On Tue, Sep 1, 2015 at 8:29 AM, Julian Andrej <j...@tf.uni-kiel.de> wrote:
> I'm trying to get into libMesh, so i tried to convert an existing project.
>
> So far i could reproduce the lid driven cavity case for the Stokes
> equations like in
> example examples/systems_of_equations/systems_of_equations_ex1.
>
> Now i'm trying to build a mass matrix so i can solve the generalized
> eigenproblem in order to retrieve the physical eigenvalues in the following
> domain:
>
> build_square (mesh,
> 16, 16,
>
> -1., 1.,
>
> -1., 1.,
>
> TRI6);
>
> So the eigenvalues should be (rounded to int) [13, 23, 23, 32, 38, 41...].
>
> My approach is that i add a matrix
>
> system.add_matrix("mass");
>
> in the assemble loop i add:
>
> DenseMatrix<Number> Me;
> Me.resize (n_dofs, n_dofs);
>
> and to the integration parts:
> Me(i,j) += JxW[qp]*(phi[i][qp]*phi[j][qp]);
>
> then i close the matrices
> system.get_matrix("mass").close();
>
> and convert them to PETSc so i can use my own SLEPc object
> Mat A = (static_cast<PetscMatrix<Number> *>(system.matrix))->mat();
>
> Mat M = (static_cast<PetscMatrix<Number>
> &>(system.get_matrix("mass"))).mat();
>
> The problem is, the calculated eigenvalues are not the ones i expect (so
> they're wrong).
> This method worked for me for the poisson equation.
> Do i miss something?
>
So are you trying to solve the generalized eigenvalue problem
A*x = lambda*B*x,
where A corresponds to the Stokes operator and B to the "mass" matrix,
which should have a zero block for the pressure equation?
If yes, then
.) Are you building both matrices, since you only talk about the mass
matrix?
.) Are you building the correct mass matrix for Stokes?
Another question is BCs: what are they, and how are you imposing them (e.g.
penalty method, constraints, etc.)? I can't remember if BCs should be
imposed in both the A and B matrices or not...
--
John
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