Network: Numerical Algorithms and High Performance Computing.

Lead Research Organisation: University of Manchester
Department Name: Mathematics


Two factors are creating major new challenges at the interface between numerical analysis and high performance computing (HPC). The use of more realistic but complicated mathematical models is leading to problems for which new algorithms need to be developed for efficient solution (or, in many cases, solution at all). Meanwhile, recent developments in computer architectures (the drive to multi-core chips and the increasing use of GPUs and FPGAs as accelerators) are affecting the ability of current algorithms and software to fully exploit the hardware. The long-standing lack of investment in the development of high quality mathematical software exacerbates these problems. The net effect is that scientists are unable to make the best use of computational resources and hence are unable to tackle problems of the size that the hardware potentially allows. For all these reasons, new algorithms need to be developed that employ novel mathematical, algorithmic and coding techniques.The purpose of this network is to provide a focus for a new collaboration between numerical analysts, computer scientists and developers and users of software and HPC within the nodes, supported by the necessary administrative organization. The network will build a new interdisciplinary community at the numerical algorithms/HPC interface and thereby provide added value to existing funded research at the nodes in numerical algorithms and in HPC and its applications.By partnering with NAIS (Centre for Numerical Algorithms and Intelligent Software, a joint project between Edinburgh, Heriot-Watt, and Strathclyde Universities) the network will build on EPSRC's recent investment in numerical algorithms for HPC.The activities of the network will be - seminars, - graduate courses, - short courses, - a workshop on the interface between NA and HPC, in which HPC users (including HECToR users) will be encouraged to describe the computational requirements of their applications and NA researchers will describe their latest algorithmic developments, - an international workshop, - an industrial workshop, - hosting of international visitors, and - movement of node members (and especially their PhD students and PDRAs) between nodes for visits of a day to a few weeks. These activities will raise awareness of the numerical aspects of HPC, including challenges, applications and their needs, and available software. It will also facilitate work on the underlying research at the nodes, which is funded through other means. A website will advertise the network activities and disseminate them to the wider community.Expansion of the network during its life is planned, and it is expected that upon completion of the project new ideas, connections and synergies developed within the network activities will have led to responsive mode applications to EPSRC and other bodies that sustain the collaborations.

Planned Impact

High performance computing (HPC) has growing areas of application not just within academia but also within government and industry. New areas of application include the study of climate change, the behaviour of human social interaction networks, financial markets, and personalized medicine, where the last of these aims to simulate complex physiological and pathological processes fast enough for the output to have a direct impact on clinical decision making. By targeting key scientific application problems by developing numerical algorithms and the necessary supporting theory, and translating them into software that runs efficiently on computers ranging from desktop to HPC systems with many thousands of CPUs, this network has the potential to impact all the above areas by enabling more accurate and faster prediction, simulation, or diagnosis. The short courses and workshops, and the researcher mobility programme, will help to train a new generation of research students and postdoctoral researchers in numerical algorithms and HPC. They will help build UK capacity at this important interface, providing highly qualified researchers not only for academia but also for other employment sectors including industry and government. One of our most important economic impacts will be technology transfer effected by the movement of trained personnel between academic and non-academic environments. An important output of the research facilitated by the network is software. Library products such as LAPACK, NAG and HSL/GALAHAD are widely used across industries and application areas, including in finance, pharmaceuticals, visualization, earth sciences, and engineering, and on a diverse range of machines. The software outputs of this project are therefore of great value to the knowledge economy. Through the inclusion in the network of NAG and STFC-RAL there is a direct path to market in terms of software library products to the benefit of UK plc. Open source software will also be produced, documented and made freely available to all. A particular target for the software is HECToR, for which improvements in performance of codes can create major savings in access costs or allow larger, and often more realistic, problems to be solved. Industrial involvement in the network activities provides a means for knowledge transfer from academia to industry, as well as a way to focus researchers' attention on (possibly new) problems of particular industrial relevance. The node members collectively have many links to software companies and technology companies in various sectors, while CSED at STFC, NAG, and NAIS (through the Edinburgh Parallel Computing Centre) have extensive links to HPC companies worldwide; all these links will be exploited. The universities' existing EPSRC KTA awards provide an additional source of funding that will enable technology transfer outside academia. The network website will be a key vehicle for advertising upcoming network activities and dissemination past activities, and it will provide links to other related activities (for example relevant international conferences). We will carefully design the website to combine ease of use and adherence to relevant W3 standards, ensuring accessibility and good search engine coverage and thereby widening its impact. The general public will benefit from increased understanding of the research carried out within the network, though dissemination activities such as media interviews and popular articles. In summary, our activities will benefit diverse people, organizations and institutions, ranging from academia, through industry and commerce, to individuals and the general public, within the UK and internationally. The timescales for the impact range from short to long. Rapid impact can be expected when, for example, algorithmic improvements can be quickly incorporated into new or improved library codes.


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Liao Q (2012) Robust stabilized Stokes approximation methods for highly stretched grids in IMA Journal of Numerical Analysis

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Liao Q (2012) Implicit solvers using stabilized mixed approximation in International Journal for Numerical Methods in Fluids

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Smethurst C (2013) Unstructured finite element method for the solution of the Boussinesq problem in three dimensions in International Journal for Numerical Methods in Fluids

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Higham N (2014) Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number in SIAM Journal on Matrix Analysis and Applications

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Higham N (2016) Bounds for the Distance to the Nearest Correlation Matrix in SIAM Journal on Matrix Analysis and Applications

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Higham N (2014) Estimating the Condition Number of the Fréchet Derivative of a Matrix Function in SIAM Journal on Scientific Computing

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G├╝ttel S (2015) Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver in SIAM Journal on Scientific Computing

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Al-Mohy A (2015) New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously in SIAM Journal on Scientific Computing

Description Formed a new interdisciplinary research community in numerical algorithms
and high performance computing (HPC) and stimulate UK research at an
internationally leading level. Organized short courses
and workshops in numerical algorithms and HPC in order to
facilitate the exchange of ideas from different fields and
disciplines. Promoted intensive interactions between research groups
across the UK, and expand the network over the
lifetime of the project. Raised the level of training and involvement of
research students and PDRAs in multi-disciplinary NA/HPC research and
thereby build capacity. Produced software that addresses application
Exploitation Route Further grant applications, software widely used.
Sectors Aerospace, Defence and Marine,Construction,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Financial Services, and Management Consultancy,Healthcare,Pharmaceuticals and Medical Biotechnology

Description Diverse applications though algorithms and software (open sourc and commerical) prouced .
First Year Of Impact 2014
Sector Aerospace, Defence and Marine,Creative Economy,Financial Services, and Management Consultancy,Healthcare,Manufacturing, including Industrial Biotechology
Impact Types Economic