GPU-parallelisation of Haar wavelet-based grid resolution adaptation for fast finite volume modelling: application to shallow water flows

Author:

Chowdhury Alovya Ahmed1ORCID,Kesserwani Georges1,Rougé Charles1,Richmond Paul2

Affiliation:

1. a Department of Civil and Structural Engineering, University of Sheffield, Mappin St, Sheffield, UK

2. b Department of Computer Science, University of Sheffield, Mappin St, Sheffield, UK

Abstract

Abstract Wavelet-based grid resolution adaptation driven by the ‘multiresolution analysis’ (MRA) of the Haar wavelet (HW) allows to devise an adaptive first-order finite volume (FV1) model (HWFV1) that can readily preserve the modelling fidelity of its reference uniform-grid FV1 counterpart. However, the MRA entails an enormous computational effort as it involves ‘encoding’ (coarsening), ‘decoding’ (refining), analysing and traversing modelled data across a deep hierarchy of nested, uniform grids. GPU-parallelisation of the MRA is needed to handle its computational effort, but its algorithmic structure (1) hinders coalesced memory access on the GPU and (2) involves an inherently sequential tree traversal problem. This work redesigns the algorithmic structure of the MRA in order to parallelise it on the GPU, addressing (1) by applying Z-order space-filling curves and (2) by adopting a parallel tree traversal algorithm. This results in a GPU-parallelised HWFV1 model (GPU-HWFV1). GPU-HWFV1 is verified against its CPU predecessor (CPU-HWFV1) and its GPU-parallelised reference uniform-grid counterpart (GPU-FV1) over five shallow water flow test cases. GPU-HWFV1 preserves the modelling fidelity of GPU-FV1 while being up to 30 times faster. Compared to CPU-HWFV1, it is up to 200 times faster, suggesting that the GPU-parallelised MRA could be used to speed up other FV1 models.

Funder

Engineering and Physical Sciences Research Council

Publisher

IWA Publishing

Subject

Atmospheric Science,Geotechnical Engineering and Engineering Geology,Civil and Structural Engineering,Water Science and Technology

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