Application of the monolithic, parallel FROSch solver framework to a saddle-point formulation in chemo-mechanics
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The solution of large-scale, multi-physical coupled boundary values problems by means of the Finite Element Method typically requires the application of domain decomposition techniques and iterative solvers. The current contribution describes a monolithic parallel solver, which is suitable for both minimization and saddle-point problems and is built on the FROSch domain decomposition framework within the Trilinos software library. A parallel implementation of the GDSW two-level overlapping Schwarz domain decomposition preconditioner with an energy-minimizing coarse space is included in this framework, which allows for a fully algebraic construction. This solver framework is applied to a fully coupled chemo-mechanical deformation-diffusion boundary value problem, which is employed to model the swelling behavior of hydrogels and is characterized by a saddle-point structure. The corresponding weak form is implemented in the Finite Element software library deal.II. The recently proposed Tpetra interface is utilized to enable the coupling with the FROSch framework. Strong and weak scalability studies of this saddle-point will be presented and compared to the results obtained with an equivalent minimization formulation.