[Users] reduction in carpet + mismatched declaration in ML_ADMQuantities

[Scott Noble]

Hello All,

I just want to remind the users that

dens = \sqrt(\gamma) rho W  = \sqrt(-g)  rho u^t

where  \gamma is the determinant of the spatial metric, rho is the rest-mass density,  W is the lorentz factor,
u^t is the time-component of the 4-velocity, and "g" is the determinant of the full spacetime metric.

That means that Erik's first M integral has a factor of  u^t  that does not appear in the integrand of the second M 
integral.   Using "dens" and other already defined grid functions,  one would need to integrate
the following integrand in order to recover  the second M integral:   (dens * alp / w_lorentz) .


cheers, scott n.




Erik Schnetter wrote:
> Hee Il
> 
> I'm not quite sure what you mean by "volume measure", so let me
> explain from the beginning.
> 
> 1. Since GRHydro defines the density "dens" as a tensor density, not
> as a tensor, the total mass is defined as
> 
> M := \int dens dV
> 
> where no power of the determinant of the metric is necessary any more.
> I believe you could instead also write
> 
> M := \int rho sqrt(det g) dV
> 
> where rho is the non-densitized rest mass density as defined in HydroBase.
> 
> 2. Carpet's reduction operators take the relative size of the grid
> cells into account. That is, they take into account that finer grid
> cells are smaller, and they also take into account that only fractions
> of grid cells may contribute near refinement boundaries. (Refinement
> boundaries can cut grid cells if you use vertex centered refinement.)
> However, Carpet's reduction operators do not take the coordinate
> system into account.
> 
> This means that you need to multiply the result with the coarse grid
> coordinate volume. (This should probably be changed at some point.)
> 
> -erik
> 
> On Fri, Jan 7, 2011 at 12:00 AM, Hee Il Kim <heeilkim at gmail.com> wrote:
>> Hi,
>>
>> Still I'm confused with the carpet reduction. The basic reduction method in
>> Christian's code was same with mine. But I thought what I did before should
>> be improved. First of all my expression "integration over only the coarsest
>> level" is very inaccurate. Anyway let me ask again.
>>
>> What people do in reduction of , e.g. "Mass = Integration of density *
>> volume_measure" is;
>>
>> ------  Method I --------
>> * In local mode at mol_pseudoevolution or poststep
>> define Integrand = density      ! note it's not "density * volume_measure"
>>
>> * In global mode at analysis
>> CCTK_Reduce(Integrand --> Mass_temp)
>> Mass = Mass_temp * product(cctk_delta_space)
>> ------------------------------
>>
>> Why do people define "integrand = density" not as "density *
>> volume_measure"? However, if i do take the latter, then I get very weird
>> result, so people might have not taken that. To my understanding, the above
>> Method I will produce;
>>
>> Result I: Mass = (Sum_reflev=0 of capret weighted density(i,j,k) * dV_0) +
>> (Sum_reflev=1 of carpet weighted density(i,j,k) * dV_0) + ...
>>
>> But what I wanted (expected) to get by defining integrand = density *
>> volume_measure" is more accurate one;
>>
>> Result II: Mass = (Sum_reflev=0 of carpet weighted density(i,j,k) * dV_0) +
>> (Sum_reflev=1 of carpet weighted density(i,j,k) * 1/8 * dV_0) + ...
>>
>> What is the above Method I doing for? Result I or Result II, or something
>> else?
>> The new reduction API mentioned in the reference manual is still
>> underdevelopment?
>>
>> Thanks in advance,
>>
>> Hee Il
>>
>>
>>
>> 2011/1/6 Hee Il Kim <heeilkim at gmail.com>
>>> Christian, thanks so much !
>>>
>>> Your code seems to contain everything I wanted to calculate.
>>>
>>> There's one minor mismatched declaration in ML_ADMQuantities which should
>>> be fixed anyhow.
>>>
>>> ####
>>>
>>> [khi at zenith src]$ diff ML_ADMQuantities.c.ori ML_ADMQuantities.c
>>> 56c56
>>> <   const char *groups[] =
>>> {"grid::coordinates","Grid::coordinates","McLachlan::ML_curv","McLachlan::ML_Gamma","McLachlan::ML_lapse","McLachlan::ML_log_confac","McLachlan::ML_metric","McLachlan::ML_shift","McLachlan::ML_trace_curv","ML_ADMQuantities::ML_Jadm","ML_ADMQuantities::ML_Madm"};
>>> ---
>>>>    const char *groups[] =
>>>> {"grid::coordinates","Grid::coordinates","ML_BSSN::ML_curv","ML_BSSN::ML_Gamma","ML_BSSN::ML_lapse","ML_BSSN::ML_log_confac","ML_BSSN::ML_metric","ML_BSSN::ML_shift","ML_BSSN::ML_trace_curv","ML_ADMQuantities::ML_Jadm","ML_ADMQuantities::ML_Madm"};
>>> ####
>>>
>>> Thanks again,
>>>
>>> Hee Il
>>>
>>> 2011/1/5 Christian D. Ott <cott at tapir.caltech.edu>
>>>> Dear Hee Il,
>>>>
>>>> I agree that getting this right is tricky. You must set up your grid
>>>> functions that you want to reduce in MoL_PseudoEvolution in local
>>>> mode, then do the reduction in CCTK_Analysis in global mode.
>>>>
>>>> I am attaching a Thorn called ZelmaniAnalysis that I use for the
>>>> kinds of things you want. The reduction works with Carpet.
>>>>
>>>> Best,
>>>>
>>>>  - Christian
>>>>
>>>>
>>>>
>>>> On Wed, Jan 05, 2011 at 09:18:21PM +0900, Hee Il Kim wrote:
>>>>> Hi,
>>>>>
>>>>> Belated Happy New Year !
>>>>>
>>>>> I am writing a simple code for the calculation of ADM mass and angular
>>>>> momentum by using ML_ADMQuantities. As you know,  it requires reduction
>>>>> procedure for the summation of the integrand, e.g., density * volume
>>>>> measure. I've tried various reduction APIs including old deprecated
>>>>> one, but
>>>>> I could only succeed in the integration only over the coarsest grid
>>>>> level,
>>>>> which was not accurate.
>>>>>
>>>>> If I use the new reduction API in the reference manual of Cactus,
>>>>> CCTK_ReduceGridArrays;
>>>>>
>>>>> CCTK_ReduceGridArrays(const cGH *GH,
>>>>> int dest_processor,
>>>>> int local_reduce_handle,
>>>>> int param_table_handle,
>>>>> int N_input_arrays,
>>>>> const CCTK_INT input_array_variable_indices[],
>>>>> int M_output_values,
>>>>> const CCTK_INT output_value_type_codes[],
>>>>> void* const output_values[]);
>>>>>
>>>>> , I encounter the following error
>>>>> ....
>>>>> WARNING[L3,P0] (Cactus): CCTK_ReduceGridArrays: no grid array reduction
>>>>> registered
>>>>> WARNING level 0 in thorn ML_Analysis processor 0 host compute-0-5.local
>>>>>   (line 159 of Evaluate_ADMQuantities.F90):
>>>>>   -> Failed to integrate J_z
>>>>>
>>>>> Param_table_handle is not clear to me but it seems not causing the
>>>>> problem.
>>>>> The reduction operators are registered by CactusBase/LocalReduce.
>>>>>
>>>>> Could you let me know which reduction function I have to use for this
>>>>> calculation? I mean the integration over the whole grid levels. Should
>>>>> I do
>>>>> loop over refinenment levels;
>>>>> ...
>>>>> do loop over reflev
>>>>>   call CCTK_Reduce
>>>>> enddo
>>>>> ...
>>>>>
>>>>> Thanks in advance,
>>>>>
>>>>> Hee Il
>>>>> _______________________________________________
>>>>> Users mailing list
>>>>> Users at einsteintoolkit.org
>>>>> http://lists.einsteintoolkit.org/mailman/listinfo/users
>>
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> 
> 
>