Compact Object Studies in Computational Relativistic Astrophysics via Discontinuous Galerkin Finite Element Methods

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The field of Computational Relativistic Astrophysics has arrived at the verge of predictive modeling of many observed and expected sources of radiation. As the community strives to increase the realism in the employed physics models, progress is severely hindered by the complexity and difficulties in using computational methods at large scales. As hardware architectures evolve, many formerly highly efficient algorithms can exploit only a fraction of the power of newer hardware, and novel algorithms need to be developed and refined. Modern numerical methods, such as Discontinuous Galerkin Finite Elements (DGFE) have enjoyed much success in the past decade in other fields, but have not yet managed to make an inroad to Computational Relativistic Astrophysics. I will research DGFE methods suitable for the Einstein and General Relativistic Magneto-Hydrodynamics equations, design respective efficient implementations suitable for modern hardware architectures, and make these available as part of my open-source software infrastructure. I will employ these to study astrophysical systems, in particular black hole binaries and core-collapse supernovae, increasing accuracy and/or reducing simulation waiting times by at least an order of magnitude. This will in turn allow incorporating new physics into the study of these systems that is far out of reach today.