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@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@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@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@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@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users

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Scott

Thanks for the clarification. I should have looked up the definition of the variables to get things right...

-erik

On Fri, Jan 7, 2011 at 11:46 AM, Scott Noble scn@astro.rit.edu wrote:

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@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@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@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@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@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users

---

Users mailing list Users@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users