History for Singular matrix in fem solve

changed:
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It seems that you always have to use the GMRES solver, the LU solver usually fails with a singular matrix. The simple examples that I looked at use it and they fail if you change it to LU.

Why is this?

In the case of 5g1 (according to VJ) it's because the wrong pressure basis function has been used. (see also comments below)

Make sure you have the correct basis specfied in all places that it's required. Specifying the wrong basis for the pressure field can cause this error.
            
I have a test problem with a 6 element tricubic mesh that solves,
but when I split one of the rectangular/cube elements into two
triangular wedge elements and add versions I get a singular
matrix. I think this has something to do with the the boundary
conditions, but I'm not sure how to go about diagnosing the
problem.

What is the best way to inspect the matrices?  Is there an example
of how to do this somewhere?  There are some options during
'define solve' that control matrix output.  Is 'fem write matrix'
helpful?

>>Warning: Volume at ng= X ne= X less than zero
-----------------------------------------------

update: This is caused by an element becoming inverted. One possible cause is when using collapsed nodes and there is a wrinkle near a collapsed node. See `UsingVersions <http://www.cmiss.org/cmgui/wiki/UsingVersions>`_ for a discussion of this. 

What do you do when you get the warning message: >>Warning: Volume at ng= X ne= X less than zero ?
this warning occurs sometimes when attempting to solve a finite elasticity problem, and is usually followed by the problem failing to solve.

According to the comment in fe50/ZERE50.f, where the message comes from, it is triggered when the determinant of the deformation gradient, DET(DZDX), ie the volume, is less than 0.
 
In the problem I am trying to solve I get this error when I have collapsed nodes in the mesh.

I have a simplified test case with plain hexahedral elements that solves OK, but the mesh I want use to has some elements split into 2 using collapsed nodes and versions as shown in the image below.

.. image:: snapshot1.png
   :width: 400

The warning happens when using this mesh with everything else the same as the case without the collapsed nodes that works OK.

The command causing the warning is fem solve inc 0.

How is the volume becoming less than zero if there is no deformation?

How do I diagnose the problem and fix it?
How is the volume becoming less than zero if there is no deformation?

The finite difference calculation of derivatives of the stiffness matrix may "deform" the mesh. 

From karl Fri Jul 28 11:13:00 +1200 2006
From: karl
Date: Fri, 28 Jul 2006 11:13:00 +1200
Subject: singular matrix
Message-ID: <20060728111300+1200@www.cmiss.org>

If the matrix is singular, then it seems that something is wrong: perhaps with the boundary conditions or perhaps in the material law.

GMRES will not notice a singular matrix.  I guess there is a chance that there is problem in the LU solver, but this could be checked by trying a different LU solver.

From glennr Fri Jul 28 14:56:27 +1200 2006
From: glennr
Date: Fri, 28 Jul 2006 14:56:27 +1200
Subject: only when using cellml
Message-ID: <20060728145627+1200@www.cmiss.org>

I did some more testing and it appears that this is only the case when using finite elasticity with a material law defined using cellml. For example changing 5g1 to use SuperLU causes a segfault and using Umfpack has a singular matrix.



From karl Thu Aug 17 13:31:15 +1200 2006
From: karl
Date: Thu, 17 Aug 2006 13:31:15 +1200
Subject: mesh integrity
Message-ID: <20060817133115+1200@www.cmiss.org>

It is often worth checking that the mesh behaves as expected internally by viewing a wireframe of the mesh at sufficiently high graphical discretization.

A the versions of the wedges sufficiently tied?
Do they remain connected after a GMRES solve?

It may be helpful to constrain the degrees of freedom in the wedge elements to determine whether there is a subset of dofs causing the problem.