  We consider the swelling of hydrogels as an example of a chemo-mechanical
problem with strong coupling between the mechanical balance relations and the
mass diffusion. The problem is cast into a minimization formulation using a
time-explicit approach for the dependency of the dissipation potential on the
deformation and the swelling volume fraction to obtain symmetric matrices,
which are typically better suited for iterative solvers. The MPI-parallel
implementation uses the software libraries deal.II, p4est and FROSch (Fast of
Robust Overlapping Schwarz). FROSch is part of the Trilinos library and is used
in fully algebraic mode, i.e., the preconditioner is constructed from the
monolithic system matrix without making explicit use of the problem structure.
Strong and weak parallel scalability is studied using up to 512 cores,
considering the standard GDSW (Generalized Dryja-Smith-Widlund) coarse space
and the newer coarse space with reduced dimension. The FROSch solver is
applicable to the coupled problems within in the range of processor cores
considered here, although numerical scalablity cannot be expected (and is not
observed) for the fully algebraic mode. In our strong scalability study, the
average number of Krylov iterations per Newton iteration is higher by a factor
of up to six compared to a linear elasticity problem. However, making mild use
of the problem structure in the preconditioner, this number can be reduced to a
factor of two and, importantly, also numerical scalability can then be achieved
experimentally. Nevertheless, the fully algebraic mode is still preferable
since a faster time to solution is achieved.
