Performance evaluation of the scalable asynchronous DG method

The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method at extreme scales is significantly affected by data communication/synchronization across processing elements (PEs). To overcome such challenges, an asynchronous DG (ADG) method has been recently proposed that can provide high-order accurate solutions with relaxed communication/synchronization at a mathematical level. This study focuses on evaluating the performance of the ADG method in solving the compressible flow problems. The method is implemented in the open-source finite element library, deal.II, incorporating a communication-avoiding algorithm. The results show the accuracy limitations of standard DG schemes implemented with communication avoidance. Furthermore, the effectiveness of the newly developed asynchrony-tolerant fluxes in recovering accuracy is demonstrated. Strong scaling results are obtained for both the synchronous and asynchronous DG solvers, demonstrating a speedup of up to 80% with the ADG method at 9216 cores. The results highlight the potential benefits of the asynchronous approach for the development of accurate and scalable PDE solvers, paving the way for simulations of complex problems on massively parallel supercomputers.