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

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