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