Minisymposium Presentation

The solution of the Einstein--Euler equations by the vast majority of numerical codes is still based on traditional finite difference schemesfor the Einstein sector, while it relies on conservative schemes for the matter part. Discontinuous Galerkin (DG) schemes, in spite of many potentialadvantages, have not reached a mature stage yet. I will compare performances of a new class of finite difference schemes for the full Einstein--Eulerequations with DG schemes, showing possible future directions of research that may promote DG schemes to be the dominant ones in a future with exascale hardware. In the last part of the talk I will discuss the impact of machine learning on the data analysis of gravitational waves observations.