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From: "Tim Davis" <davis@cise.ufl.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FEM substructuring  (static condensation) -> out ot memory; ANSYS can do it
Date: Sat, 31 May 2008 20:56:02 +0000 (UTC)
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"A B" <gitsnedbutzi@hotmail.com> wrote in message 

...
> K*u = F
> 
> u= [ua; ub];
> F = [Fa; Fb];
> K = [Kaa Kab; Kba Kbb]
> Kab=Kba';
> 
> ua are the degrees of freedom i want to keep, whereas ub are
> the ones which should be removed. Therefore I obtain a new
> matrix for the left side and a new vector on the right side;
> 
> K_new = [Kaa - Kab*Kbb^-1*Kba]
> F_new = [Kaa - Kab*Kbb^-1*Fb]
> 
> Now of course I'm not computing the full inverse of Kbb, but 
> 
> Kaa-Kab/Kbb*Kba

what are the dimensions of these matrices?  Kbb is dimension
5000?

What's happening here is that you're computing your own
Schur complement.  It might be too much to represent this
explicitly.  Perhaps ANSYS does this implicitly, and
updates/downdates the factorization of K accordingly.

MATLAB uses the same compressed-sparse column form that the
Harwell-Boeing format uses (mostly, except for different
methods used inside LU, Chol, backslash, etc, that aren't
visible to the user - M or mex or otherwise).