep notch (40 dB) and resonance-splitting phenomenon are demonstrated for silicon ring resonators. It is challenging to couple light into photonic integrated circuits directly from a single-mode fiber. The butt-coupled light-injecting method usually causes large insertion loss due to small overlap of the mode profiles and large index mismatch. Practically it is not easy to cleave silicon sample with smooth facet where the waveguide exposes. By adding gold gratings to the waveguides, light can be injected and collected vertically from single-mode fiber. The coupling efficiency is much higher. There is no need to cleave the sample. The access waveguides are much shortened and the stitch problem in E-beam lithography is avoided. In summary, this thesis introduces parallel simulations for the design of modern large-scale photonic devices, addresses various issues with Si-based fabrication, and analyses the data from the characterization. Several novel devices using silicon nanowire waveguides and 2D photonic crystal structures have been demonstrated for the first time. / QC 20100923