[mesa-users] The MLT Jacobian

Pablo Marchant pamarca at gmail.com
Fri Aug 26 16:27:52 EDT 2016

> The new smoothing options looked quite appealing. Now that you offer
> giving more info, then I would ask: On which basics you came across this
> specific form of polynomial smoothing function, with constant coefficients?
> Does it succeed to smooth out gredT across all kind of boundaries (core,
> shell, envelope)?

The smoothing works well so long as the composition terms are not
important, that's part of the situations where it needs more work. As an
example, you can see the kind of smoothing being done in the attached plot,
which is for one of the sub-surface convection zones in an 80 solar mass
star, it shows both the unsmoothed gradT provided my MLT and the smoothed
one (vertical lines indicate the region where the smoothing is being done).
By default MLT produces a kink in gradT when moving from a purely radiative
zone, which the solver doesn't like. To compensate for this, I slightly
adjust gradT on both sides of the convective boundary, the trick to doing
this is that it has to be completely local, I can't use information on
neighboring cells to define gradT, otherwise the newton solver will have a
hard time. Perhaps to avoid creating a long technical thread in mesa-users
(like, for instance, to discuss what motivates a particular choice for a
smoothing polynomial) we can email each other directly, though I'm happy to
discuss things here if more people are interested.

> 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!
> I absolutely agree with you here. My whole point in the first email was to
> treat the Jacobian even more consistently than the current, by
> incorporating partials of the constants too, although it might help the
> solver find the solution only a little bit.

Just from poking around I've slightly messed up a couple of partials,
usually with disastrous results in terms of convergence. So I would not be
surprised if some small fixes would have a large effect. I'll actually test
the fixes you reported to Bill now.

> Regards,
> Ehsan.
> 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.
>>> ------------------------------------------------------------
>>> ------------------
>>> _______________________________________________
>>> mesa-users mailing list
>>> mesa-users at lists.sourceforge.net
>>> https://lists.sourceforge.net/lists/listinfo/mesa-users
> --
> Pablo Marchant Campos
> M.Sc on Astrophysics, Universidad Católica de Chile
> PhD student, Argelander-Institut für Astronomie

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