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

Einstein Toolkit trac-noreply at einsteintoolkit.org
Mon Mar 17 05:43:10 CDT 2014

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

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 -> …,

 calcADMBase = {
   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
 ADMBase variables.

 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.

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