Self-Dual Codes

Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page

Open TURNS: An industrial software for uncertainty quantification in simulation

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, and health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an Open Source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for Open source Treatment of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency, genericity, modularity and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: openTURNS is an open source software under the LGPL license, that presents itself as a C++ library and a Python TUI, and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis and metamodeling. A section also explains the generic wrappers way to link openTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dyke that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years

Automated cache optimisations of stencil computations for partial differential equations

This thesis focuses on numerical methods that solve partial differential equations. Our focal point is the finite difference method, which solves partial differential equations by approximating derivatives with explicit finite differences. These partial differential equation solvers consist of stencil computations on structured grids. Stencils for computing real-world practical applications are patterns often characterised by many memory accesses and non-trivial arithmetic expressions that lead to high computational costs compared to simple stencils used in much prior proof-of-concept work. In addition, the loop nests to express stencils on structured grids may often be complicated. This work is highly motivated by a specific domain of stencil computations where one of the challenges is non-aligned to the structured grid ("off-the-grid") operations. These operations update neighbouring grid points through scatter and gather operations via non-affine memory accesses, such as {A[B[i]]}. In addition to this challenge, these practical stencils often include many computation fields (need to store multiple grid copies), complex data dependencies and imperfect loop nests. In this work, we aim to increase the performance of stencil kernel execution. We study automated cache-memory-dependent optimisations for stencil computations. This work consists of two core parts with their respective contributions.The first part of our work tries to reduce the data movement in stencil computations of practical interest. Data movement is a dominant factor affecting the performance of high-performance computing applications. It has long been a target of optimisations due to its impact on execution time and energy consumption. This thesis tries to relieve this cost by applying temporal blocking optimisations, also known as time-tiling, to stencil computations. Temporal blocking is a well-known technique to enhance data reuse in stencil computations. However, it is rarely used in practical applications but rather in theoretical examples to prove its efficacy. Applying temporal blocking to scientific simulations is more complex. More specifically, in this work, we focus on the application context of seismic and medical imaging. In this area, we often encounter scatter and gather operations due to signal sources and receivers at arbitrary locations in the computational domain. These operations make the application of temporal blocking challenging. We present an approach to overcome this challenge and successfully apply temporal blocking.In the second part of our work, we extend the first part as an automated approach targeting a wide range of simulations modelled with partial differential equations. Since temporal blocking is error-prone, tedious to apply by hand and highly complex to assimilate theoretically and practically, we are motivated to automate its application and automatically generate code that benefits from it. We discuss algorithmic approaches and present a generalised compiler pipeline to automate the application of temporal blocking. These passes are written in the Devito compiler. They are used to accelerate the computation of stencil kernels in areas such as seismic and medical imaging, computational fluid dynamics and machine learning. \href{www.devitoproject.org}{Devito} is a Python package to implement optimised stencil computation (e.g., finite differences, image processing, machine learning) from high-level symbolic problem definitions. Devito builds on \href{www.sympy.org}{SymPy} and employs automated code generation and just-in-time compilation to execute optimised computational kernels on several computer platforms, including CPUs, GPUs, and clusters thereof. We show how we automate temporal blocking code generation without user intervention and often achieve better time-to-solution. We enable domain-specific optimisation through compiler passes and offer temporal blocking gains from a high-level symbolic abstraction. These automated optimisations benefit various computational kernels for solving real-world application problems.Open Acces

Quasi-One Dimensional Flow Through a Nozzle With a Shock

The Soave-Redlich-Kwong cubic equation of state (EoS) was used in real-gas investigations for a mixture of species. An algorithm for a direct solution using a modified version of the Cardano’s method is described in order to solve the cubic EoS more efficiently compared to previous methods. Isentropic, choked flow through a convergent-divergent nozzle was investigated using classical mixing rules and compared to flow with the ideal-gas law. Two novel methods were described to solve for the downstream conditions of a normal shock and the results compared to ideal-gas solutions. A computer script was written to solve the cubic EoS. A wide range of stagnation pressure and stagnation temperatures were investigated to analyze the effects on the real-gas solutions. Upon tabulation of results, it was concluded that most solutions with lower stagnation temperatures and higher stagnation pressures are furthest in value to ideal-gas solutions. However, the range of agreement is dependent upon the species present as well as the concentration of those species in a gas

Propellant tank pressurization modeling for a hybrid rocket

A basic hybrid rocket oxidizer delivery system utilizes the self-pressurizing nature of a liquid oxidizer at ambient temperatures in conjunction with a non-condensable pressurant to provide a high oxidizer tank pressure that drives liquid oxidizer flow to the combustion chamber. In this study, the oxidizer fluid is nitrous oxide which produces high vapor pressures at ambient temperatures, and helium is the pressurant. The goal of this thesis is to provide a theoretical model that predicts the pressure draining history of the oxidizer tank to within ± 5% of experiment. The validity of simple thermodynamically-based models has not been considered for self-pressurizing, draining propellant tanks under high pressure conditions. In this study, two models are produced, both assuming thermodynamic equilibrium states at every point in time throughout draining. The first model assumes the P-V-T behavior of the nitrous oxide/helium mixture is ideal; the second model assumes that the mixture adheres to the non-ideal Peng-Robinson equation-of-state. Both models are compared to experimental data from pure nitrous oxide draining tests, published in G. Zilliac and M. Karabeyoglu (Modeling of Propellant Tank Pressurization, AIAA 2005-3549, 41st AIAA/ASME/ASEE Joint Propulsion Conference). Theoretical draining histories for the Peregrine hybrid sounding rocket (a joint effort between NASA Ames Research Center and Stanford University), soon to be launched from NASA Wallops Flight Facility, have also been examined. A variety of comparisons with available experimental data, theoretical sensitivity studies, and theoretical launch data demonstrates that the non-ideal draining model provides favorable agreement. The additional complexity introduced by a non-ideal equation-of-state is necessary due to the high pressures encountered in the tank during draining. It is found that despite the highly nonlinear nature of the draining process, the liquid flow rate from the tank remains reasonably constant, which is a highly desirable characteristic of a rocket oxidizer delivery system

Feasibility study of a synthesis procedure for array feeds to improve radiation performance of large distorted reflector antennas

Virginia Tech has several activities which support the NASA Langley effort in the area of large aperture radiometric antenna systems. This semi-annual report discusses the major areas of research and progress made

Development of a surface isolation estimation technique suitable for application of polar orbiting satellite data

A technique is developed for the estimation of total daily insolation on the basis of data derivable from operational polar-orbiting satellites. Although surface insolation and meteorological observations are used in the development, the algorithm is constrained in application by the infrequent daytime polar-orbiter coverage

Computer program for aerodynamic and blading design of multistage axial-flow compressors

A code for computing the aerodynamic design of a multistage axial-flow compressor and, if desired, the associated blading geometry input for internal flow analysis codes is presented. Compressible flow, which is assumed to be steady and axisymmetric, is the basis for a two-dimensional solution in the meridional plane with viscous effects modeled by pressure loss coefficients and boundary layer blockage. The radial equation of motion and the continuity equation are solved with the streamline curvature method on calculation stations outside the blade rows. The annulus profile, mass flow, pressure ratio, and rotative speed are input. A number of other input parameters specify and control the blade row aerodynamics and geometry. In particular, blade element centerlines and thicknesses can be specified with fourth degree polynomials for two segments. The output includes a detailed aerodynamic solution and, if desired, blading coordinates that can be used for internal flow analysis codes

Supersonic throughflow fans

Supersonic throughflow fan research, and technology needs are reviewed. The design of a supersonic throughflow fan stage, a facility inlet, and a downstream diffuser is described. The results from the analysis codes used in executing the design are shown. An engine concept intended to permit establishing supersonic throughflow within the fan on the runway and maintaining the supersonic throughflow condition within the fan throughout the flight envelope is presented