While I can do what Wolfgang wrote below, I was being lazy and did the
following
I store the inverse mass matrix as following
dealii::PreconditionBlockSOR<dealii::SparseMatrix<double>,double>
inv_mass_matrix;
Then
CompressedSparsityPattern c_sparsity(dof_handler.n_dofs());
DoFTools::make_sparsity_pattern (dof_handler, c_sparsity);
sparsity_pattern.copy_from(c_sparsity);
system_matrix.reinit (sparsity_pattern);
MatrixCreator::create_mass_matrix (mapping,
dof_handler,
QGauss<dim>(fe.degree+1),
system_matrix);
// Compute the inverse of the blocks
inv_mass_matrix.initialize (system_matrix, fe.dofs_per_cell);
Once I assemble the rhs in M*du/dt = rhs into right_hand_side, I use
inv_mass_matrix.vmult (newton_update, right_hand_side);
where now newton_update = du/dt and I can apply an RK scheme.
Does the above look ok ? The code is not yet working (blow up after 2-3 time
steps) so I might be making a mistake.
Note that fe is of type FE_DGQ.
praveen
On Fri, Apr 29, 2011 at 7:47 PM, Wolfgang Bangerth
<[email protected]>wrote:
>
> > This needs the mass matrix M which is a block diagonal matrix and does
> not
> > change with time. I am planning to compute its inverse and store it. In
> the
> > RK scheme, I will just use vmult to multiply the inverse with the right
> > hand side, to get du/dt and update the solution.
> >
> > I am not sure how to compute/store the inverse.
>
> If your matrix is block diagonal, the inverse is the matrix that consists
> of
> the inverse blocks. In other words, to store the inverse, rather than
> assemble
> the matrix of the blocks you compute on each cell and then invert the whole
> thing, you could compute the local contributions, invert them, and copy the
> inverses into the global matrix.
>
>
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