Block Fusion on Dynamically Adaptive Spacetree Grids for Shallow Water Waves

Weinzierl, Tobias; Bader, Michael; Unterweger, Kristof; Wittmann, Roland

Abstract

Spacetrees are a popular formalism to describe dynamically adaptive Cartesian grids. Even though they directly yield a mesh, it is often computationally reasonable to embed regular Cartesian blocks into their leaves. This promotes stencils working on homogeneous data chunks. The choice of a proper block size is sensitive. While large block sizes foster loop parallelism and vectorisation, they restrict the adaptivity's granularity and hence increase the memory footprint and lower the numerical accuracy per byte. In the present paper, we therefore use a multiscale spacetree-block coupling admitting blocks on all spacetree nodes. We propose to find sets of blocks on the finest scale throughout the simulation and to replace them by fused big blocks. Such a replacement strategy can pick up hardware characteristics, i.e. which block size yields the highest throughput, while the dynamic adaptivity of the fine grid mesh is not constrained—applications can work with fine granular blocks. We study the fusion with a state-of-the-art shallow water solver at hands of an Intel Sandy Bridge and a Xeon Phi processor where we anticipate their reaction to selected block optimisation and vectorisation.

Citation

Weinzierl, T., Bader, M., Unterweger, K., & Wittmann, R. (2014). Block Fusion on Dynamically Adaptive Spacetree Grids for Shallow Water Waves. Parallel Processing Letters, 24(3), Article 1441006. https://doi.org/10.1142/s0129626414410060

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2014
• Online Publication Date: Sep 30, 2014
• Publication Date: Sep 30, 2014
• Deposit Date: Oct 6, 2014
• Publicly Available Date: Oct 6, 2014
• Journal: Parallel Processing Letters
• Print ISSN: 0129-6264
• Electronic ISSN: 1793-642X
• Publisher: World Scientific Publishing
• Peer Reviewed: Not Peer Reviewed
• Volume: 24
• Issue: 3
• Article Number: 1441006
• DOI: https://doi.org/10.1142/s0129626414410060
• Keywords: Spacetrees, Shallow water, Adaptive Cartesian meshes, Vectorisation, Block fusion, Shared memory parallelisation.
• Public URL: https://durham-repository.worktribe.com/output/1444485