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Subject: Re: condition number of FE matrix -> improving iterative solver
Date: Mon, 9 Nov 2009 15:18:04 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hd8g6a$pi7$1@fred.mathworks.com>...
> "A B" <gitsnedbutzi@hotmail.com> wrote in message <hd6pba$84c$1@fred.mathworks.com>...

> The condition number get bad if you forget to impose appropriate (boundary) condition to make the problem well posed. If boundary is correctly setup, then note that the condition number goes up when mesh size decreases. However a typical characteristic is the smallest eigenvalue of your stiffness matrix is inferior bounded, and the largest eigenvalue goes to infinity as the square of the mesh size for a second order operator.
> 
> If you have the mass matrix, check for the first eigenmode, which is the lowest "resonance" mode of your operator. The shape of such eigenmode should look *physical*, whatever it means. This ensures that the boundary condition is correctly setup.
> 
> Bruno

A number of appropriate boundary conditions is imposed, to lock rigid body motions, and so there isn't a solution which would result in a zero energy. Unfortunatly I'm not calculating the mass matrix, so I can't check the lowest mode.

What I noticed however is that incomplete factorization lead don't result in good preconditioners, no matter how I set the drop tolerance and other options. Using pcg without any preconditioners surprisingly gives better results. If I rescale the matrix with a left and right preconditioner, being the inverse of the square root of the main diagonal elements (as a result the main diagonal will be scaled to ones), the convergence slightly improves.

Why is it that incomplete factorization preconditioners don't perform that well?
Aren't they well suited for problems from structural mechanics?