[petsc-users] Nullspaces for schur complement PCs

[Barry Smith]

> On Nov 12, 2014, at 7:49 PM, Jed Brown <jed at jedbrown.org> wrote:
> 
> Barry Smith <bsmith at mcs.anl.gov> writes:
>>   Perhaps we need a generic way of attaching null spaces to parts of
>>   matrices and to parts of matrices in different basis (which is what
>>   a Schur complement is). So (and this is likely overly simplistic)
>>   one could supply a null space, an index set, and a flag indicating
>>   either "part of the matrix" or the "Schur complement of the matrix
>>   with respect to an index set".  These provided null spaces could
>>   then be used by the preconditioners (like Fieldsplit) that
>>   manipulate parts of the matrix or Schur complement.
> 
> Yes, this is conceptually right, but it looks to me like it gets hairy
> for recursive splitting.

  Indeed it could. Perhaps we could start by unifying the concept of a sub matrix and a Schur complement of the same part of the matrix? I'm not sure how to do that.

  Barry