Asynchronous and Multiprecision Linear Solvers - Scalable and Fault-Tolerant Numerics for Energy Efficient High Performance Computing

Asynchronous methods minimize idle times by removing synchronization barriers, and therefore allow the efficient usage of computer systems. The implied high tolerance with respect to communication latencies improves the fault tolerance. As asynchronous methods also enable the usage of the power and energy saving mechanisms provided by the hardware, they are suitable candidates for the highly parallel and heterogeneous hardware platforms that are expected for the near future

High performance computing of explicit schemes for electrofusion jointing process based on message-passing paradigm

The research focused on heterogeneous cluster workstations comprising of a number of CPUs in single and shared architecture platform. The problem statements under consideration involved one dimensional parabolic equations. The thermal process of electrofusion jointing was also discussed. Numerical schemes of explicit type such as AGE, Brian, and Charlies Methods were employed. The parallelization of these methods were based on the domain decomposition technique. Some parallel performance measurement for these methods were also addressed. Temperature profile of the one dimensional radial model of the electrofusion process were also given

A survey of some aspects of parallel and distributed iterative algorithms

Cover title.Includes bibliographical references (p. 29-33).Research supported by the NSF. ECS-8519058 ECS-8552419 Research supported by the ARO. DAAL03-86-K-0171 Research supported by Bellcore, Du Pont and IBM.Dimitri P. Bertsekas, John N. Tsitsiklis

Implementing Asynchronous Linear Solvers Using Non-Uniform Distributions

Asynchronous iterative methods present a mechanism to improve the performance of algorithms for highly parallel computational platforms by removing the overhead associated with synchronization among computing elements. This paper considers a class of asynchronous iterative linear system solvers that employ randomization to determine the component update orders, specifically focusing on the effects of drawing the order from non-uniform distributions. Results from shared-memory experiments with a two-dimensional finite-difference discrete Laplacian problem show that using distributions favoring the selection of components with a larger contribution to the residual may lead to faster convergence than selecting uniformly. Multiple implementations of the randomized asynchronous linear system solvers are considered and tested with various distributions and parameters. In the best case of parameter choices, average times for the normal and exponential distributions were, respectively, 13.3% and 17.3% faster than the performance with a uniform distribution, and were able to converge in approximately 10% fewer iterations than traditional stationary solvers

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.