Simulation of mechanical problems makes use of the following parts: making
a model consisting of partial differential equations, discretization by
the Finite Element Method, linearization and solution of the resulting
linear systems. It appears that in many three dimensional problems the
solution of the linear system is the most time-consuming part. Direct
solvers can be used up to a certain number of grid-points. However for
large problems the amount of memory is not available on present day
computers and the required CPU time becomes excessive.

Another possibility is to use iterative solution methods which cost much
less memory and can be more efficient. Krylov methods are the most popular
iterative method nowadays. It appears that a good preconditioner is crucial
to make the method to converge in a reasonable amount of iterations. The
construction of fast and robust parallel preconditioners is the subject of
this minisymposium. Mechanical contact problems are considered as typical
applications. Specific issues for systems originating from this
application are: loss of banded structure and the critical nature of
domain decomposition. In order to develop good preconditioners these
features should be taken into account.