Multidomain spectral method for the helically reduced wave equation

  • Authors:

  • Stephen R. Lau;Richard H. Price

  • Affiliations:

  • Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87111, USA and Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;Center for Gravitational Wave Astronomy, Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, TX 78520, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.45

Visualization

Abstract

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the ''eigenspectral method.'' Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.