ARCHER2 Capability Days - a user report

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ARCHER2 Capability Days, which take place periodically (every few months or so), provide an excellent opportunity for testing and refining pre-existing codes, when used to carry out some large-scale calculations/simulations.

In my case, back in 2024 I was awarded an eCSE project to design and disseminate high performance algorithms for the computation of the Hardy function Z(t) – an important function in pure mathematics which can, for example, be used for the study of prime numbers. In the main the code was developed and tested using either 4 or 8 nodes, depending upon the user prescribed value/s of t for the calculation in question. However, during the Capability Days window, account holders can run large scale jobs (which are not charged) on as many as 512-4096 nodes for up to three hours, which obviously offers users the scope to carry out some ambitious calculations to obtain some potentially ground-breaking results.

Being able to take advantage of a number of recent capability sessions to submit jobs has allowed me to take advantage of the quite significant performance advances of my codes, to carry out some additional Z(t) calculations for t values beyond anything previously published in the literature and provide some inklings about the design of potentially even faster, more efficient, computational algorithms.

Insights obtained from calculating the distribution of zeros using the Riemann function can improve algorithms for prime testing and factoring, which have applications in cryptography.

Dr D. M. Lewis (University of Liverpool).

Link to example large-scale calculations successfully completed for very high values of t during the ARCHER2 Capability Days in March 2026, as well as details of the resources used

Link to David’s GitHub repository of Fortran / C codes for the rapid calculation of the Hardy function Z(t)