[petsc-users] lying about nullspaces

[Jed Brown]

If you make a consistent RHS, then ICC with a positive definite shift might
be fine. You could certainly define a dynamic ordering that puts the "good"
blocks first. If the transformation can identify the bad blocks, you could
solve the embedded problem with PCREDISTRIBUTE.
On Jan 9, 2012 6:24 PM, "Geoffrey Irving" <irving at naml.us> wrote:

> On Mon, Jan 9, 2012 at 3:20 PM, Geoffrey Irving <irving at naml.us> wrote:
> > Ah, right.  I'm using incomplete Cholesky as a preconditioner, which
> > usually won't be stable on the subspace.  The subspace is derived from
> > freezing the normal velocity of points involved in collisions, so it
> > has no useful algebraic properties.
> >
> > It's not too difficult to symbolically apply P to A (it won't change
> > the sparsity), but unfortunately that would make the sparsity pattern
> > change each iteration, which would significantly increase the cost of
> > ICC.
>
> Sorry, that sentence was poorly phrased.  I meant that it's not too
> difficult to symbolically eliminate the relevant subspace from A, but
> that this would produce a matrix whose size changes each time around.
> I could also replace A with PAP directly without changing the sparsity
> pattern, but I imagine incomplete Cholesky might choke on the result,
> which would be a 3x3 block matrix with a lot of singular diagonal
> blocks.
>
> Geoffrey
>
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