Parallel Scalable Domain Decomposition Methods for Incompressible Fluid Flow Problems
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Monolithic GDSW (generalized Dryja--Smith--Wildund) preconditioners are two-level Schwarz domain decomposition preconditioners for block systems. They are robust because they account for the coupling terms in the system matrix on both levels, that is, in the local and coarse problems. In comparison, block preconditioners, mostly based on block-diagonal and block-triangular preconditioners, such as the SIMPLE (semi-implicit method for pressure linked equations) preconditioner, often yield higher iteration counts while having a lower setup cost compared to monolithic approaches. These highly-scalable parallel GDSW preconditioners have been implemented in the solver framework FROSch, which is part of the software library Trilinos. These methods have also been extended to suit fluid flow problems. In this talk, the parallel performance of the different preconditioning methods for incompressible fluid flow problems is investigated and compared using a finite element implementation based on the FEDDLib finite element software and the overlapping Schwarz preconditioners from the Trilinos package FROSch.
