Unique Aspects of the BBH Problem
Difficulties for H(HPF), H2(HPF-2) and D(DAGH) are given from 1-3, where 1=easy, 2=medium and 3 =difficult implement.
Difficulties inherent to the BBH Problem H H2 D Comments
Linear wave problem. No “inner boundaries” 1 1 1 lapse=1, shift=0, no holes.
Linear wave problem with matching outer
Boundary condition for grav. wave extraction. 2 1 3 The outer boundary requires a 1d evolution.
Adaptive Mesh Refinements (AMR) 3 2 1 DAGH was designed for this purpose.
Multigrid/MLAT + AMR 3 2 1-3 Only a certain class of problems can
Spherical “inner boundary” in Cartesian coords 2 2 2 DAGH: large stencils on the inner
boundary-expensive communications.
HPF: 3D “sparse” array or extrinsic.
Moving “inner boundary”. 3 1 1 Irregular boundary makes it difficult to implement in HPF.
Finding the Apparent Horizon 1 1 1 Expand Spherical Harmonics.
Causal Differencing with a “real” shift. 2 2 1 Requires additional storage in HPF.
NOTE:The mass curves spacetime, the shift tells us where to