Parallel-In-Time Magnus Integrators
Published Web Locationhttps://doi.org/10.1137/18M1174854
Magnus integrators are a subset of geometric integration methods for the numerical solution of ordinary differential equations that conserve certain invariants in the numerical solution. This paper explores temporal parallelism of Magnus integrators, particularly in the context of nonlinear problems. The approach combines the concurrent computation of matrix commutators and exponentials within a time step with a pipelined iteration applied to multiple time steps in parallel. The accuracy and efficiency of time-parallel Magnus methods up to order six are highlighted through numerical examples and demonstrate that significant parallel speedup is possible compared to serial methods.