A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems

The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism time. goal of this article is develop and analyze a MGRIT algorithm using FCF-relaxation with time-dependent time-grid propagators seek the finite element approximations unsteady fractional Laplacian problems. multigrid line smoother proposed Chen et al. (2016) chosen spatial solver. Motivated Southworth (2019), we provide new temporal eigenvalue approximation property then deduce generalized two-level convergence theory which removes previous unitary diagonalization assumption on fine coarse required Yue (2019). Numerical computations are included confirm theoretical predictions demonstrate sharpness derived upper bound.