[Users] Meeting minutes

[Erik Schnetter]

On Tue, May 24, 2011 at 11:43 PM, Bruno C. Mundim <bcmsma at astro.rit.edu> wrote:
> Hi Erik and Ian,
>
> Erik Schnetter wrote:
>>
>> On Tue, May 24, 2011 at 2:11 AM, Ian Hinder <ian.hinder at aei.mpg.de> wrote:
>>>
>>> On 23 May 2011, at 23:49, Bruno Coutinho Mundim wrote:
>>>
>>>>> * Bruno still has troubles with RotatingSymmetry180 when using the
>>>>> development version of ET for the BBH example (parfile is in
>>>>> subversion)
>>>>> * will try running without RotatingSymmetry180
>>>>
>>>> Just got the results: no problem without RotatingSymmetry180.
>>>
>>> OK good, so we know where the problem is.
>>>
>>>>> * convergence in norms is bad, somewhat better in 1D data for a short
>>>>> time after simulation startup
>>>>
>>>> A closer look into the initial data revealed that both the l2-norm of
>>>> the hamiltonian constraint and its value along the x-axis converge to
>>>> the expected order, 4th order. This convergence is not observed anymore
>>>> in the very next coarse step when the comparison is done again.
>>>
>>> The time prolongation is only 3rd order accurate so I wouldn't expect
>>> convergence at 4th order.
>>
> Thanks! I missed that...
>
>> Time prolongation is second order accurate.
>>
> Right. We use three time levels (equivalently three points) to
> prolongate, so it should be second order, O(dt^2), accurate.

Yes, it uses three points. Not everybody counts orders the same way I did here.

>> You can use tapered grids, which avoids all time interpolation except
>> possibly during regridding. If you are careful about regridding you
>> don't need time interpolation for this either. This gives you clean
>> fourth order convergence, except near the outer boundary if you are
>> cheating there (and we all are).
>>
> What do you mean by "If you are careful about regridding you
> don't need time interpolation for this either. "? You mean besides using
> tapered grids, only regrid when all grids are aligned (in time), ie in
> only at the coarsest time steps?

Not quite. All the grids that are changing need to be aligned with
their next coarser grids. If e.g. the first three levels don't change,
then you can regrid much more often than just at full coarse grid time
steps.

>> Another issue to consider is how you set up the past timelevels. If
>> you copy the data from the current time level, then you are
>> introducing a first order error.
>
> Good point. I guess that's how it is set right now:
> Carpet::init_fill_timelevels     = "yes"
> InitBase::initial_data_setup_method = "init_all_levels"

Yes, this will introduce a very large error during time
"interpolation", because by doing so, you essentially copy the initial
data to the future times instead of interpolating.

> If you use the
>>
>> three-timelevel-initialisation, then you are second order accurate.
>> Again, these past timelevels are used only for time interpolation, but
>> they can reduce the convergence order even further if they are not
>> well initialised.
>>
> But to use init_3_timelevels we need to have all time levels on the
> ratio 2:1 (for example). We can't have as it is set there right now:
>
> Carpet::time_refinement_factors = "[1, 1, 2, 4,...]"

Yes. Sorry.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/