[ET Trac] [Einstein Toolkit] #1560: Calculate solution error in EinsteinExact

Mon Mar 17 05:43:10 CDT 2014

#1560: Calculate solution error in EinsteinExact
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Reporter:  eschnett               |       Owner:
Type:  enhancement            |      Status:  closed
Priority:  major                  |   Milestone:
Component:  EinsteinToolkit thorn  |     Version:  development version
Resolution:  fixed                  |    Keywords:
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Comment (by hinder):

The way I have done this in the past is to add new variables for the exact
solution rather than using the ADM variables.  You can then output these,
which give you the exact solution, and add a calculation which subtracts
the ADM variables from the exact solution, and populates the error
variables.  This way, you can have all quantities available, and as a side
benefit, you don't need to do the pattern matching on the calculation.

So you would have this:

{{{
calcExact = {
gxxExact -> …,
…}

gxx -> gxxExact,
…}

calcError = {
gxxError -> gxx - gxxExact,
…}
}}}

You would then schedule this so that the exact, ADMBase and error
calculations are always run at INITIAL.  Then, depending on the
parameters, you would either:

1. Calculate exact, ADMBase and error also during evolution.  This would
preserve the current expected behaviour of the ADMBase variables
containing the exact solution for the whole evolution.  OR
2. Calculate just the exact and error variables during evolution, so that
the error variables contain the error of the (separate) evolution of the

It is also useful to compute the gridfunction whose norm is the norm of
the whole solution error.  i.e.
{{{
uErr = sqrt((gErr_ij)^2 + (KErr_ij)^2 + alpErr^2 + (betaErr^i)^2).
}}}
Then you can output the norm of this from Cactus, and you can look at
convergence for the entire (ADM) solution very easily.

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Ticket URL: <https://trac.einsteintoolkit.org/ticket/1560#comment:4>
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