A Parallel Space-Time Algorithm

Abstract

With the continued evolution of computing architectures towards many-core computing, algorithms that can effectively and efficiently use many cores are crucial. In this paper, we propose, as a proof of principle, a parallel space-time algorithm that layers time parallelization together with a parallel elliptic solver to solve time dependent partial differential equations (PDEs). The parallel elliptic solver utilizes domain decomposition to divide a spatial grid into subdomains, and applies a parallel Schwarz iteration to find consistent solutions. The high-order parallel time integrator employed belongs to the family of revisionist integral deferred correction methods (RIDC) introduced by Christlieb, Macdonald, and Ong [SIAM J. Sci. Comput., 32 (2010), pp. 818--835], which allows for the small scale parallelization of solutions to initial value problems. The two established algorithms are combined in this proposed space-time algorithm to add parallel scalability. As a proof of concept, we utilize a framew...