[petsc-users] Integrating TAO into SNES and TS

Tue Sep 1 04:15:05 CDT 2015

But if I add those linear equality constraint equations to my original
problem, would they not be satisfied anyway? Say I add this to my weak form:

Ax = b

But once i subject x to some bounded constraints, Ax != b. Unless I add
some sort of penalty where extra weighting is added to this property...

On Tue, Sep 1, 2015 at 3:02 AM, Matthew Knepley <knepley at gmail.com> wrote:

> 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20150901/9e253e5e/attachment.html>