Locality Improvement of Data-Parallel Adams–Bashforth Methods through Block-Based Pipelining of Time Steps
Adams–Bashforth methods are a well-known class of explicit linear multi-step methods for the solution of initial value problems of ordinary differential equations. This article discusses different data-parallel implementation variants with different loop structures and communication patterns and compares the resulting locality and scalability. In particular, pipelining of time steps is employed to improve the locality of memory references. The comparison is based on detailed runtime experiments performed on parallel computer systems with different architectures, including the two supercomputer systems JUROPA and HLRB II.
KeywordsProcessing Element Loop Structure Cache Line Sequential Implementation Access Distance
Unable to display preview. Download preview PDF.
- 3.Chen, J., Watson III, W.: Software barrier performance on dual quad-core Opterons. In: Proceedings of the 2008 International Conference on Networking, Architecture, and Storage, pp. 303–309. IEEE Computer Society (2008)Google Scholar
- 5.Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd rev. edn. Springer, Berlin (2000)Google Scholar
- 6.Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd rev. edn. Springer, Berlin (2002)Google Scholar
- 10.Ley, K.: Parallele Implementierung und Analyse eines expliziten Adams-Verfahrens. Bachelor’s thesis, University of Bayreuth (November 2010)Google Scholar