Multigrid reduction in time for non-linear hyperbolic equations

Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a partial differential equation, providing possibilities for accelerating computation its solution. While parallelisation in time has allowed remarkable speed-ups applications involving parabolic equations, effectiveness hyperbolic framework remains debatable: growth instabilities and slow convergence are both strong issues this case, which often negate most advantages from time-parallelisation. Here, we focus on Multigrid Reduction Time algorithm, investigating detail performance when applied to non-linear conservation laws with variety discretisation schemes. Specific attention is given high-accuracy Weighted Essentially Non-Oscillatory reconstructions, coupled Strong Stability Preserving integrators, discretisations choice such equations. A technique improve MGRIT low-order, more dissipative scheme also outlined. This study aims at identifying main causes degradation speed algorithm finds Courant-Friedrichs-Lewy limit be principal determining factor.