[petsc-users] lying about nullspaces

[Geoffrey Irving]

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