Parallel-in-time integration of the Landau–Lifshitz–Gilbert equation with the parallel full approximation scheme in space and time.

Speeding up computationally expensive problems, such as numerical simulations of large micromagnetic systems, requires efficient use of parallel computing infrastructures. While parallelism across space is commonly exploited in micromagnetics, this strategy performs poorly once a minimum number of degrees of freedom per core is reached. We use magnum.pi, a finite-element micromagnetic simulation software, to investigate the Parallel Full Approximation Scheme in Space and Time (PFASST) as a space- and time-parallel solver for the Landau–Lifshitz–Gilbert equation (LLG). Numerical experiments show that PFASST enables efficient parallel-in-time integration of the LLG, significantly improving the speedup gained from using a given number of cores as well as allowing the code to scale beyond spatial limits. • A space-parallel micromagnetic solver is extended with parallel-in-time integration. • Numerical experiments show significantly improved parallel efficiencies and runtimes. • Implicit–explicit versions of the algorithm also perform well without parallelism. [ABSTRACT FROM AUTHOR]