Parallel in Time (PinT) methods have received renewed interest over the last decade for improving the algorithmic scalability on emerging computer architectures of time-dependent large scale simulations. However, a PinT approach may exhibit higher overheads and not necessarily a space-and-time decomposition leads to a parallel algorithm with the highest performance. Here we consider MGRIT (MultiGrid-In-Time) algorithm, which is based on MultiGrid Reduction (MGR). We provide a mathematical model for analysing performances of MGRIT algorithm, by determining the benefits arising from the decomposition. A set of matrices (decomposition, execution and storage) highlights fundamental characteristics of the algorithm, such as the inherent parallelism, some sources of overhead and memory occupancy, respectively. The aim of the proposed performance analysis is to address the algorithmic strong and weak scaling of MGRIT, regarded as a parallel iterative algorithm proceeding along the time dimension. The analysis allows us to a-priori determine the correct number of MGRIT time-levels as well as the suitable number of processing elements for efficiently implementing the algorithm.
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