Array Access and Performance Regarding Numerical Algorithms

Authors

  • Arjen Markus Deltares Research Institute, The Netherlands
  • Lenore Mullin University at Albany, SUNY, USA

DOI:

https://doi.org/10.14738/tmlai.1402.20134

Keywords:

Programming, Array operations, Mathematics, Fortran

Abstract

Arrays are an important data structure in the solution of many numerical problems. In this study, the classical Poisson equation in two dimensions is used to gain insight in the consequences of the actual implementation and various possible compiler options for the performance: what is the optimal (fastest) solution? The equation is solved using a straightforward algorithm for a wide range of grid sizes to examine the effect of the memory management. The implementations include explicit loops and array operations, as well as parallellisation via OpenMP. Some general conclusions are drawn with respect to achieving good or optimal performance.

References

Gustafson, J.L.; Mullin, L.M.R. Tensors Come of Age: Why the AI Revolution will help HPC. CoRR 2017, abs/1709.09108, [1709.09108].

Leiserson, C.E.; Thompson, N.C.; Emer, J.S.; Kusmaul, B.C.; Lampson, B.W.; Sanchez, D.; Schardl, T.B. There’s Plenty of Room at the Top: What will drive computer performance after Moore’s Law? Science 2020, 368. https://doi.org/10.1126/science.aam9744.

Backus, J.W. Can Programming Be Liberated From the von Neumann Style? A Functional Style and its Algebra of Programs. Commun. ACM 1978, 21, 613–641. https://doi.org/10.1145/359576.359579.

Iverson, K.E. A Programming Language; John Wiley and Son: New York, 1962.

Curcic, M. Modern Fortran, Building efficient parallel applications; Manning, 2020.

Metcalf, M.; Reid, J.; Cohen, M.; Bader, R. Modern Fortran Explained, Incorporating Fortran 2023; Oxford University Press, 2023.

Hermanns, M. Parallel Programming in Fortran 95 using OpenMP, 2002.

Mullin, L.; Raynolds, J. Conformal Computing: Algebraically connecting the hardware/software boundary using a uniform approach to high-performance computation for software and hardware applications 2008.

Downloads

Published

2026-03-25

How to Cite

Markus, A., & Mullin, L. (2026). Array Access and Performance Regarding Numerical Algorithms. Transactions on Engineering and Computing Sciences, 14(02), 01–14. https://doi.org/10.14738/tmlai.1402.20134

Issue

Vol. 14 No. 02 (2026): Transactions on Engineering and Computing Sciences

Section

Articles

License

Copyright (c) 2026 Arjen Markus, Lenore Mullin

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.