  In this paper, we propose and evaluate the performance of a unified
computational framework for preconditioning systems of linear equations
resulting from the solution of coupled problems with monolithic schemes. The
framework is composed by promising application-specific preconditioners
presented previously in the literature with the common feature that they are
able to be implemented for a generic coupled problem, involving an arbitrary
number of fields, and to be used to solve a variety of applications. The first
selected preconditioner is based on a generic block Gauss-Seidel iteration for
uncoupling the fields, and standard algebraic multigrid (AMG) methods for
solving the resulting uncoupled problems. The second preconditioner is based on
the semi-implicit method for pressure-linked equations (SIMPLE) which is
extended here to deal with an arbitrary number of fields, and also results in
uncoupled problems that can be solved with standard AMG. Finally, a more
sophisticated preconditioner is considered which enforces the coupling at all
AMG levels, in contrast to the other two techniques which resolve the coupling
only at the finest level. Our purpose is to show that these methods perform
satisfactory in quite different scenarios apart from their original
applications. To this end, we consider three very different coupled problems:
thermo-structure interaction, fluid-structure interaction and a complex model
of the human lung. Numerical results show that these general purpose methods
are efficient and scalable in this range of applications.
