Monolithic Multi‐Level Overlapping Schwarz Preconditioners for Fluid Problems
Stephan Köhler, Oliver Rheinbach
Source abstract
ABSTRACT Additive overlapping Schwarz methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A successful coarse space, inspired by iterative substructuring, is the generalized Dryja–Smith–Widlund (GDSW) space. Based on the GDSW approach, Heinlein, Hochmuth, and Klawonn introduced two‐level monolithic overlapping Schwarz preconditioners for saddle point problems. We present parallel results up to 32 768 MPI ranks for the solution of incompressible fluid problems for a Poiseuille flow example on the unit cube and a complex extrusion die geometry ranks using a two‐ and a three‐level monolithic overlapping Schwarz preconditioner. These results are achieved through the combination of the additive overlapping Schwarz preconditioners implemented in the Fast and Robust Overlapping Schwarz (FROSch) library, which is part of the Trilinos package ShyLU, and the FEATFLOW library using a scalable interface for the efficient coupling of the two libraries. This work is part of the project StroemungsRaum ‐ Novel Exascale‐Architectures with Heterogeneous Hardware Components for Computational Fluid Dynamics Simulations, funded by the German Bundesministerium für Forschung, Technologie und Raumfahrt BMFTR (formerly BMBF) as part of the program on New Methods and Technologies for Exascale Computing (SCALEXA).
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