Abstract
A number of features of today's high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multiple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.
| Original language | English |
|---|---|
| Article number | 20190066 |
| Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 378 |
| Issue number | 2166 |
| DOIs | |
| State | Published - Mar 6 2020 |
Funding
Data accessibility. This article has no additional data. Authors’ contributions. All authors drafted and revised the manuscript. All authors read and approved the manuscript. Competing interests. We declare we have no competing interests. Funding. The work of J.D. was supported by the Exascale Computing Project (17-SC-20-SC), a joint project of the US Department of Energy’s Office of Science and National Nuclear Security Administration. The work of L.G. has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 810367). The work of N.J.H. was supported by the Royal Society. Acknowledgements. We thank Massimilano Fasi, Theo Mary, Mantas Mikaitis, Srikara Praensh and Mawussi Zounon for their comments on a draft manuscript. The work of J.D. was supported by the Exascale Computing Project (17-SC-20-SC), a joint project of the US Department of Energy's Office of Science and National Nuclear Security Administration. The work of L.G. has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 810367). The work of N.J.H. was supported by the Royal Society. We thank Massimilano Fasi, Theo Mary, Mantas Mikaitis, Srikara Praensh and Mawussi Zounon for their comments on a draft manuscript.
| Funders | Funder number |
|---|---|
| Office of Science and National Nuclear Security Administration | |
| US Department of Energy | |
| U.S. Department of Energy | |
| National Nuclear Security Administration | |
| Horizon 2020 Framework Programme | |
| Royal Society | |
| European Research Council | |
| Horizon 2020 | 810367 |
Keywords
- Exascale computer
- Floating-point arithmetic
- High-performance computing
- Numerical algorithms
- Numerical linear algebra
- Rounding errors