Summary (English)

A general introduction to the topic of time-domain parallelism with motivation is given in Chapter 1. The ’parareal ’ algorithm itself along with pseudo-code for a simple implementation and all the basic properties are presented in chapter 2. Chapter 3 contains a comprehensive review of the research literature available as well as current state-of-the-art implementations of parareal. Investigations on the convergence rate of the algorithm applied to various types of differential equations using various numerical schemes as operators in the algorithm is pre-sented in Chapter 4, followed by an investigation in Chapter 5 on optimal coarse propagator parameter choice when considering the distribution of parallel work. In this context a heuristic for the optimal choice of coarse propagator accuracy is proposed. In Chapter 6 the parareal algorithm is applied to a non-linear free surface water wave model. The convergence rate is analysed in a Matlab implementations of the algorithm, simulating the parallelism for a range of dif-ferent wave types. As will be shown, the non-linearity of the wave and the water depth influence the parallel efficiency that can be obtained using the pararea