A Monolithic Parallel FROSch Solver Framework for Chemo-Mechanical Problems
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Solving large-scale multiphysics coupled boundary value problems with the finite element method generally requires the use of scalable preconditioned Krylov methods, e.g. a domain decomposition approach. The present work describes a monolithic parallel solver designed for both minimization and saddle-point problems and developed using the FROSch domain decomposition framework of the Trilinos software library. The framework includes a parallel implementation of the (R)GDSW overlapping Schwarz domain decomposition preconditioner with an energy-minimizing coarse space. The influence of a fully algebraic coarse space construction and a problem-specific refined coarse space is investigated. The solver is applied to a fully coupled chemo-mechanical deformation–diffusion boundary value problem that models the swelling behavior of hydrogels. The corresponding weak formulation is implemented in the finite element library deal.II, and the recently introduced Tpetra interface is used to enable coupling with the FROSch framework. Numerical and strong scalability studies of the chemo-mechanical problem are presented, and the scalability of the saddle-point formulation is compared with that of an equivalent minimization formulation.
