On the usage of triangular preconditioner updates in matrix-free
environment.


Efficient solution of sequences of linear systems is a task arising
in numerous applications in engineering and scientific computing.
Depending on the linear solver and the properties of the system
matrices, several techniques to share part of the computational
effort throughout the sequence may be used. Our contribution
considers a new black-box approximate update scheme for factorized
preconditioners that was recently introduced by the authors. It is
designed for general nonsymmetric linear systems solved by arbitrary
iterative solvers and the basic idea is to combine an incomplete
reference factorization with a Gauss-Seidel type of approximation of
the difference between the current and the reference matrix. The
updated factorizations may be particularly beneficial when
preconditioner computations from scratch are expensive, like in
matrix-free environment where the matrix has to be estimated first.
In this talk we give a brief description of the basis update
technique and then discuss their usage in matrix-free environment.
We present, among others, a new implementation strategy which is
based on mixed matrix-free/explicit triangular solves.