Dynamical excision boundaries in spectral evolutions of binary black hole spacetimes. Simulations of binary black hole systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions inside the black holes. It is imperative that the excision boundaries are outflow boundaries with respect to the hyperbolic evolution equations used in the simulation. We employ a time-dependent mapping between the fixed computational frame and the inertial frame through which the black holes move. The time-dependent parameters of the mapping are adjusted throughout the simulation by a feedback control system in order to follow the motion of the black holes, to adjust the shape and size of the excision surfaces so that they remain outflow boundaries, and to prevent large distortions of the grid. We describe in detail the mappings and control systems that we use. We show how these techniques have been essential in the evolution of binary black hole systems with extreme configurations, such as large spin magnitudes and high mass ratios, especially during the merger, when apparent horizons are highly distorted and the computational domain becomes compressed. The techniques introduced here may be useful in other applications of partial differential equations that involve time-dependent mappings.

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  1. Alcoforado, M. A.; Aranha, R. F.; Barreto, W. O.; de Oliveira, H. P.: Multidomain Galerkin-collocation method. II: Spherical collapse of scalar fields (2021)
  2. Jesse, Jerred; Duez, Matthew D.; Foucart, Francois; Haddadi, Milad; Knight, Alexander L.; Cadenhead, Courtney L.; Hébert, Francois; Kidder, Lawrence E.; Pfeiffer, Harald P.; Scheel, Mark A.: Axisymmetric hydrodynamics in numerical relativity using a multipatch method (2020)
  3. Barreto, W. O.; Crespo, J. A.; de Oliveira, H. P.; Rodrigues, E. L.: A Galerkin-collocation domain decomposition method: application to the evolution of cylindrical gravitational waves (2019)
  4. Okounkova, Maria; Scheel, Mark A.; Teukolsky, Saul A.: Numerical black hole initial data and shadows in dynamical Chern-Simons gravity (2019)
  5. Bizzozero, D. A.; Ellison, J. A.; Heinemann, K.; Lau, S. R.: Rapid evaluation of two-dimensional retarded time integrals (2017)
  6. Kidder, Lawrence E.; Field, Scott E.; Foucart, Francois; Schnetter, Erik; Teukolsky, Saul A.; Bohn, Andy; Deppe, Nils; Diener, Peter; Hébert, François; Lippuner, Jonas; Miller, Jonah; Ott, Christian D.; Scheel, Mark A.; Vincent, Trevor: SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics (2017)
  7. Miller, Jonah M.; Schnetter, Erik: An operator-based local discontinuous Galerkin method compatible with the BSSN formulation of the Einstein equations (2017)
  8. Holst, Michael; Sarbach, Olivier; Tiglio, Manuel; Vallisneri, Michele: The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools (2016)
  9. Hemberger, Daniel A.; Scheel, Mark A.; Kidder, Lawrence E.; Szilágyi, Béla; Lovelace, Geoffrey; Taylor, Nicholas W.; Teukolsky, Saul A.: Dynamical excision boundaries in spectral evolutions of binary black hole spacetimes (2013)
  10. Lau, Stephen R.; Price, Richard H.: Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains (2012)
  11. Zenginoğlu, Anıl: Hyperboloidal layers for hyperbolic equations on unbounded domains (2011)