Performance Improvements of Common Sparse Numerical Linear Algebra Computations

Manufacturers of computer hardware are able to continuously sustain an unprecedented pace of progress in computing speed of their products, partially due to increased clock rates but also because of ever more complicated chip designs. With new processor families appearing every few years, it is increasingly harder to achieve high performance rates in sparse matrix computations. This research proposes new methods for sparse matrix factorizations and applies in an iterative code generalizations of known concepts from related disciplines. The proposed solutions and extensions are implemented in ways that tend to deliver efficiency while retaining ease of use of existing solutions. The implementations are thoroughly timed and analyzed using a commonly accepted set of test matrices. The tests were conducted on modern processors that seem to have gained an appreciable level of popularity and are fairly representative for a wider range of processor types that are available on the market now or in the near future. The new factorization technique formally introduced in the early chapters is later on proven to be quite competitive with state of the art software currently available. Although not totally superior in all cases (as probably no single approach could possibly be), the new factorization algorithm exhibits a few promising features. In addition, an all-embracing optimization effort is applied to an iterative algorithm that stands out for its robustness. This also gives satisfactory results on the tested computing platforms in terms of performance improvement. The same set of test matrices is used to enable an easy comparison between both investigated techniques, even though they are customarily treated separately in the literature. Possible extensions of the presented work are discussed. They range from easily conceivable merging with existing solutions to rather more evolved schemes dependent on hard to predict progress in theoretical and algorithmic research

Parallel Computing in Water Network Analysis and Leakage Minimization

[EN] In this paper a parallel computing based software demonstrator for the simulation and leakage minimization of water networks is presented. This demonstrator, based on the EPANET package, tackles three different types of problems making use of parallel computing. First, the solution of the hydraulic problem is treated by means of the gradient method. The key point in the parallelization of the method is the solution of the underlying linear systems, which is carried out by means of a multifrontal Choleski method. Second, the water quality simulation problem is approached by using the discrete volume element method. The application of parallel computing is based on dividing the water network in several parts using the multilevel recursive bisection graph partitioning algorithm. Finally, the problem of leakage minimization using pressure reducing valves is approached. This results in the formulation of an optimization problem for each time step, which is solved by means of sequential quadratic programming. Because these subproblems are independent of each other, they can be solved in parallel.The writers wish to acknowledge the financial support provided by the ESPRIT program of the European Commission (HIPERWATER, ESPRIT project 24003), by the CICYT TIC96-1062-C03-01 project, and also by research staff training grants from the Spanish government and the autonomous government of the Comunidad Valenciana in Spain.Alonso Ábalos, JM.; Alvarruiz Bermejo, F.; Guerrero López, D.; Hernández García, V.; Ruiz Martínez, PA.; Vidal Maciá, AM.; Martínez Alzamora, F.... (2000). Parallel Computing in Water Network Analysis and Leakage Minimization. Journal of Water Resources Planning and Management. 126(4):251-260. https://doi.org/10.1061/(ASCE)0733-9496(2000)126:4(251)S251260126

Task scheduling for parallel multifrontal methods

Abstract. We present a new scheduling algorithm for task graphs arising from parallel multifrontal methods for sparse linear systems. This algorithm is based on the theorem proved by Prasanna and Musicus [1] for tree-shaped task graphs, when all tasks exhibit the same degree of parallelism. We propose extended versions of this algorithm to take communication between tasks and memory balancing into account. The efficiency of proposed approach is assessed by a set of experiments on a set of large sparse matrices from several libraries

Fine-Grained Multithreading for the Multifrontal QR Factorization of Sparse Matrices

International audienceThe advent of multicore processors represents a disruptive event in the history of computer science as conventional parallel programming paradigms are proving incapable of fully exploiting their potential for concurrent computations. The need for different or new programming models clearly arises from recent studies which identify fine-granularity and dynamic execution as the keys to achieving high efficiency on multicore systems. This work presents an approach to the parallelization of the multifrontal method for the $QR$ factorization of sparse matrices specifically designed for multicore based systems. High efficiency is achieved through a fine-grained partitioning of data and a dynamic scheduling of computational tasks relying on a dataflow parallel programming model. Experimental results show that an implementation of the proposed approach achieves higher performance and better scalability than existing equivalent software