An Aggregation-Based Algebraic Multigrid Method with Deflation Techniques and Modified Generic Factored Approximate Sparse Inverses

In this paper, we examine deflation-based algebraic multigrid methods for solving large systems of linear equations. Aggregation of the unknown terms is applied for coarsening, while deflation techniques are proposed for improving the rate of convergence. More specifically, the V-cycle strategy is adopted, in which, at each iteration, the solution is computed by initially decomposing it utilizing two complementary subspaces. The approximate solution is formed by combining the solution obtained using multigrids and deflation. In order to improve performance and convergence behavior, the proposed scheme was coupled with the Modified Generic Factored Approximate Sparse Inverse preconditioner. Furthermore, a parallel version of the multigrid scheme is proposed for multicore parallel systems, improving the performance of the techniques. Finally, characteristic model problems are solved to demonstrate the applicability of the proposed schemes, while numerical results are given

Simulating fog and edge computing scenarios: an overview and research challenges

The fourth industrial revolution heralds a paradigm shift in how people, processes, things, data and networks communicate and connect with each other. Conventional computing infrastructures are struggling to satisfy dramatic growth in demand from a deluge of connected heterogeneous endpoints located at the edge of networks while, at the same time, meeting quality of service levels. The complexity of computing at the edge makes it increasingly difficult for infrastructure providers to plan for and provision resources to meet this demand. While simulation frameworks are used extensively in the modelling of cloud computing environments in order to test and validate technical solutions, they are at a nascent stage of development and adoption for fog and edge computing. This paper provides an overview of challenges posed by fog and edge computing in relation to simulation

On issues concerning Cloud environments in scope of scalable multi-projection methods

Over the last decade, Cloud environments have gained significant attention by the scientific community, due to their flexibility in the allocation of resources and the various applications hosted in such environments. Recently, high performance computing applications are migrating to Cloud environments. Efficient methods are sought for solving very large sparse linear systems occurring in various scientific fields such as Computational Fluid Dynamics, N-Body simulations and Computational Finance. Herewith, the parallel multi-projection type methods are reviewed and discussions concerning the implementation issues for IaaS-type Cloud environments are given. Moreover, phenomena occurring due to the "noisy neighbor" problem, varying interconnection speeds as well as load imbalance are studied. Furthermore, the level of exposure of specialized hardware residing in modern CPUs through the different layers of software is also examined. Finally, numerical results concerning the applicability and effectiveness of multi-projection type methods in Cloud environments based on OpenStack are presented

Towards simulation and optimization of cache placement on large virtual Content Distribution Networks

IP video traffic is forecast to be 82% of all IP traffic by 2022. Traditionally, Content Distribution Networks (CDN) were used extensively to meet the quality of service levels for IP video services. To handle the dramatic growth in video traffic, CDN operators are migrating their infrastructure to the cloud and fog in order to leverage its greater availability and flexibility. For hyper-scale deployments, energy consumption, cache placement, and resource availability can be analyzed using simulation in order to improve resource utilization and performance. Recently, a discrete-time simulator for modelling hierarchical virtual CDNs (vCDNs) was proposed with reduced memory requirements and increased performance using multi-core systems to cater to the scale and complexity of these networks. The first iteration of this discrete-time simulator featured a number of limitations impacting accuracy and applicability: it supports only tree-based topology structures, the results are computed per level, and requests of the same content differ only in time duration. In this paper, we present an improved simulation framework that (a) supports graph-based network topologies, (b) requests have been reconstituted for differentiation of requirements, and (c) statistics are now computed per site and network metrics per link, improving the granularity and parallel performance. Moreover, we also propose a two-phase optimization scheme that makes use of simulation outputs to guide the search for optimal cache placements. In order to evaluate our proposal, we simulate a vCDN network based on real traces obtained from the BT vCDN infrastructure and analyze performance and scalability aspects

Heterogeneity, high performance computing, self-organization and the Cloud

This open access book addresses the most recent developments in cloud computing such as HPC in the Cloud, heterogeneous cloud, self-organising and self-management, and discusses the business implications of cloud computing adoption. Establishing the need for a new architecture for cloud computing, it discusses a novel cloud management and delivery architecture based on the principles of self-organisation and self-management. This focus shifts the deployment and optimisation effort from the consumer to the software stack running on the cloud infrastructure. It also outlines validation challenges and introduces a novel generalised extensible simulation framework to illustrate the effectiveness, performance and scalability of self-organising and self-managing delivery models on hyperscale cloud infrastructures. It concludes with a number of potential use cases for self-organising, self-managing clouds and the impact on those businesses

Parallel Preconditioned Conjugate Gradient Square Method Based on Normalized Approximate Inverses

A new class of normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse matrix techniques for solving efficiently sparse linear systems on distributed memory systems, using Message Passing Interface (MPI) communication library, is also presented along with theoretical estimates on speedups and efficiency. The implementation and performance on a distributed memory MIMD machine, using Message Passing Interface (MPI) is also investigated. Applications on characteristic initial/boundary value problems in three dimensions are discussed and numerical results are given

ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES

Normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. Normalized implicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate factorization procedures are presented for the efficient solution of sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. Application of the proposed method on characteristic three dimensional boundary value problems is discussed and numerical results are given

On the performance of parallel normalized explicit preconditioned conjugate gradient - type methods

A new class of parallel normalized preconditioned conjugate gradient type methods in conjunction with normalized approximate inverses algorithms, based on normalized approximate factorization procedures, for solving sparse linear systems of irregular structure, which are derived from the finite element method of a two dimensional boundary value problem, is introduced. Parallel normalized explicit preconditioned conjugate gradient- type methods for distributed memory systems based on the block – row distribution (for the vectors and the explicit approximate inverse), using Message Passing Interface (MPI) communication library, is also presented with theoretical estimates on speedups and efficiency, in order to examine the parallel behavior of these methods using normalized explicit approximate inverses as the suitable preconditioner. Collective communications have been utilized at the synchronization points and non – blocking communications have been used, where the exchanging of messages can be overlapped with computations, where applicable. Application of the methods on a two dimensional boundary value problem is discussed and numerical results are given, concerning the parallel performance in terms of speedups and efficiency. 1