Design and analysis of numerical algorithms for the solution of linear systems on parallel and distributed architectures

The increasing availability of parallel computers is having a very significant impact on all aspects of scientific computation, including algorithm research and software development in numerical linear algebra. In particular, the solution of linear systems, which lies at the heart of most calculations in scientific computing is an important computation found in many engineering and scientific applications. In this thesis, well-known parallel algorithms for the solution of linear systems are compared with implicit parallel algorithms or the Quadrant Interlocking (QI) class of algorithms to solve linear systems. These implicit algorithms are (2x2) block algorithms expressed in explicit point form notation. [Continues.

Parallel Two-Stage Least Squares algorithms for Simultaneous Equations Models on GPU

Today it is usual to have computational systems formed by a multicore together with one or more GPUs. These systems are heterogeneous, due to the di erent types of memory in the GPUs and to the di erent speeds of computation of the cores in the CPU and the GPU. To accelerate the solution of complex problems it is necessary to combine the two basic components (CPU and GPU) in the heterogeneous system. This paper analyzes the use of a multicore+multiGPU system for solving Simultaneous Equations Models by the Two-Stage Least Squares method with QR decomposition. The combination of CPU and GPU allows us to reduce the execution time in the solution of large SEM.Ramiro Sánchez, C.; López-Espín, JJ.; Giménez, D.; Vidal, AM. (2012). Parallel Two-Stage Least Squares algorithms for Simultaneous Equations Models on GPU. http://hdl.handle.net/10251/1496

Hybrid static/dynamic scheduling for already optimized dense matrix factorization

We present the use of a hybrid static/dynamic scheduling strategy of the task dependency graph for direct methods used in dense numerical linear algebra. This strategy provides a balance of data locality, load balance, and low dequeue overhead. We show that the usage of this scheduling in communication avoiding dense factorization leads to significant performance gains. On a 48 core AMD Opteron NUMA machine, our experiments show that we can achieve up to 64% improvement over a version of CALU that uses fully dynamic scheduling, and up to 30% improvement over the version of CALU that uses fully static scheduling. On a 16-core Intel Xeon machine, our hybrid static/dynamic scheduling approach is up to 8% faster than the version of CALU that uses a fully static scheduling or fully dynamic scheduling. Our algorithm leads to speedups over the corresponding routines for computing LU factorization in well known libraries. On the 48 core AMD NUMA machine, our best implementation is up to 110% faster than MKL, while on the 16 core Intel Xeon machine, it is up to 82% faster than MKL. Our approach also shows significant speedups compared with PLASMA on both of these systems

An assessment of the connection machine

The CM-2 is an example of a connection machine. The strengths and problems of this implementation are considered as well as important issues in the architecture and programming environment of connection machines in general. These are contrasted to the same issues in Multiple Instruction/Multiple Data (MIMD) microprocessors and multicomputers

Performance and Memory Space Optimizations for Embedded Systems

Embedded systems have three common principles: real-time performance, low power consumption, and low price (limited hardware). Embedded computers use chip multiprocessors (CMPs) to meet these expectations. However, one of the major problems is lack of efficient software support for CMPs; in particular, automated code parallelizers are needed. The aim of this study is to explore various ways to increase performance, as well as reducing resource usage and energy consumption for embedded systems. We use code restructuring, loop scheduling, data transformation, code and data placement, and scratch-pad memory (SPM) management as our tools in different embedded system scenarios. The majority of our work is focused on loop scheduling. Main contributions of our work are: We propose a memory saving strategy that exploits the value locality in array data by storing arrays in a compressed form. Based on the compressed forms of the input arrays, our approach automatically determines the compressed forms of the output arrays and also automatically restructures the code. We propose and evaluate a compiler-directed code scheduling scheme, which considers both parallelism and data locality. It analyzes the code using a locality parallelism graph representation, and assigns the nodes of this graph to processors.We also introduce an Integer Linear Programming based formulation of the scheduling problem. We propose a compiler-based SPM conscious loop scheduling strategy for array/loop based embedded applications. The method is to distribute loop iterations across parallel processors in an SPM-conscious manner. The compiler identifies potential SPM hits and misses, and distributes loop iterations such that the processors have close execution times. We present an SPM management technique using Markov chain based data access. We propose a compiler directed integrated code and data placement scheme for 2-D mesh based CMP architectures. Using a Code-Data Affinity Graph (CDAG) to represent the relationship between loop iterations and array data, it assigns the sets of loop iterations to processing cores and sets of data blocks to on-chip memories. We present a memory bank aware dynamic loop scheduling scheme for array intensive applications.The goal is to minimize the number of memory banks needed for executing the group of loop iterations

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

A distributed-memory package for dense Hierarchically Semi-Separable matrix computations using randomization

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable representations (HSS). Such matrices appear in many applications, e.g., finite element methods, boundary element methods, etc. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. This work is part of a more global effort, the STRUMPACK (STRUctured Matrices PACKage) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver

Computational methods and software systems for dynamics and control of large space structures

This final report on computational methods and software systems for dynamics and control of large space structures covers progress to date, projected developments in the final months of the grant, and conclusions. Pertinent reports and papers that have not appeared in scientific journals (or have not yet appeared in final form) are enclosed. The grant has supported research in two key areas of crucial importance to the computer-based simulation of large space structure. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area, as reported here, involves massively parallel computers

Parallel architectures and runtime systems co-design for task-based programming models

The increasing parallelism levels in modern computing systems has extolled the need for a holistic vision when designing multiprocessor architectures taking in account the needs of the programming models and applications. Nowadays, system design consists of several layers on top of each other from the architecture up to the application software. Although this design allows to do a separation of concerns where it is possible to independently change layers due to a well-known interface between them, it is hampering future systems design as the Law of Moore reaches to an end. Current performance improvements on computer architecture are driven by the shrinkage of the transistor channel width, allowing faster and more power efficient chips to be made. However, technology is reaching physical limitations were the transistor size will not be able to be reduced furthermore and requires a change of paradigm in systems design. This thesis proposes to break this layered design, and advocates for a system where the architecture and the programming model runtime system are able to exchange information towards a common goal, improve performance and reduce power consumption. By making the architecture aware of runtime information such as a Task Dependency Graph (TDG) in the case of dataflow task-based programming models, it is possible to improve power consumption by exploiting the critical path of the graph. Moreover, the architecture can provide hardware support to create such a graph in order to reduce the runtime overheads and making possible the execution of fine-grained tasks to increase the available parallelism. Finally, the current status of inter-node communication primitives can be exposed to the runtime system in order to perform a more efficient communication scheduling, and also creates new opportunities of computation and communication overlap that were not possible before. An evaluation of the proposals introduced in this thesis is provided and a methodology to simulate and characterize the application behavior is also presented.El aumento del paralelismo proporcionado por los sistemas de cómputo modernos ha provocado la necesidad de una visión holística en el diseño de arquitecturas multiprocesador que tome en cuenta las necesidades de los modelos de programación y las aplicaciones. Hoy en día el diseño de los computadores consiste en diferentes capas de abstracción con una interfaz bien definida entre ellas. Las limitaciones de esta aproximación junto con el fin de la ley de Moore limitan el potencial de los futuros computadores. La mayoría de las mejoras actuales en el diseño de los computadores provienen fundamentalmente de la reducción del tamaño del canal del transistor, lo cual permite chips más rápidos y con un consumo eficiente sin apenas cambios fundamentales en el diseño de la arquitectura. Sin embargo, la tecnología actual está alcanzando limitaciones físicas donde no será posible reducir el tamaño de los transistores motivando así un cambio de paradigma en la construcción de los computadores. Esta tesis propone romper este diseño en capas y abogar por un sistema donde la arquitectura y el sistema de tiempo de ejecución del modelo de programación sean capaces de intercambiar información para alcanzar una meta común: La mejora del rendimiento y la reducción del consumo energético. Haciendo que la arquitectura sea consciente de la información disponible en el modelo de programación, como puede ser el grafo de dependencias entre tareas en los modelos de programación dataflow, es posible reducir el consumo energético explotando el camino critico del grafo. Además, la arquitectura puede proveer de soporte hardware para crear este grafo con el objetivo de reducir el overhead de construir este grado cuando la granularidad de las tareas es demasiado fina. Finalmente, el estado de las comunicaciones entre nodos puede ser expuesto al sistema de tiempo de ejecución para realizar una mejor planificación de las comunicaciones y creando nuevas oportunidades de solapamiento entre cómputo y comunicación que no eran posibles anteriormente. Esta tesis aporta una evaluación de todas estas propuestas, así como una metodología para simular y caracterizar el comportamiento de las aplicacionesPostprint (published version