Asynchronous numerical solution of PDEs on parallel computers

Asynchronous and partially-synchronous finite difference schemes are investigated for the one-dimensional steady-state and nonsteady-state heat equation, respectively. It is shown experimentally that the asynchronous scheme runs twice as fast as the parallel synchronous scheme. For relatively small values of time levels, however, the asynchronous scheme produces the least accurate results, while the partially-asynchronous scheme is almost as accurate as its synchronous counterpart.