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

TL;DR

This paper presents a GPU-parallelised wavelet-based grid adaptation method for finite volume models, significantly accelerating shallow water flow simulations while maintaining accuracy.

Contribution

It redesigns the multiresolution analysis algorithm for GPU parallelisation using space-filling curves and parallel tree traversal, enabling faster adaptive finite volume modeling.

Findings

GPU-HWFV1 is up to 30 times faster than CPU-HWFV1.

GPU-HWFV1 maintains fidelity of the uniform-grid model.

GPU-parallelised MRA can accelerate other finite volume models.

Abstract

Wavelet-based grid 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 incurs a high computational cost 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 reduce its computational cost, 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 addressing (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 the GPU-parallelised MRA could be used to speed up other FV1 models.