Domain decomposition methods - Towards extreme scalability using new nonlinear approaches
Axel Klawonn, University of Cologne,Oliver Rheinbach, TU Bergakademie Freiberg
The solution of nonlinear problems, e.g., in material science requires fast and highly scalable parallel solvers. FETI-DP (Finite Element Tearing and Interconnecting) domain decomposition (DD) methods are such parallel solution methods for implicit problems discretized by finite elements. A common iterative DD approach for nonlinear problems is a Newton-Krylov-DD strategy where the nonlinear problem is linearized using a Newton method. Then, the linear system associated with the tangent stiffness matrix is solved with a preconditioned Krylov space method. The preconditioner is obtained by a domain decomposition method. In an efficient and parallel scalable domain decomposition method, local subdomain problems and a sufficiently small global problem have to be solved. The local problems are inherently parallel, the global problem is needed to obtain numerical and parallel scalability.
Recently, nonlinear versions of the FETI-DP methods for linear problems have been introduced. Here, the nonlinear problem is decomposed directly before linearization. The new approaches have the potential to reduce communication and to show a significantly improved performance, especially for problems with localized nonlinearities, compared to a standard Newton-Krylov-FETI-DP approach. In another new approach, the nonlinear domain decomposition method has been combined with an algebraic multigrid method. Computational results are shown for up to 262.144 cores on the MIRA BlueGene/Q supercomputer (Argonne National Laboratory, USA) for our new implementation.
Workshop: Exploiting Different Levels of Parallelism for Exascale Computing
as part of the ACM International Conference on Supercomputing - ICS 2014Date
June 10, 2014Venue
Bavarian Academy of Sciences, MunichContact
Miriam Mehl, miriam.mehl@ipvs.uni-stuttgart.deDirk Pflüger, dirk.pflueger@ipvs.uni-stuttgart.de