[ET Trac] [Einstein Toolkit] #362: Improve roundoff accuracy of efficient RK4

[Einstein Toolkit]

#362: Improve roundoff accuracy of efficient RK4
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 Reporter:  eschnett     |       Owner:     
     Type:  enhancement  |      Status:  new
 Priority:  major        |   Milestone:     
Component:  Cactus       |     Version:     
 Keywords:               |  
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 I just encountered a weird case where evolving Minkowski with the
 efficient RK4 implementation was not static. It turns out that the reason
 was floating-point round-off error in RK4. During each of the substeps,
 RK4 adds terms with factors of 1/3 and 2/3, and for the final step, adds a
 term with a factor of 4/3. Due to round-off, these terms do not cancel
 exactly, so that the time-evolved lapse is slightly different from 1
 (although all the lapse RHS terms are 0). The same goes for the diagonal
 terms of the metric.

 The attached patch keeps track of the round-off error when adding these
 terms, leading to a more accurate integration result.

 The problem described above is not always visible, but also depends on
 optimisation settings.

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Ticket URL: <https://trac.einsteintoolkit.org/ticket/362>
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