Enchancing HSL for HPC architectures

这个项目的重点是开发健壮、高效和可移植的数学软件，用于解决工程和科学中可能出现的大规模线性系统。可以从该软件中受益的实际应用程序比比皆是。工程师需要能够准确地预测桥梁的振动频率，以确保其安全施工。汽车制造商使用计算机模拟车祸来正确制造零部件。制造商在其生产流程的设计中寻求最大的效率。投资者的目标是在避免高风险的同时获得良好的回报。交通规划者需要决定交通路线的水平和方式，以将拥堵降至最低。各国政府和各组织寻求结成最能代表其利益的联盟，并在以解决冲突为特征的谈判中取得成功。为这类过程找到“最佳”解决方案通常涉及构建一个描述问题的数学模型。所得到的模型通常是复杂和大规模的，取决于大量的参数。具有数百万和数十亿变量和限制的模型并不少见。因此，在计算机上实现模型并使用计算机算法来求解该模型是势在必行的。几乎所有这样的大规模问题都表现出潜在的数学结构或稀疏性。也就是说，大系统参数之间的相互作用往往是局部性的，很少涉及所有组件之间的任何直接相互作用。例如，一个电力网络可以用一个图来表示，其中节点相当于网络中的支路，元件在边上。该图将是稀疏的，因为大多数节点仅连接到极少数其他节点。工程结构和许多其他问题都可以用类似的图来表示。随着更详细的数学模型的使用，需要求解更大的方程组。要做到这一点，需要开发充分利用现代计算机体系结构能力的算法和软件。这个项目建立在卢瑟福·阿普尔顿实验室数值分析小组在设计和开发数值算法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。目的是提高数学软件库HSL中稀疏求解器的性能，以便在现代高性能计算机上使用。HSL作为健壮和高效的数值软件的来源在国际上享有盛誉，英国学者可以免费获得他们的研究和教学。建议的HSL增强项目可以总结如下：(I)研究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包含在HSL中。(Iii)在HSL稀疏求解器中加入专门调整的稠密线性代数内核，以增强多核处理器上的性能。

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.