[petsc-users] Jacobian matrix for dual porosity model

[Jed Brown]

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.
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