Partial differential equations (PDEs) are essential for modeling various physical processes, such as atmospheric dynamics and the diffusion of heat in space and time. Since analytical solutions
are often unavailable or too complex to compute, numerical methods are required to solve PDEs. These methods discretize PDEs in space, using approaches such as finite volume, finite element, or spectral methods, and combine them with time integration schemes, such as Runge-Kutta methods. Since numerically solving PDEs requires significant computational effort, techniques have been developed to efficiently solve the equations in parallel on High-Performance-Computing (HPC) systems.
The Parallel Full Approximation Scheme in Space and Time (PFASST) is a parallel-in-time method addressing the current saturation of spatial parallelization in HPC, by introducing parallelization in the temporal domain. PFASST combines the high-order Spectral Deferred Correction (SDC) method in its multi-level form MLSDC, allowing efficient parallelization in space and time. While PFASST has been shown to be both robust and scalable, it is also computationally demanding. Therefore, recent research has focused on dynamically adapting assigned computational resources during PFASST execution, allowing efficient resource manage-
ment. The open-source Fortran implementation LibPFASST has already been enhanced with an interface for this purpose. However, systematic criteria for resource adaptions are still missing. This thesis evaluates the influence of PFASST parameters on the accuracy of solutions and runtime of the solving process to provide a basis for dynamic resource management criteria. To this end, we conducted investigative experiments with LibPFASST on the Dahlquist test equation, the two-dimensional heat equation, and the two-dimensional advection equation. Our analysis focused on the influence of increasing the degree of temporal parallelization in
PFASST on accuracy and runtime, as well as its weak scaling and strong scaling behavior. The parameters which we considered in this context are number of processors, time step size, number of quadrature nodes and spatial points on the different coarsening levels, and number of sweeps in prediction and iteration phase.