A multisolver numerical relativity code with on-the-fly data assessment and comparisons of different numerical schemes

  • Stokes, Timothy (Durham University)
  • Weinzierl, Tobias (Durham University)
  • Zhang, Han (Durham University)

Please login to view abstract download link

Simulating binary black hole mergers is a central focus of modern numerical relativity. The resulting gravitational wave patterns are used to distill, interpret, and classify observational data. In principle, this poses a classical digital twin challenge, as scientists would like to continuously calibrate simulations to experimental data. In practice, the challenge cannot be phrased as a digital twin/online calibration challenge, as we can only observe a small time interval of the actual merger process: the initial approach of black holes as well as the final merger produce signals that can hardly be detected currently. Consequently, many simulation codes run numerous forward simulations and label the resulting outcome as a catalogue of wave patterns. While this is feasible, it is not the optimal solution, as such catalogues may waste compute power on irrelevant output data, and scientists might struggle to understand correct parameter-effect relationships once the volumetric data over time is lost and we have distilled only the waveform patterns at certain probe locations. We introduce our numerical relativity code ExaGRyPE based upon higher-order Finite Difference, DG, and Finite Volume discretisations of CCZ4. One selling point of ExaGRyPE is the ability to run multiple numerical schemes and solvers in parallel on the same mesh. This allows users to compare solutions on-the-fly. We propose to use this multi-solver ability to inject online simulation validation into simulations. If a particular solver variant for particular initial conditions yields physically irrelevant reference data, we immediately remove this solver from the simulation and continue to develop those solutions which are promising from an observational point of view. This approach allows us to amortise other effort such as mesh administration. It also gives us the opportunity to increase the arithmetic intensity per mesh cell massively and, hence, to exploit GPUs better. Unlike other pieces of software, ExaGRyPE is able to run different solvers with different numerical schemes in different subdomains. We therefore propose to translate the concept of on-the-fly comparisons against observational data for digital twins into the world of numerical solvers, where we can compare different numerical schemes on-the-fly, i.e., we make one numerical scheme the digital twin of the other ones and vice versa.