Project

FROSch [36, 87] is a solver software package of the open-source software library Trilinos [88], which is primarily developed at UzK and TUF in cooperation with Sandia National Laboratories, USA. In FROSch, we will extend parallel overlapping domain decomposition methods for fluid problems in terms of scalability towards exascale, improve the use of GPU accelerators, and make the methods usable for StrömungsRaum®. Starting from already developed monolithic, overlapping Schwarz methods for linear Stokes and nonlinear Navier-Stokes equations [32, 33], we will pursue two different strategies to make the user software StrömungsRaum® exascale-capable. In the first strategy (TUF), we will combine it with the latest variants of the algebraic 3-level FROSch methods [39]. For such variants of the recently developed algebraic 3-level FROSch solvers [39], scalability was achieved for up to 220,000 cores of the Theta supercomputer (Argonne) [40], after scalability for up to almost 100,000 cores of the SuperMUC-NG supercomputer (LRZ, Munich) had been demonstrated before [40]. Differences in the performance of Theta compared to SuperMUC-NG in [40] suggest further flexibility of the coarse grid communication patterns in FROSch, which should occur for the new methods in this project. Due to the algebraic structure of FROSch, no grid hierarchies are required for the construction of coarse grid problems on the second and third level, as they are usually required for geometric multigrid methods. Such difficult grids occur regularly in typical applications of IANUS due to complex geometries, see example 1 and fig. 1. In the second strategy (UzK), we will combine nonlinear overlapping Schwarz methods [38] with the monolithic domain decomposition methods for the Navier-Stokes equations [32, 33]. Nonlinear non-overlapping domain decomposition methods of the FETI-DP type have already scaled in parallel on the supercomputer Mira (Argonne) on up to 786,432 cores [46] as well as on almost the entire Theta (Argonne) [47]. Based on these experiences, the approaches from [38] are to be further developed and combined with the methods from [32, 33]. In the present project, the algorithms thus obtained will be implemented in FROSch. This is expected to greatly reduce the number of (pseudo-)time steps necessary for convergence of the respective nonlinear solution procedure. In combination with the nonlinear flow problems, significant parallel scalability progress towards exascale is expected. By using Kokkos [11], the use of GPU accelerator hardware by these new linear and nonlinear algorithms is made possible. The current FROSch implementation [36, 87] will be connected to FEATFLOW and thus to the StrömungsRaum® platform through an abstract interface. Both the integration of FROSch into Trilinos and the connection to FEATFLOW, as well as the use by IANUS in StrömungsRaum®, ensure sustainable software development and availability. The further development of the FROSch framework is also being driven forward in two DFG-funded research projects: one project in SPP2256 deals with the thermo-chemo-mechanics of nonlinear materials; the project in SPP2311 deals with pharmaco-mechanical fluid-structure interaction. However, in both projects the target architecture is not exascale, but parallel computers of conventional size and architecture are targeted.