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Enchancing HSL for HPC architectures

增强 HPC 架构的 HSL

基本信息

批准号：
EP/F006535/1
负责人：
Jennifer Scott
金额：
$ 16.15万
依托单位：
Science and Technology Facilities Council
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF006535%2F1
关键词：
Enchancing HSL HPC architectures

项目摘要

This project is focused on the development of robust, efficient and portable mathematical software for solving large-scale linear systems as may occur in engineering and science. Real-life applications that can benefit from this software abound. Engineers need to beable to accurately predict the vibration frequencies of bridges for theirsafe construction. Vehicle manufacturers use computer simulations of carcrashes to correctly build the component parts. Manufacturers seek maximumefficiency in the design of their production processes. Investors aim atcreating portofolios that avoid high risk while yielding a good return.Traffic planners need to decide on the level and ways of routing trafficto minimize congestion. Governments and organizations seek to formcoalitions that best represent their interests and that would besuccessful in the bargaining that characterizes a conflict resolutionprocess. Finding the 'best' solution for such processes commonly involvesconstructing a mathematical model to describe the problem. The resultingmodels are usually complex and large scale, depending on a large number ofparameters. Models with millions and billions of variables andrestrictions are not uncommon. It is therefore imperative to implement themodel on a computer and to use computer algorithms for solving it. Nearly all such large-scale problems exhibit an underlying mathematicalstructure or sparsity. That is to say, the interactions between theparameters of a large system are often localized and seldom involve anydirect interaction between all the components. For example, an electricalnetwork can be represented by a graph where nodes are equivalent tobranches in the network and components are on the edges. This graph willbe sparse inasmuch as most nodes are only connected to very few othernodes. Engineering structures, and many other problems, can be representedby a similar graph. As ever more detailed mathematical models are used, there is a need to solveever larger systems of equations. To do this, algorithms and softwareneed to be developed that fully exploit the capabilities of modern computerarchitectures. This project builds on the existing expertise of the Numerical AnalysisGroup at the Rutherford Appleton Laboratory in the design and developmentof numerical algorithms and their implementation as high quality mathematical software.The aim is to enhance the performance of the sparse solvers in the mathematical software library HSL for use on modern high performance computers. HSL has an international reputation as a source of robust and efficient numerical software and is freely available for UKacademics for their research and teaching.The proposed project for the enhancement of HSL can be summarised as follows:(i) To investigate the feasibility of mixed precision sparse solvers(ii) To design and develop mixed precision implementations of key HSL sparse solversand to include them within HSL.(iii) To incorporate into HSL sparse solvers specially tuned dense linear algebra kernelsto enhance performance on multicore processors.

该项目的重点是开发强大，高效和便携式的数学软件，用于解决工程和科学中可能出现的大规模线性系统。可以从这个软件中受益的现实应用程序比比皆是。工程师们需要能够准确地预测桥梁的振动频率，以保证桥梁的安全施工。汽车制造商使用计算机模拟车祸来正确制造零部件。制造商在其生产过程的设计中寻求最大的效率。投资者的目标是建立港口，避免高风险，同时产生良好的回报。交通规划者需要决定的水平和方式的路线交通，以尽量减少拥堵。政府和组织寻求形成最能代表他们利益的联盟，这在冲突解决过程中的讨价还价中是有利的。为这类过程寻找“最佳”解决方案通常涉及构建一个数学模型来描述问题。由此产生的模型通常是复杂的和大规模的，取决于大量的参数。具有数百万和数十亿个变量和约束的模型并不罕见。因此，在计算机上实现该模型并使用计算机算法来解决它是势在必行的。几乎所有这样的大规模问题都表现出潜在的几何结构或稀疏性。也就是说，一个大系统的参数之间的相互作用往往是局部的，很少涉及所有组件之间的任何直接的相互作用。例如，一个电网络可以用一个图来表示，图中的节点相当于网络中的分支，而组件位于网络的边缘。这个图将是稀疏的，因为大多数节点只连接到很少的其他节点。工程结构和许多其他问题都可以用类似的图来表示。随着越来越详细的数学模型的使用，需要求解越来越大的方程组。要做到这一点，算法和软件需要开发，充分利用现代计算机架构的能力。该项目建立在卢瑟福阿普尔顿实验室数值分析小组在数值算法设计和开发及其作为高质量数学软件实施方面的现有专业知识的基础上。目的是增强数学软件库HSL中稀疏求解器的性能，以供现代高性能计算机使用。HSL作为一个强大而高效的数值软件源在国际上享有盛誉，并免费提供给英国学者用于他们的研究和教学。建议的HSL增强项目可以概括如下：（i）调查混合精度稀疏求解器的可行性（ii）设计和开发关键HSL稀疏求解器的混合精度实现，并将其纳入HSL。(iii)为了融入HSL稀疏求解器，专门调整了密集线性代数内核，以增强多核处理器上的性能。