[petsc-users] Jacobian matrix for dual porosity model

[Matthew Knepley]

On Wed, Jun 14, 2017 at 11:48 PM, Adrian Croucher <a.croucher at auckland.ac.nz
> wrote:

> On 14/06/17 07:45, Jed Brown wrote:
>
>> Barry Smith <bsmith at mcs.anl.gov> writes:
>>
>> On Jun 13, 2017, at 10:06 AM, Jed Brown <jed at jedbrown.org> wrote:
>>>>
>>>> Adrian Croucher <a.croucher at auckland.ac.nz> writes:
>>>>
>>>> One way might be to form the whole Jacobian but somehow use a modified
>>>>> KSP solve which would implement the reduction process, do a KSP solve
>>>>> on
>>>>> the reduced system of size n, and finally back-substitute to find the
>>>>> unknowns in the matrix rock cells.
>>>>>
>>>> You can do this with PCFieldSplit type Schur, but it's a lot heavier
>>>> than you might like.
>>>>
>>>     Is it clear that it would produce much overhead compared to doing a
>>> custom "reduction to a smaller problem". Perhaps he should start with this
>>> and then profiling can show if there are any likely benefits to
>>> "specializing more"?
>>>
>> Yeah, that would be reasonable.  We don't have a concept of sparsity for
>> preconditioners so don't have a clean way to produce the exact (sparse)
>> Schur complement.  Computing this matrix using coloring should be
>> relatively inexpensive due to the independence in each cell and its
>> tridiagonal structure.
>>
>
> Thanks for those ideas, very helpful.
>
> If I try this approach (forming whole Jacobian matrix and using
> PCFieldSplit Schur), I guess I will first need to set up a modified DMPlex
> for the whole fracture + matrix mesh- so I can use it to create vectors and
> the Jacobian matrix (with the right sparsity pattern), and also to work out
> the coloring for finite differencing.
>
> Would that be straight-forward to do? Currently my DM just comes from
> DMPlexCreateFromFile(). Presumably you can use DMPlexInsertCone() or
> similar to add points into it?


You can certainly modify the mesh. I need to get a better idea what kind of
modification, and then
I can suggest a way to do it. What do you start with, and what exactly do
you want to add?

  Thanks,

    Matt


>
> - Adrian
>
> --
> Dr Adrian Croucher
> Senior Research Fellow
> Department of Engineering Science
> University of Auckland, New Zealand
> email: a.croucher at auckland.ac.nz
> tel: +64 (0)9 923 4611
>
>


-- 
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

http://www.caam.rice.edu/~mk51/
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