Algebraic, Block and Multiplicative Preconditioners based on Fast Tridiagonal Solves on GPUs

This thesis contributes to the field of sparse linear algebra, graph applications, and preconditioners for Krylov iterative solvers of sparse linear equation systems, by providing a (block) tridiagonal solver library, a generalized sparse matrix-vector implementation, a linear forest extraction, and a multiplicative preconditioner based on tridiagonal solves. The tridiagonal library, which supports (scaled) partial pivoting, outperforms cuSPARSE's tridiagonal solver by factor five while completely utilizing the available GPU memory bandwidth. For the performance optimized solving of multiple right-hand sides, the explicit factorization of the tridiagonal matrix can be computed. The extraction of a weighted linear forest (union of disjoint paths) from a general graph is used to build algebraic (block) tridiagonal preconditioners and deploys the generalized sparse-matrix vector implementation of this thesis for preconditioner construction. During linear forest extraction, a new parallel bidirectional scan pattern, which can operate on double-linked list structures, identifies the path ID and the position of a vertex. The algebraic preconditioner construction is also used to build more advanced preconditioners, which contain multiple tridiagonal factors, based on generalized ILU factorizations. Additionally, other preconditioners based on tridiagonal factors are presented and evaluated in comparison to ILU and ILU incomplete sparse approximate inverse preconditioners (ILU-ISAI) for the solution of large sparse linear equation systems from the Sparse Matrix Collection. For all presented problems of this thesis, an efficient parallel algorithm and its CUDA implementation for single GPU systems is provided

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Parallel prefix operations on heterogeneous platforms

Programa Oficial de Doutoramento en Investigación en Tecnoloxías da Información. 524V01[Resumo] As tarxetas gráficas, coñecidas como GPUs, aportan grandes vantaxes no rendemento computacional e na eficiencia enerxética, sendo un piar clave para a computación de altas prestacións (HPC). Sen embargo, esta tecnoloxía tamén é custosa de programar, e ten certos problemas asociados á portabilidade entre as diferentes tarxetas. Por autra banda, os algoritmos de prefixo paralelo son un conxunto de algoritmos paralelos regulares e moi empregados nas ciencias compuacionais, cuxa eficiencia é esencial en moita."3 aplicacións. Neste eiclo, aínda que as GPUs poden acelerar a computación destes algoritmos, tamén poden ser unha limitación cando non explotan axeitadamente o paralelismo da arquitectura CPU. Esta Tese presenta dúas perspectivas. Dunha parte, deséñanse novos algoritmos de prefixo paralelo para calquera paradigma de programación paralela. Pola outra banda, tamén se propón unha metodoloxÍa xeral que implementa eficientemente algoritmos de prefixo paralelos, de xeito doado e portable, sobre arquitecturas GPU CUDA, mais que se centrar nun algoritmo particular ou nun modelo concreto de tarxeta. Para isto, a metodoloxía identifica os paramétros da GPU que inflúen no rendemento e, despois, seguindo unha serie de premisas teóricas, obtéñense os valores óptimos destes parámetros dependendo do algoritmo, do tamaño do problema e da arquitectura GPU empregada. Ademais, esta Tese tamén prové unha serie de fUllciólls GPU compostas de bloques de código CUDA modulares e reutilizables, o que permite a implementación de calquera algoritmo de xeito sinxelo. Segundo o tamaño do problema, propóñense tres aproximacións. As dúas primeiras resolven problemas pequenos, medios e grandes nunha única GPU) mentras que a terceira trata con tamaños extremad8.1nente grandes, usando varias GPUs. As nosas propostas proporcionan uns resultados moi competitivos a nivel de rendemento, mellorando as propostas existentes na bibliografía para as operacións probadas: a primitiva sean, ordenación e a resolución de sistemas tridiagonais.[Resumen] Las tarjetas gráficas (GPUs) han demostrado gmndes ventajas en el rendimiento computacional y en la eficiencia energética, siendo una tecnología clave para la computación de altas prestaciones (HPC). Sin embargo, esta tecnología también es costosa de progTamar, y tiene ciertos problemas asociados a la portabilidad de sus códigos entre diferentes generaciones de tarjetas. Por otra parte, los algoritmos de prefijo paralelo son un conjunto de algoritmos regulares y muy utilizados en las ciencias computacionales, cuya eficiencia es crucial en muchas aplicaciones. Aunque las GPUs puedan acelerar la computación de estos algoritmos, también pueden ser una limitación si no explotan correctamente el paralelismo de la arquitectura CPU. Esta Tesis presenta dos perspectivas. De un lado, se han diseñado nuevos algoritmos de prefijo paralelo que pueden ser implementados en cualquier paradigma de programación paralela. Por otra parte, se propone una metodología general que implementa eficientemente algoritmos de prefijo paralelo, de forma sencilla y portable, sobre cualquier arquitectura GPU CUDA, sin centrarse en un algoritmo particular o en un modelo de tarjeta. Para ello, la metodología identifica los parámetros GPU que influyen en el rendimiento y, siguiendo un conjunto de premisas teóricas, obtiene los valores óptimos para cada algoritmo, tamaño de problema y arquitectura. Además, las funciones GPU proporcionadas están compuestas de bloques de código CUDA reutilizable y modular, lo que permite la implementación de cualquier algoritmo de prefijo paralelo sencillamente. Dependiendo del tamaño del problema, se proponen tres aproximaciones. Las dos primeras resuelven tamaños pequeños, medios y grandes, utilizando para ello una única GPU i mientras que la tercera aproximación trata con tamaños extremadamente grandes, usando varias GPUs. Nuestras propuestas proporcionan resultados muy competitivos, mejorando el rendimiento de las propuestas existentes en la bibliografía para las operaciones probadas: la primitiva sean, ordenación y la resolución de sistemas tridiagonales.[Abstract] Craphics Processing Units (CPUs) have shown remarkable advantages in computing performance and energy efficiency, representing oue of the most promising trends fúr the near-fnture of high perfonnance computing. However, these devices also bring sorne programming complexities, and many efforts are required tú provide portability between different generations. Additionally, parallel prefix algorithms are a 8et of regular and highly-used parallel algorithms, whose efficiency is crutial in roany computer sCience applications. Although GPUs can accelerate the computation of such algorithms, they can also be a limitation when they do not match correctly to the CPU architecture or do not exploit the CPU parallelism properly. This dissertation presents two different perspectives. Gn the Oile hand, new parallel prefix algorithms have been algorithmicany designed for any paranel progrannning paradigm. On the other hand, a general tuning CPU methodology is proposed to provide an easy and portable mechanism tú efficiently implement paranel prefix algorithms on any CUDA CPU architecture, rather than focusing on a particular algorithm or a CPU mode!. To accomplish this goal, the methodology identifies the GPU parameters which influence on the performance and, following a set oí performance premises, obtains the cOllvillient values oí these parameters depending on the algorithm, the problem size and the CPU architecture. Additionally, the provided CPU functions are composed of modular and reusable CUDA blocks of code, which allow the easy implementation of any paranel prefix algorithm. Depending on the size of the dataset, three different approaches are proposed. The first two approaches solve small and medium-large datasets on a single GPU; whereas the third approach deals with extremely large datasets on a Multiple-CPU environment. OUT proposals provide very competitive performance, outperforming the stateof- the-art for many parallel prefix operatiOllS, such as the sean primitive, sorting and solving tridiagonal systems

USRA/RIACS

The Research Institute for Advanced Computer Science (RIACS) was established by the Universities Space Research Association (USRA) at the NASA Ames Research Center (ARC) on 6 June 1983. RIACS is privately operated by USRA, a consortium of universities with research programs in the aerospace sciences, under a cooperative agreement with NASA. The primary mission of RIACS is to provide research and expertise in computer science and scientific computing to support the scientific missions of NASA ARC. The research carried out at RIACS must change its emphasis from year to year in response to NASA ARC's changing needs and technological opportunities. A flexible scientific staff is provided through a university faculty visitor program, a post doctoral program, and a student visitor program. Not only does this provide appropriate expertise but it also introduces scientists outside of NASA to NASA problems. A small group of core RIACS staff provides continuity and interacts with an ARC technical monitor and scientific advisory group to determine the RIACS mission. RIACS activities are reviewed and monitored by a USRA advisory council and ARC technical monitor. Research at RIACS is currently being done in the following areas: Parallel Computing; Advanced Methods for Scientific Computing; Learning Systems; High Performance Networks and Technology; Graphics, Visualization, and Virtual Environments

Optimization Techniques for Mapping Algorithms and Applications onto CUDA GPU Platforms and CPU-GPU Heterogeneous Platforms

An emerging trend in processor architecture seems to indicate the doubling of the number of cores per chip every two years with same or decreased clock speed. Of particular interest to this thesis is the class of many-core processors, which are becoming more attractive due to their high performance, low cost, and low power consumption. The main goal of this dissertation is to develop optimization techniques for mapping algorithms and applications onto CUDA GPUs and CPU-GPU heterogeneous platforms. The Fast Fourier transform (FFT) constitutes a fundamental tool in computational science and engineering, and hence a GPU-optimized implementation is of paramount importance. We first study the mapping of the 3D FFT onto the recent, CUDA GPUs and develop a new approach that minimizes the number of global memory accesses and overlaps the computations along the different dimensions. We obtain some of the fastest known implementations for the computation of multi-dimensional FFT. We then present a highly multithreaded FFT-based direct Poisson solver that is optimized for the recent NVIDIA GPUs. In addition to the massive multithreading, our algorithm carefully manages the multiple layers of the memory hierarchy so that all global memory accesses are coalesced into 128-bytes device memory transactions. As a result, we have achieved up to 375GFLOPS with a bandwidth of 120GB/s on the GTX 480. We further extend our methodology to deal with CPU-GPU based heterogeneous platforms for the case when the input is too large to fit on the GPU global memory. We develop optimization techniques for memory-bound, and computation-bound application. The main challenge here is to minimize data transfer between the CPU memory and the device memory and to overlap as much as possible these transfers with kernel execution. For memory-bounded applications, we achieve a near-peak effective PCIe bus bandwidth, 9-10GB/s and performance as high as 145 GFLOPS for multi-dimensional FFT computations and for solving the Poisson equation. We extend our CPU-GPU based software pipeline to a computation-bound application-DGEMM, and achieve the illusion of a memory of the CPU memory size and a computation throughput similar to a pure GPU

Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units

The split-step Fourier method is a powerful technique for solving partial differential equations and simulating ultracold atomic systems of various forms. In this body of work, we focus on several variations of this method to allow for simulations of one, two, and three-dimensional quantum systems, along with several notable methods for controlling these systems. In particular, we use quantum optimal control and shortcuts to adiabaticity to study the non-adiabatic generation of superposition states in strongly correlated one-dimensional systems, analyze chaotic vortex trajectories in two dimensions by using rotation and phase imprinting methods, and create stable, threedimensional vortex structures in Bose–Einstein condensates through artificial magnetic fields generated by the evanescent field of an optical nanofiber. We also discuss algorithmic optimizations for implementing the split-step Fourier method on graphics processing units. All computational methods present in this work are demonstrated on physical systems and have been incorporated into a state-of-the-art and open-source software suite known as GPUE, which is currently the fastest quantum simulator of its kind.Okinawa Institute of Science and Technology Graduate Universit

Adaptive heterogeneous parallelism for semi-empirical lattice dynamics in computational materials science.

With the variability in performance of the multitude of parallel environments available today, the conceptual overhead created by the need to anticipate runtime information to make design-time decisions has become overwhelming. Performance-critical applications and libraries carry implicit assumptions based on incidental metrics that are not portable to emerging computational platforms or even alternative contemporary architectures. Furthermore, the significance of runtime concerns such as makespan, energy efficiency and fault tolerance depends on the situational context. This thesis presents a case study in the application of both Mattsons prescriptive pattern-oriented approach and the more principled structured parallelism formalism to the computational simulation of inelastic neutron scattering spectra on hybrid CPU/GPU platforms. The original ad hoc implementation as well as new patternbased and structured implementations are evaluated for relative performance and scalability. Two new structural abstractions are introduced to facilitate adaptation by lazy optimisation and runtime feedback. A deferred-choice abstraction represents a unified space of alternative structural program variants, allowing static adaptation through model-specific exhaustive calibration with regards to the extrafunctional concerns of runtime, average instantaneous power and total energy usage. Instrumented queues serve as mechanism for structural composition and provide a representation of extrafunctional state that allows realisation of a market-based decentralised coordination heuristic for competitive resource allocation and the Lyapunov drift algorithm for cooperative scheduling

Energy-Aware High Performance Computing

High performance computing centres consume substantial amounts of energy to power large-scale supercomputers and the necessary building and cooling infrastructure. Recently, considerable performance gains resulted predominantly from developments in multi-core, many-core and accelerator technology. Computing centres rapidly adopted this hardware to serve the increasing demand for computational power. However, further performance increases in large-scale computing systems are limited by the aggregate energy budget required to operate them. Power consumption has become a major cost factor for computing centres. Furthermore, energy consumption results in carbon dioxide emissions, a hazard for the environment and public health; and heat, which reduces the reliability and lifetime of hardware components. Energy efficiency is therefore crucial in high performance computing