Leonhard,
I find that if FE_Q is replaced by FESystem in step-36 it reports that
error.
I printed all diagonal element of two matrices and they are all
non-zero, so the matrices are invertable.
That is not the right criterion. The following matrix also has all
nonzero diagonal entries and it still isn't invertible:
[1 1]
[1 1]
My problem is a 3-dim beam eigenvalue calculation and I use FESystem
just like step-18.
And if I use FE_Q rather than FESystem, the function
shape_grad_component will report error.
I use that function to calculate stiffness_matrix, called by
get_strain() like step-18.
And the theoretical formulae are as follows:
\begin{array}{l}
K = \int {{D^{\rm{T}}}ED{\rm{d}}{V_e}} \\
\varepsilon = Du\\
\sigma = \varepsilon E
\end{array}%
I guess that here exits conflict between FESystem and SolverKrylovSchur
or just because it is a vector-value problem?
Is it a vector-value the 3-dim eigenvalue calculation?
There are many things that can go wrong, of course. You need to start
with a simple problem and make incremental changes to find out where the
problem is. I would start with using a bilinear form for the stiffness
matrix that matches what step-36 does, so
(grad u, grad v)
where now u,v are vector valued. Make sure you have zero Dirichlet
boundary conditions for all components. That should work. If it does,
move on to more complicated bilinear forms; with each modification, make
sure that it continues to work, and if it doesn't, you know what
modification was the problem.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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