Scalable Overlapping Schwarz Domain Decomposition Preconditioners Using Extension-Based Coarse Spaces

The FROSch (Fast and Robust Overlapping Schwarz) domain decomposition preconditioning framework is part of the Trilinos software framework and provides scalable multilevel Schwarz preconditioners, with a particular emphasis on the fully algebraic construction of coarse spaces for large-scale systems arising from the discretization of partial differential equations. The algorithmic backbone of FROSch is formed by extension-based coarse spaces, such as those employed in generalized Dryja–Smith–Widlund (GDSW) methods. In this talk, we focus on recent algorithmic developments in monolithic coarse spaces for block-structured systems, such as those arising in fluid flow, as well as robust algebraic multiscale coarse spaces for strongly heterogeneous problems. We present results that validate these algorithmic advances, together with performance results for challenging applications, including land ice simulations, blood flow, and porous media flow.