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

TL;DR

This paper compares partitioned and monolithic solver approaches for the coupled Stokes-Darcy system, demonstrating that both can improve performance over direct solvers, with monolithic methods offering faster solutions when properly preconditioned.

Contribution

It provides a comparative analysis of partitioned and monolithic preconditioning strategies for Stokes-Darcy systems, highlighting the importance of preconditioner choice and optimization.

Findings

Partitioned coupling can solve large problems faster with suitable iterative solvers.

Monolithic approach achieves faster runtimes with optimized block preconditioners.

Specialized Uzawa preconditioners may increase runtimes compared to algebraic multigrid.

Abstract

We consider the time-dependent Stokes-Darcy problem as a model case for the challenges involved in solving coupled systems. Keeping the model, its discretization, and the underlying numerics for the subproblems in the free-flow domain and the porous medium constant, we focus on different solver approaches for the coupled problem. We compare a partitioned coupling approach using the coupling library preCICE with a monolithic block-preconditioned one that is tailored to different formulations of the problem. Both approaches enable the reuse of already available iterative solvers and preconditioners, in our case, from the DuMux framework. Our results indicate that the approaches can yield performance and scalability improvements compared to using direct solvers: Partitioned coupling is able to solve large problems faster if iterative solvers with suitable preconditioners are applied for the subproblems. The monolithic approach shows even stronger requirements on preconditioning, as standard simple solvers fail to converge. Our monolithic block preconditioning yields the fastest runtimes for large systems, but they vary strongly with the preconditioner configuration. Interestingly, using a specialized Uzawa preconditioner for the Stokes subsystem leads to overall increased runtimes compared to block preconditioners utilizing a more general algebraic multigrid. This highlights that optimizing for the non-coupled cases does not always pay off.