<div class="gmail_quote">On Mon, Jan 9, 2012 at 18:20, Geoffrey Irving <span dir="ltr"><<a href="mailto:irving@naml.us">irving@naml.us</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div id=":1t">The subspace is derived from<br>
freezing the normal velocity of points involved in collisions, so it<br>
has no useful algebraic properties.<br></div></blockquote><div><br></div><div>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.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div id=":1t">
<br>
It's not too difficult to symbolically apply P to A (it won't change<br>
the sparsity), but unfortunately that would make the sparsity pattern<br>
change each iteration, which would significantly increase the cost of<br>
ICC.</div></blockquote><div><br></div><div>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.</div>
<div><br></div><div>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.</div>
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