| Title: |
Separable projection integrals for higher-order correlators of the cosmic microwave sky: Acceleration by factors exceeding 100 |
| Authors: |
Briggs, JP; Pennycook, SJ; Fergusson, JR; Jäykkä, J; Shellard, EPS |
| Publisher Information: |
Elsevier; //doi.org/10.1016/j.jcp.2016.01.019 |
| Publication Year: |
2016 |
| Collection: |
Apollo - University of Cambridge Repository |
| Subject Terms: |
4006 Communications Engineering; 40 Engineering |
| Description: |
© 2016. We present a case study describing efforts to optimise and modernise "Modal", the simulation and analysis pipeline used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum (or three-point correlator) of the cosmic microwave background radiation. We focus on one particular element of the code: the projection of bispectra from the end of inflation to the spherical shell at decoupling, which defines the CMB we observe today. This code involves a three-dimensional inner product between two functions, one of which requires an integral, on a non-rectangular domain containing a sparse grid. We show that by employing separable methods this calculation can be reduced to a one-dimensional summation plus two integrations, reducing the overall dimensionality from four to three. The introduction of separable functions also solves the issue of the non-rectangular sparse grid. This separable method can become unstable in certain scenarios and so the slower non-separable integral must be calculated instead. We present a discussion of the optimisation of both approaches.We demonstrate significant speed-ups of ≈100×, arising from a combination of algorithmic improvements and architecture-aware optimisations targeted at improving thread and vectorisation behaviour. The resulting MPI/OpenMP hybrid code is capable of executing on clusters containing processors and/or coprocessors, with strong-scaling efficiency of 98.6% on up to 16 nodes. We find that a single coprocessor outperforms two processor sockets by a factor of 1.3× and that running the same code across a combination of both microarchitectures improves performance-per-node by a factor of 3.38×. By making bispectrum calculations competitive with those for the power spectrum (or two-point correlator) we are now able to consider joint analysis for cosmological science exploitation of new data. ; This research is supported by an STFC consolidated grant ST/L000636/1, and funded in part by the Intel R ... |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
J. Briggs et al. Journal of Computational Physics (2016). DOI:10.1016/j.jcp.2016.01.019; https://www.repository.cam.ac.uk/handle/1810/253535 |
| Availability: |
https://www.repository.cam.ac.uk/handle/1810/253535 |
| Rights: |
Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.97BC2FF5 |
| Database: |
BASE |