# p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures

arXiv: https://arxiv.org/abs/2311.11348 · HTML: https://mlsanity.com/paper/2311.11348/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Downscaling Neural Network for Coastal Simulations](https://mlsanity.com/paper/2408.16553/) (2024)

## Abstract (arXiv)

Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method (DG) for the shallow water equations (SWE). Our new approach separates the computations of the non-adaptive (lower-order) and adaptive (higher-order) parts of the discretization form each other. Thereby, we can overlap computations of the lower-order and the higher-order DG solution components. Furthermore, we investigate execution times of main computational kernels and use automatic code generation to optimize their distribution between the CPU and GPU. Several setups, including a prototype of a tsunami simulation in a tide-driven flow scenario, are investigated, and the results show that significant performance improvements can be achieved in suitable setups.