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7.6 Criteria for assessing algorithms

Ideally, an apparent horizon finder should have several attributes:

Robust:
The algorithm/code should find an (the) apparent horizon in a wide range of numerically-computed slices, without requiring extensive tuning of initial guesses, iteration parameters, etc. This is often relatively easy to achieve for “tracking” the time evolution of an existing apparent horizon (where the most recent previously-found apparent horizon provides an excellent initial guess for the new apparent horizon position) but may be difficult for detecting the appearance of a new (outermost) apparent horizon in an evolution, or for initial-data or other studies where there is no “previous time step”.
Accurate:
The algorithm/code should find an (the) apparent horizon to high accuracy and should not report spurious “solutions” (“solutions” which are not actually good approximations to apparent horizons or, at least, to MOTSs).
Efficient:
The algorithm/code should be efficient in terms of its memory use and CPU time; in practice CPU time is generally the major constraint. It is often desirable to find apparent horizons at each time step (or, at least, at frequent intervals) during a numerical evolution. For this to be practical the apparent horizon finder must be very fast.

In practice, no apparent horizon finder is perfect in all these dimensions, so trade-offs are inevitable, particularly when ease of programming is considered.


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