[petsc-dev] API changes in MatIS

[Jed Brown]

On Fri, May 11, 2012 at 6:11 PM, Stefano Zampini
<stefano.zampini at gmail.com>wrote:

> Isn't PtAP still the right operation, you just have a particular
>> implementation that takes advantage of structure?
>>
>
> yes it is, but since it is an expensive operations (P is dense), in BDDC,
> once you solved the local problems to create P, you have almost straigthly
> (and at a very low cost) the columns of the coarse matrix. The latter can
> be obtained (as it is implemented in the code) as C^T\Lambda where C is the
> local sparse  matrix of constraints, and \Lambda is a dense and small
> matrix of lagrange multipliers.
>
>> I know you can also assemble B A^{-1} B^T, which is the same thing, and
>> maybe we should provide a generic op for that.
>>
> What is B? the jump operator?
>

Your C above.

I have other algorithms in mind where the the interpolants would be
constructed somewhat differently. I may need to think a bit about what the
right common operation is for that case. I just feel like we may be getting
too tightly dependent on the specific BDDC algorithm (which has exponential
condition number growth in the number of levels), which we probably want to
generalize in the future.
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