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We consider the time-dependent Stokes-Darcy problem as a model case for thechallenges involved in solving coupled systems. Keeping the model, itsdiscretization, and the underlying numerics for the subproblems in thefree-flow domain and the porous medium constant, we focus on different solverapproaches for the coupled problem. We compare a partitioned coupling approachusing the coupling library preCICE with a monolithic block-preconditioned onethat is tailored to different formulations of the problem. Both approachesenable the reuse of already available iterative solvers and preconditioners, inour case, from the DuMux framework. Our results indicate that the approachescan yield performance and scalability improvements compared to using directsolvers: Partitioned coupling is able to solve large problems faster ifiterative solvers with suitable preconditioners are applied for thesubproblems. The monolithic approach shows even stronger requirements onpreconditioning, as standard simple solvers fail to converge. Our monolithicblock preconditioning yields the fastest runtimes for large systems, but theyvary strongly with the preconditioner configuration. Interestingly, using aspecialized Uzawa preconditioner for the Stokes subsystem leads to overallincreased runtimes compared to block preconditioners utilizing a more generalalgebraic multigrid. This highlights that optimizing for the non-coupled casesdoes not always pay off.

Partitioned Coupling vs. Monolithic Block-Preconditioning Approaches for Solving Stokes-Darcy Systems