Discontinuous collocation methods and gravitational self-force applications

Charalampos Markakis, Michael F. O'Boyle, Pablo D. Brubeck, Leor Barack

Research output: Contribution to journalArticlepeer-review


Numerical simulations of extreme mass ratio inspirals, the most important sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations of the self-force acting on point particles orbiting supermassive black holes. Such equations are distributionally sourced, and standard numerical methods, such as finite-difference or spectral methods, face difficulties associated with approximating discontinuous functions. However, in the self-force problem we typically have access to full a priori information about the local structure of the discontinuity at the particle. Using this information, we show that high-order accuracy can be recovered by adding to the Lagrange interpolation formula a linear combination of certain jump amplitudes. We construct discontinuous spatial and temporal discretizations by operating on the corrected Lagrange formula. In a method-of-lines framework, this provides a simple and efficient method of solving time-dependent partial differential equations, without loss of accuracy near moving singularities or discontinuities. This method is well-suited for the problem of time-domain reconstruction of the metric perturbation via the Teukolsky or Regge-Wheeler-Zerilli formalisms. Parallel implementations on modern CPU and GPU architectures are discussed.
Original languageEnglish (US)
Article number075031
JournalClassical and Quantum Gravity
Issue number7
StatePublished - Apr 8 2021


  • black hole perturbation theory
  • collocation methods
  • discontinuous interpolation
  • extreme mass ratio inspiral
  • gravitational self-force
  • LISA source modeling
  • pseudospectral methods


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