GPU-parallelisation and integration of multiwavelet grid adaptation for fast discontinuous Galerkin modelling of multiscale flooding on LISFLOOD-FP

The second-order discontinuous Galerkin (DG2) solver in LISFLOOD-FP 8.0 incurs an enormous computational effort in simulating multiscale rapid flow phenomena like tsunamis due to using a uniform mesh, even with parallelisation on a graphics processing unit (GPU). To reduce the computational effort -- while still achieving similiar levels of DG2 accuracy as on a uniform mesh or grid -- integrating multiwavelet (MW) grid adaptation into the GPU-parallelised DG2 solver (GPU-DG2) is a compelling research aim for this thesis. Nonetheless, implementing a grid adaptation algorithm on a GPU is challenging due to major obstacles in achieving coalesced memory access (aligned memory access by threads) and avoiding warp divergence (different execution paths within a warp). To overcome these obstacles, initially for a Haar wavelet (HW) grid adaptation algorithm, three computational ingredients are proposed -- a Z-order space-filling curve, a parallel tree traversal algorithm and an array data structure -- to redesign its algorithmic structure and thereby enable its implementation on the GPU. After assessing the extent to which the proposed computational ingredients indeed allow for an efficient GPU implementation of the HW grid adaptation algorithm, their use is extended to now implement a MW grid adaptation algorithm on the GPU and thereby develop a GPU-parallelised MW adaptive DG2 model (GPU-MWDG2), which is then integrated into LISFLOOD-FP. To finally analyse the impact of GPU-MWDG2's grid adaptation capability on the computational effort and accuracy of DG2 modelling, GPU-MWDG2 is compared against GPU-DG2 by simulating four realistic test cases of tsunami-induced flooding. The analyses suggest that GPU-MWDG2 is a better choice than GPU-DG2 for simulating tsunami-induced flooding when considering test cases that require setting a parameter called the maximum refinement level $L$ to ten or higher, and where the tsunami complexity is low. For such test cases, GPU-MWDG2 is up to four times faster than GPU-DG2 while achieving similar levels of DG2 accuracy.