A Critical Analysis Of Multigrid Methods On Massively Parallel Computers
Download A Critical Analysis Of Multigrid Methods On Massively Parallel Computers PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Critical Analysis Of Multigrid Methods On Massively Parallel Computers book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
A Critical Analysis of Multigrid Methods on Massively Parallel Computers
Author: Princeton University. Dept. of Computer Science
language: en
Publisher:
Release Date: 1993
Abstract: "The hierarchical nature of multigrid algorithms leaves domain parallel strategies with a deficiency of parallelism as the computation moves to coarser and coarser grids. To introduce more parallelism several strategies have been designed to project the original problem space into non-interfering subspaces, allowing all grids to relax concurrently. Our objective is to understand the potential efficiency of standard and concurrent multigrid algorithms on existing and proposed massively parallel machines. We study model problems on simple domains discretized with finite difference techniques on block structured meshes in two and three dimensions with up to 106 and 109 points, respectively. Performance of the standard domain parallel V and F cycle schemes is compared to several proposed concurrent algorithms. The multigrid strategies are studied in several models of parallel computation, designed to reflect both the characteristics of existing machines and those of the proposed next generation of multicomputers. These models include a SIMD fine-grain model which contains a large number (104-106) of small (bit- serial) processors as well as a SPMD medium-grain model with a more modest number (256-16,384) of powerful (single chip) processors interconnected through a single stage or multistage communication network. Our analysis suggests that obtaining acceptable levels of performance requires optimization techniques which address the salient characteristics of each architectural class of massively parallel computers. With the appropriate optimization techniques, a comparison indicates that the F-cycle is potentially more efficient than the V-cycle despite the relative increase in coarse grid activity. In addition, the analysis suggests that subspace parallelism is too expensive to be practical, except under a very limited set of conditions, on either class of massively parallel computers."
Parallel Numerical Algorithms
Author: David E. Keyes
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
Progress in Computational Physics of Matter
The aim of the book is to describe some of the recent advances, through computer simulation in a broad sense, in the understanding of the complex processes occurring in solids and liquids.The rapid growth of computer power, including the new parallel processors, has stimulated a ferment of new theoretical and computational ideas, which have been developed in particular by the authors in a pluriennal research project supported by Consiglio Nazionale delle Ricerche (CNR) for the development of novel software for large scale computations.The book will cover advances in ab initio (Car-Parrinello) molecular dynamics, quantum monte carlo simulations, self-consistent density functional computation of electronic states, classical molecular dynamics simulation of thermodynamic processes, chemical reactions and transport properties.Besides the description of the results of these techniques in leading edge applications, the book will address specific aspects of the algorithms and software which have been developed by the authors in order to implement in an efficient way the new theoretical advances in these computationally intensive problems.These aspects which are generally not discussed in any detail in the literature, can be of great help for newcomers in the field.