Main Features

Formalism

• Bimetric equations in standard 3+1 form (with the evolution of p and the explicit bimetric lapse ratio).

• Matter equations for the perfect fluid in conservative form.

• Equations regularized for spherical symmetry.

Gauge setup

• Lapse:
  • Maximal slicing (boundary value problem at each slice, see maximalSlice.h).
  • Bona-Massó slicing condition and the K-driver (evolution).
  • Algebraic slicing (normal coordinates, and (1+erf)^{-2}).

• Shift:
  • Planned: Minimal distortion and Gamma-driver.

Boundary conditions

• Imposed parity conditions for local flattness at r = 0 (on the inner boundary).

• Extrapolation (linear 2nd, or 4th order) or Sommerfeld outgoing wave radiative condition on the outer boundary.

Spatial discretization

• 2nd, 4th, or 6th order centered differences on a staggered grid (see finiteDifferences.h).

• Planned: Upwind differences on shift advection terms.

Temporal discretization

• Method of Lines:
  • Runge-Kutta: 2, 3, and 4 steps
  • Iterated Crank-Nicolson (ICN): 2 and 3 steps
  • Averaged ICN: 2 and 3 steps
  • Generic N-step algorithm with arbitrary coefficients (see methodOfLines.h)

• Kreiss-Oliger dissipation (2nd and 4th order) in all of the evolution equations.

• Courant-Friedrichs-Lewy factor (CFL) 0.5 as default.

Grid-driver code

• Uniform spatial grid (see gridDriver.h).

Numerics

• Implemented classes: Matrix, Vector, BandLUDecomposition (band-diagonal matrix LU decomposition with Crout factorization), CubicSpline (normal cubic spline interpolation), arbirary FD extrapolation, and arbitrary FD derivatives.

• 64-bit and 128-bit floating point

• C++ code with OpenMP and MPI support adapted for high-performance computing.

• Planned: Transition to Cactus

Horizons

• Apparent horizon finder.

Initial Data

• Minkowski GR (opt. with a gauge wave)

• Bimetric Minkowski (opt. with a gauge wave)

• GR collisionless matter (dust) with Gaussian profile (as the main testbed).

• Bimetric Gaussian dust with a "polytropic" conformally flat g and f.