[mesa-users] The MLT Jacobian

[Pablo Marchant]

I'm all in to improve the partials from MLT, and I'm actually working on
that. Not in the sense of looking for bugs, but rather slightly modifying
MLT to provide a gradT that is smooth. This slight modification of the
physics can actually result in quite improved performance for some cases
(you can check the experimental smooth_gradT option, I'd be happy to
explain it in more detail if you want), but it still needs plenty of work.

Just wanted to be clear that the partials are just a tool for the solver to
find solutions, and should not have an impact other than on
performance/accuracy as you say. There are many instances where the solver
runs into performance bottlenecks, and sorting these out would be great. So
keep digging!

On Fri, Aug 26, 2016 at 8:19 PM, Ehsan Moravveji <e.moravveji at gmail.com>
wrote:

> HI Pablo,
>
> Thanks for your words on this.
> So, perhaps the Newton solver, at the current stage is so robust that an
> improved partials would not change the accuracy/performance to better.
> It’s like giving a Ferrari for a Lamborghini ;-)
>
> Best wishes,
> Ehsan.
>
> On 26 Aug 2016, at 09:44, Pablo Marchant <pamarca at gmail.com> wrote:
>
> Hi Ehsan. In general, the better the partials are, the easier it will be
> for the newton solver to provide an answer. But whatever solution the
> solver ends up accepting needs to satisfy the stellar structure equations.
> Sure, if you modify the partials provided by mlt you won't have the same
> results up to machine precision, but the solutions should be physically
> equivalent.
>
> Am 26.08.2016 1:15 vorm. schrieb "Ehsan Moravveji" <e.moravveji at gmail.com
> >:
>
>> Dear mesa users,
>>
>> I’ve been taking a peek at the ml.f90 module, and came across two naive
>> questions. So, I thought of sharing them with you, and ask for your kind
>> feedbacks.
>>
>> 1. The MLT module returns the Jacobian of the output quantities w.r.t.
>> the input, e.g. partial_gradT_div_partial_grada and so on.
>> On the other hand, the cgrav, mixing_length_alpha, and gradr_factor are
>> three additional inputs, which are allowed to have spatial dependence too,
>> e.g. s% cgrav(:).
>> Furthermore, gradr in the convective region depends on alpha_MLT; e.g.
>> see Eqs. (14.98), (14.94), and (14.107) in Cox and Giuli.
>>
>> Consequently, I was speculating that derivatives of cgrav,
>> mixing_length_alpha and grad_factor may also need be incorporated in the
>> Jacobian matrix.
>> Is anyone willing to enlighten me on this?
>>
>> 2. Currently, the derivative of gradL_composition_term w.r.t. to all
>> quantities is ignored when evaluating the derivative of Ledoux temperature
>> gradient; see line 485 in mlt.f90. From Eq. (8) in MESA_II paper, the
>> B-term depends explicitly on chi_T. So, I was wondering, as a rough,
>> first-order estimate, it would be possible to include the derivative of
>> B-term w.r.t. to chi_T, e.g.
>>
>>          gradL = grada + gradL_composition_term
>>          d_gradL_composition_term_dvb(mlt_dchiT) = -
>> gradL_composition_term / chiT
>>          d_gradL_dvb = d_grada_dvb + d_gradL_composition_term_dvb
>>
>> I am aware that working out the composition dependence of
>> gradL_composition_term could be involved; so, that might be ignored for now.
>> It is possible that a modified gradL derivative would influence, even
>> slightly, the behaviour of growing convective cores. This "might be"
>> important for seismic modelling Kepler F stars. I have to admit this is my
>> naive speculation, and shall be exploited and tested first.
>>
>> I appreciate and welcome your feedbacks.
>>
>> Best regards,
>> Ehsan.
>>
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>
>


-- 
Pablo Marchant Campos
M.Sc on Astrophysics, Universidad Católica de Chile
PhD student, Argelander-Institut für Astronomie
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