I wonder if there was any follow up replies about this.
I started to work a few days ago on an eigensolver for linear elasticity
with the use of the SLEPc wrappers in deal.II (based on step-8 and
step-36), and I came across the same issue Leonhard described above. After
some debugging I realised the issue was in the fact that I was not
assembling the mass matrix correctly. Essentially, if following step-8,
then you need to only add terms to the local mass matrix whenever comp(i)
== comp(j) (following the notation in step-8 documentation), as it is done
for the \nabla\phi_i\dot\nabla\phi_j term.
Another way to go around this issue is to use "FEValuesExtractors::Vector"
for the displacement (the only unknown in the system). With this way the
assemble looks a lot more closer to how one would write a primal
formulation for linear elasticity. So far, both ways give the same
eigenvalues, which also make sense (in 2 and 3D, and on different domains).
On Monday, February 28, 2022 at 11:16:50 a.m. UTC-6 Wolfgang Bangerth wrote:
>
> 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.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
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