The HPC community was faced with a stagnation of the increase of clock speeds about one decade ago. With the ongoing trend of successively increasing the number of computational units to compensate for this, also the parallelization overheads become more dominant. Therefore, such massively parallel architectures pose a natural strong-scalability limitation and this change in architectures requires redesigning existing algorithms towards this massive parallelism.

A recent development are parallelization-in-time methods with various concepts currently developed. Here, a new parallelism is exploited by mathematically redesigning algorithms for an increase in parallelization. These methods have the potential to further reduce the wallcock time even if the strong-scalability limitation with a parallelization-in-space is already reached.

In this talk, a massively parallel solver for oscillatory problems is discussed. With a standard time stepping method, solving these problems typically requires a computational time which directly depends on the number of time steps. The recently developed method of a "rational approximation of exponential integrator" (REXI) exploits characteristic features of such oscillatory problems. Instead of increasing the number of inherently sequential time steps, this method increases the degree of parallelism. We will discuss this parallelization-in-time method and show results which lead to further speedups of 300 compared to a parallelization-in-space method.