Parallel Iterative Discontinuous Galerkin Finite-Element Methods

We compare an iterative asynchronous parallel algorithm for the solution of partial differential equations, with a synchronous algorithm, in terms of termination detection schemes and performance. Both algorithms are based on discontinuous Galerkin finite-element methods, in which the local elements provide a natural decomposition of the problem into computationally-independent sets. We demonstrate the superiority of the asynchronous algorithm over the synchronous one in terms of the overall execution time. Our goal is to persuade parallel developers that it is worthwhile to implement the more complex asynchronous algorithm.