[petsc-users] conditioning of snes with dmcomposite & grid sequencing

[Gideon Simpson]

Got it.  I wanted to follow up on something that I had been suspicious of for some time.  I took my initial solution, the one which we want to apply grid sequencing to, and did the following.  I loved into spicy, and manually did grid refinement using SciPy, dumped to disk, and then ran that through petsc, with the refined mesh.  When I say “manual” here, I just mean that I called the SciPy spline interplant commands on uniform meshes that had twice the resolution, not that I manually picked out the refinement points.  When I use a linear interpolant, and run my solver on it, it fails miserably, just as the first grid sequence refinement does.  The numbers are a little different, but the residuals are still O(100).

If, instead, I use a second order interpolant, it solves it 11 iterations, wiithout a problem, and the result is physically consistent.  While this may be two sides of the same coin, it makes me think that the real challenge in my is the interpolation strategy used under grid refinement.  Is there a way to, manually, I suppose, set the interpolation that will be used under the grid sequence?



-gideon

> On Sep 12, 2015, at 7:14 AM, Matthew Knepley <knepley at gmail.com> wrote:
> 
> On Fri, Sep 11, 2015 at 4:30 PM, Gideon Simpson <gideon.simpson at gmail.com <mailto:gideon.simpson at gmail.com>> wrote:
> Are there any built in routines for freezing variables in SNES, or will that need to be handled by hand.
> 
> We used to have this for KSP, but it looks like someone removed it. The only thing left is KSPMonitorRange().
> What we did is find the few largest residual elements, take a small halo around them, project the problem to this
> small space using MatGetSubMatrix() and VecScatter, solve, and VecScatter back.
> 
> We do not have this for nonlinear stuff (like many other things) because there is no explicit matrix to manipulate,
> and language support for computing only parts of the nonlinear function is really weak. What we really want
> is something like what Victor Eijkout was proposing a few years ago, namely automatic discovery of index sets
> for communication, in this case with main memory. We would need the residual code, given an output set, to tell
> us what input set is needed. Then we make a Scatter, select part of the DM, and we could compute. Now it has
> to be done by hand.
> 
>   Thanks,
> 
>      Matt
>  
> Also, I remain curious about the starting guess that the grid sequence uses during each refinement.  Is there a way to dump those to disk for inspection?
> 
> -gideon
> 
>> On Sep 11, 2015, at 4:05 PM, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>> 
>> On Fri, Sep 11, 2015 at 1:05 PM, Gideon Simpson <gideon.simpson at gmail.com <mailto:gideon.simpson at gmail.com>> wrote:
>> Since the problem has not only the two components in the DM, but the second component has 4 degrees of freedom per mesh point, I thought it best to do the post processing separately.  See attached
>> 
>> So the whole thing is being controlled by 1 variable.
>> 
>> We should try freezing everything else, and just solving that scalar equation I guess.
>> 
>>    Matt
>>  
>> -gideon
>> <Screen Shot 2015-09-11 at 2.04.25 PM.png>
>> 
>>> On Sep 11, 2015, at 10:16 AM, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>> 
>>> On Fri, Sep 11, 2015 at 9:08 AM, Gideon Simpson <gideon.simpson at gmail.com <mailto:gideon.simpson at gmail.com>> wrote:
>>> Following up on the previous thread, for my dm composite problem, I find that at the end of the first grid sequence,where it fails to converge, the distribution of the norms between the two pieces are:
>>> 
>>>  39 SNES Function norm 2.253098577796e+02 
>>>  40 SNES Function norm 2.253098577331e+02 
>>>  41 SNES Function norm 2.253098577228e+02 
>>>  42 SNES Function norm 2.253098577212e+02 
>>>  43 SNES Function norm 2.253098577174e+02 
>>>  44 SNES Function norm 2.253098577166e+02 
>>>  45 SNES Function norm 2.253098577158e+02 
>>>  46 SNES Function norm 2.253098577157e+02 
>>>  47 SNES Function norm 2.253098577156e+02 
>>>  48 SNES Function norm 2.253098577156e+02 
>>> Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 48
>>>  ||r|| = 225.31, 7999 entries
>>>  ||rp|| = 140.021, 3 entries
>>>  ||rQ|| = 176.518, 7996 entries
>>> 
>>> Since I think we were convinced that this was intrinsic to the problem, and not a function of the Jacobian function, I am using my Jacobian.
>>> 
>>> Okay, I see no pattern in the fields. Lets plot these 2 vectors, -vec_view draw, and screenshot.
>>> 
>>>   Matt
>>>  
>>> -gideon
>>> 
>>> 
>>> 
>>> -- 
>>> 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
> 
> 
> 
> 
> -- 
> 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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