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

TL;DR

This paper presents a p-adaptive discontinuous Galerkin method optimized for heterogeneous CPU-GPU architectures to efficiently solve the shallow water equations, demonstrating significant performance gains in tsunami simulation scenarios.

Contribution

It introduces a novel separation and overlapping of adaptive and non-adaptive computations, along with automatic code generation for optimized CPU-GPU execution.

Findings

Significant performance improvements in tsunami simulation scenarios

Effective overlap of computation tasks on CPU and GPU

Optimized kernel distribution via automatic code generation

Abstract

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.