An optimal load balancing strategy is required for High Performance Computing (HPC) simulations to both evenly and efficiently distribute the computational load among the computing resources. This thesis focuses on load balancing for the grid creation in "An Exascale Hyperbolic PDE Engine" (ExaHyPE). The advantages and disadvantages of existing strategies are examined. A trade-off is shown between splitting sooner and achieving an earlier parallelization of grid creation against more knowledge of the domain and a more even load distribution. This thesis illustrates that the load balancing quality for strategies with premature space tree splitting is more susceptible to being affected by Adaptive Mesh Refinement (AMR) due to a lack of available threads to split oversized trees resulting from AMR. Paraview visualizations indicate that an earlier spacetree splitting leads to more regularly shaped sub-regions, which causes a decrease in total virtual cells. A new strategy is implemented for 2D and 3D applications without AMR. This strategy achieves near-ideal scaling of grid creation time by parallelizing the grid creation sooner whilst maintaining an ideal load balancing quality of local cells. Another strategy is implemented to handle 2D applications with AMR. This strategy achieves a better load balancing quality of local cells than some strategies but is not ideal. This strategy serves as a stepping stone for future load balancing strategies to cope with AMR.