11.6 Finite-difference multi-block orbiting binary black-hole simulations
In  orbiting binary black-hole simulations using a high-order FD multi-domain approach were
presented. The basic layout of the full domain used is shown in Figures 15 and 16, where the centers of the
excised black-hole spheres are located along the axis at . The computational domain is
based on two types of building blocks, shown in Figure 17, which are essentially variations of
cubed spheres. In the simulations of  the optimized difference operator described in
Section 8.3 was used, the patches were communicated using the penalty technique (see Section 10),
and the resulting equations were evolved in time using an embedded fourth- and fifth-order
Runge–Kutta stepper (see Section 7.5). The formulations of the equations used, boundary
conditions and dual frame technique are exactly those of the spectral evolutions discussed above,
only the numerical and domain decomposition approaches differ, which follow building work
from [281, 141, 385, 145, 324]. Strong and weak scaling is observed up to at least several thousand
Figure 15: Equatorial cut of the computational domain used in multi-block simulations of orbiting
black-hole binaries (left). Schematic figure showing the direction considered as radial (red arrows)
for the cuboidal blocks (right). Reprinted with permission from ; copyright by APS.
Figure 16: Multi-block domain decomposition for a binary black-hole simulation. Reprinted with
permission from ; copyright by APS.
Figure 17: Equatorial cross-section of varations of cubed sphere patches. Reprinted with permission
from ; copyright by APS.