[petsc-users] Integrating TAO into SNES and TS

[Justin Chang]

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.

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
>
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