[petsc-users] lying about nullspaces

[Jed Brown]

On Mon, Jan 9, 2012 at 18:20, Geoffrey Irving <irving at naml.us> wrote:

> The subspace is derived from
> freezing the normal velocity of points involved in collisions, so it
> has no useful algebraic properties.
>

About how many in practice, both as absolute numbers and as fraction of the
total number of nodes? Are the elastic bodies closely packed enough to
undergo locking (as in granular media). I ask because it affects the
locality of the response to the constraints.


>
> 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.
>

It changes each time step or each nonlinear iteration, but as long as you
need a few linear iterations, the cost of the fresh symbolic factorization
is not likely to be high. I'm all for reusing data structures, but if you
are just using ICC, it might not be worth it. Preallocating for the reduced
matrix might be tricky.

Note that you can also enforce the constraints using Lagrange multipliers.
If the effect of the Lagrange multipliers are local, then you can likely
get away with an Uzawa-type algorithm (perhaps combined with some form of
multigrid for the unconstrained system). If the contact constraints cause
long-range response, Uzawa-type methods may not converge as quickly, but
there are still lots of alternatives.
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