Enchancing HSL for HPC architectures

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.