A different kind of lagged preconditioner

Rafael Santos Coelho rafaelsantoscoelho at gmail.com
Mon Mar 23 18:41:43 CDT 2009

Well, let me explain myself again. I've implemented a serial matrix-free
uniparametric LU-SGS
non-linear problems using the PETSc PCSHELL module. It's matrix-free
the sense that whenever the jacobian matrix (and by that I mean the L, D and
U factors of the jacobian matrix) is required within the linear solver in
the form of a matrix-vector product, I resort to a finite-difference formula
in order to approximate the jacobian entries. So the jacobian matrix is
never actually formed. To use my preconditioner, I just have to set the
"-user_precond" command-line option along with "-snes_mf".

Now, the cost to apply that preconditioner obviously grows according to the
problem dimensions, so it is built and applied within the linear solver to
form the vectors of the Krylov subspace basis in each linear iteration. I
want to change that, and only have it applied every "p" linear iterations to
make it less costlier.

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