A scalable asynchronous discontinuous-Galerkin method for massively parallel PDE solvers

In recent years, the discontinuous-Galerkin (DG) method has received broad interest in developing PDE solvers due to their ability to provide high-order accurate solutions in complex geometries and capture discontinuities in solutions of non-linear hyperbolic problems. The method provides high-arithmetic intensity than finite-difference or finite-volume methods, resulting in good parallel efficiency. However, at an extreme scale, data communication and synchronization remain a bottleneck in the scalability of DG solvers. In this work, we present an asynchronous DG method, which relaxes communication and/or synchronization between processing elements at a mathematical level, thus allowing computations to proceed regardless of the status of communications. The numerical properties of the proposed asynchronous DG method are investigated, where a loss in conservation and poor accuracy are observed. To mitigate these issues, new asynchrony-tolerant (AT) fluxes are derived that can provide arbitrary levels of accuracy. Preliminary results on the stability analysis of the asynchronous DG method will be presented. The computational performance of the method is verified with numerical experiments based on the simple linear equations as well as the reacting compressible flow equations.