[petsc-users] Integrating TAO into SNES and TS

[Matthew Knepley]

On Tue, Sep 1, 2015 at 3:46 AM, Justin Chang <jychang48 at gmail.com> wrote:

> I would like to simultaneously enforce both discrete maximum principle and
> local mass/species balance. Because even if a locally conservative scheme
> like RT0 is used, as soon as these bounded constraints are applied, i lose
> the mass balance.
>

What I am saying is, can't you just add "linear equality constraints" as
more equations?

  Thanks,

    Matt


> On Tue, Sep 1, 2015 at 2:33 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Tue, Sep 1, 2015 at 3:11 AM, Justin Chang <jychang48 at gmail.com> wrote:
>>
>>> Barry,
>>>
>>> That's good to know thanks.
>>>
>>> On a related note, is it possible for VI to one day include linear
>>> equality constraints?
>>>
>>
>> How are these different from just using more equations?
>>
>>   Thanks,
>>
>>     Matt
>>
>>
>>> Thanks,
>>> Justin
>>>
>>> On Mon, Aug 31, 2015 at 7:13 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>>
>>>>
>>>> > On Aug 31, 2015, at 7:36 PM, Justin Chang <jychang48 at gmail.com>
>>>> wrote:
>>>> >
>>>> > Coming back to this,
>>>> >
>>>> > Say I now want to ensure the DMP for advection-diffusion equations.
>>>> The linear operator is now asymmetric and non-self-adjoint (assuming I do
>>>> something like SUPG or finite volume), meaning I cannot simply solve this
>>>> problem without any manipulation (e.g. normalizing the equations) using
>>>> TAO's optimization solvers. Does this statement also hold true for SNESVI?
>>>>
>>>>   SNESVI doesn't care about symmetry etc
>>>>
>>>> >
>>>> > Thanks,
>>>> > Justin
>>>> >
>>>> > On Fri, Apr 3, 2015 at 7:38 PM, Barry Smith <bsmith at mcs.anl.gov>
>>>> wrote:
>>>> >
>>>> > > On Apr 3, 2015, at 7:35 PM, Justin Chang <jchang27 at uh.edu> wrote:
>>>> > >
>>>> > > I guess I will have to write my own code then :)
>>>> > >
>>>> > > I am not all that familiar with Variational Inequalities at the
>>>> moment, but if my Jacobian is symmetric and positive definite and I only
>>>> have lower and upper bounds, doesn't the problem simply reduce to that of a
>>>> convex optimization? That is, with SNES act as if it were Tao?
>>>> >
>>>> >   Yes, I think that is essentially correctly.
>>>> >
>>>> >   Barry
>>>> >
>>>> > >
>>>> > > On Fri, Apr 3, 2015 at 6:35 PM, Barry Smith <bsmith at mcs.anl.gov>
>>>> wrote:
>>>> > >
>>>> > >   Justin,
>>>> > >
>>>> > >    We haven't done anything with TS to handle variational
>>>> inequalities. So you can either write your own backward Euler (outside of
>>>> TS) that solves each time-step problem either as 1) an optimization problem
>>>> using Tao or 2) as a variational inequality using SNES.
>>>> > >
>>>> > >    More adventurously you could look at the TSTHETA code in TS
>>>> (which is a general form that includes Euler, Backward Euler and
>>>> Crank-Nicolson and see if you can add the constraints to the SNES problem
>>>> that is solved; in theory this is straightforward but it would require
>>>> understanding the current code (which Jed, of course, overwrote :-). I
>>>> think you should do this.
>>>> > >
>>>> > >   Barry
>>>> > >
>>>> > >
>>>> > > > On Apr 3, 2015, at 12:31 PM, Justin Chang <jchang27 at uh.edu>
>>>> wrote:
>>>> > > >
>>>> > > > I am solving the following anisotropic transient diffusion
>>>> equation subject to 0 bounds:
>>>> > > >
>>>> > > > du/dt = div[D*grad[u]] + f
>>>> > > >
>>>> > > > Where the dispersion tensor D(x) is symmetric and positive
>>>> definite. This formulation violates the discrete maximum principles so one
>>>> of the ways to ensure nonnegative concentrations is to employ convex
>>>> optimization. I am following the procedures in Nakshatrala and Valocchi
>>>> (2009) JCP and Nagarajan and Nakshatrala (2011) IJNMF.
>>>> > > >
>>>> > > > The Variational Inequality method works gives what I want for my
>>>> transient case, but what if I want to implement the Tao methodology in TS?
>>>> That is, what TS functions do I need to set up steps a) through e) for each
>>>> time step (also the Jacobian remains the same for all time steps so I would
>>>> only call this once). Normally I would just call TSSolve() and let the
>>>> libraries and functions do everything, but I would like to incorporate
>>>> TaoSolve into every time step.
>>>> > > >
>>>> > > > Thanks,
>>>> > > >
>>>> > > > --
>>>> > > > Justin Chang
>>>> > > > PhD Candidate, Civil Engineering - Computational Sciences
>>>> > > > University of Houston, Department of Civil and Environmental
>>>> Engineering
>>>> > > > Houston, TX 77004
>>>> > > > (512) 963-3262
>>>> > > >
>>>> > > > On Thu, Apr 2, 2015 at 6:53 PM, Barry Smith <bsmith at mcs.anl.gov>
>>>> wrote:
>>>> > > >
>>>> > > >   An alternative approach is for you to solve it as a (non)linear
>>>> variational inequality. See src/snes/examples/tutorials/ex9.c
>>>> > > >
>>>> > > >   How you should proceed depends on your long term goal. What
>>>> problem do you really want to solve? Is it really a linear time dependent
>>>> problem with 0 bounds on U? Can the problem always be represented as an
>>>> optimization problem easily? What are  and what will be the properties of
>>>> K? For example if K is positive definite then likely the bounds will remain
>>>> try without explicitly providing the constraints.
>>>> > > >
>>>> > > >   Barry
>>>> > > >
>>>> > > > > On Apr 2, 2015, at 6:39 PM, Justin Chang <jchang27 at uh.edu>
>>>> wrote:
>>>> > > > >
>>>> > > > > Hi everyone,
>>>> > > > >
>>>> > > > > I have a two part question regarding the integration of the
>>>> following optimization problem
>>>> > > > >
>>>> > > > > min 1/2 u^T*K*u + u^T*f
>>>> > > > > S.T. u >= 0
>>>> > > > >
>>>> > > > > into SNES and TS
>>>> > > > >
>>>> > > > > 1) For SNES, assuming I am working with a linear FE equation, I
>>>> have the following algorithm/steps for solving my problem
>>>> > > > >
>>>> > > > > a) Set an initial guess x
>>>> > > > > b) Obtain residual r and jacobian A through functions
>>>> SNESComputeFunction() and SNESComputeJacobian() respectively
>>>> > > > > c) Form vector b = r - A*x
>>>> > > > > d) Set Hessian equal to A, gradient to A*x, objective function
>>>> value to 1/2*x^T*A*x + x^T*b, and variable (lower) bounds to a zero vector
>>>> > > > > e) Call TaoSolve
>>>> > > > >
>>>> > > > > This works well at the moment, but my question is there a more
>>>> "efficient" way of doing this? Because with my current setup, I am making a
>>>> rather bold assumption that my problem would converge in one SNES iteration
>>>> without the bounded constraints and does not have any unexpected
>>>> nonlinearities.
>>>> > > > >
>>>> > > > > 2) How would I go about doing the above for time-stepping
>>>> problems? At each time step, I want to solve a convex optimization subject
>>>> to the lower bounds constraint. I plan on using backward euler and my
>>>> resulting jacobian should still be compatible with the above optimization
>>>> problem.
>>>> > > > >
>>>> > > > > Thanks,
>>>> > > > >
>>>> > > > > --
>>>> > > > > Justin Chang
>>>> > > > > PhD Candidate, Civil Engineering - Computational Sciences
>>>> > > > > University of Houston, Department of Civil and Environmental
>>>> Engineering
>>>> > > > > Houston, TX 77004
>>>> > > > > (512) 963-3262
>>>> > > >
>>>> > > >
>>>> > > >
>>>> > > >
>>>> > > > --
>>>> > > > Justin Chang
>>>> > > > PhD Candidate, Civil Engineering - Computational Sciences
>>>> > > > University of Houston, Department of Civil and Environmental
>>>> Engineering
>>>> > > > Houston, TX 77004
>>>> > > > (512) 963-3262
>>>> > >
>>>> > >
>>>> > >
>>>> > >
>>>> > > --
>>>> > > Justin Chang
>>>> > > PhD Candidate, Civil Engineering - Computational Sciences
>>>> > > University of Houston, Department of Civil and Environmental
>>>> Engineering
>>>> > > Houston, TX 77004
>>>> > > (512) 963-3262
>>>> >
>>>> >
>>>>
>>>>
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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