Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

  • Authors:

  • Stephen R. Lau;Richard H. Price

  • Affiliations:

  • Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, United States;Center for Gravitational Wave Astronomy and Center for Advanced Radio Astronomy, Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, TX 78520, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We describe a multidomain spectral-tau method for solving the three-dimensional helically reduced wave equation on the type of two-center domain that arises when modeling compact binary objects in astrophysical applications. A global two-center domain may arise as the union of Cartesian blocks, cylindrical shells, and inner and outer spherical shells. For each such subdomain, our key objective is to realize certain (differential and multiplication) physical-space operators as matrices acting on the corresponding set of modal coefficients. We then achieve sparse realizations through the integration ''preconditioning'' of Coutsias, Hagstrom, Hesthaven, and Torres. Since ours is the first three-dimensional multidomain implementation of the technique, we focus on the issue of convergence for the global solver, here the alternating Schwarz method accelerated by GMRES. Our methods may prove relevant for numerical solution of other mixed-type or elliptic problems, and in particular for the generation of initial data in general relativity.